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A semiconductor injection-switched high-pressure sub-10-picosecond carbon dioxide laser amplifier Hughes, Michael Kon Yew 2002

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A S E M I C O N D U C T O R I N J E C T I O N - S W I T C H E D H I G H - P R E S S U R E S U B - 1 0 - P I C O S E C O N D C A R B O N D I O X I D E L A S E R A M P L I F I E R by M i c h a e l K o n Y e w H u g h e s B.Sc. (Eng), Queen's University, 1990 M.A.Sc, The University of British Columbia, 1993 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Physics and Astronomy) We accept this thesis as, conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA February 2002 ©Michael Kon Yew Hughes, 2002 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract A multiatmospheric-pressure-broadened CO2 laser amplifier was constructed to amplify sub-10-picosecond pulses generated with semiconductor switch-ing. High-intensity, mid-infrared, amplified pulses have many applications: especially in fields such as non-linear optics, laser-plasma interaction, and laser particle acceleration. The injected pulses are produced by exciting GaAs (or an engineered, fast-recombination time semiconductor) with an ultrafast visible laser pulse to induce transient free carriers with sufficient density to reflect a co-incident hybrid-CC>2 laser pulse. The short pulse is injected directly into the regenerative amplifier cavity from an intra-cavity semicon-ductor switch. The C02-gas-mix amplifier is operated at 1.24 M P a which is sufficient to collisionally broaden the individual rotational spectral lines so that they merge to produce a gain spectrum wide enough to support pulses less than 10 ps long. After sufficient amplification, the pulse is switched out with another semiconductor switch pumped with a synchronized visible-laser pulse. This system is demonstrated and analysed spectrally and temporally. The pulse-train spectral analysis is done for a GaAs-GaAs double-switch arrangement using a standard spectrometer and two HgCdTe detectors; one of which is used for a reference signal. An infrared autocorrelator was de-signed and constructed to temporally analyse the pulse trains emerging from the amplifier. Interpretation of the results was aided by the development of a computer model for short-pulse amplification which incorporated satura-tion effects, rotational- and vibrational-mode energy redistribution between pulse round trips, and the gain enhancement due to one sequence band. The results show that a sub-10-picosecond pulse is injected into the cavity and that it is amplified with some trailing pulses at 18 ps intervals generated by coherent effects. The energy level reached, estimated through modelling, was >100 mJ/cm 2 . i i Contents Abstract ii Table of contents iii List of tables vi List of figures vii 1 Introduction 1 2 Mid-infrared short-pulse generation: Practice and applica-tions 4 2.1 Introduction 4 2.2 Short-pulse generation at CO2 wavelengths 5 2.2.1 Frequency down-conversion 5 2.2.2 Free-electron lasers 6 2.2.3 Quantum cascade lasers 7 2.3 Short-pulse generation with C 0 2 lasers 7 2.3.1 Optical free-induction decay 8 2.3.2 Mode locking 9 2.3.3 Ultrafast switching 11 2.4 Short-pulse amplification in multiatmospheric-pressure C 0 2 • 13 2.4.1 Power and pulse width limitations of methods for gen-erating fast mid-infrared pulses 13 2.4.2 Previous work on injection-locked C 0 2 lasers 15 2.5 Applications 15 3 The C 0 2 laser system 18 3.1 C 0 2 regular-band energy levels 18 ii i 3.2 Discharge kinetics 20 3.3 C 0 2 laser-gain spectrum 21 3.4 Modelling the C 0 2 system 27 3.4.1 Five-temperature model 27 3.4.2 Hot and sequence bands 28 3.5 Short-pulse amplification 29 3.5.1 Accounting for redistributions 30 3.5.2 Coherent effects in pulse amplification 31 4 Ultrafast semiconductor-switching materials 39 4.1 Introduction 39 4.2 Carrier excitation and recombination 40 4.3 Modelling a semiconductor switch 41 4.3.1 Refractive index as a function of carrier density . . . . , 44 4.4 Experimental investigation of switch materials 47 4.4.1 GaAs switching characteristics 48 4.4.2 Silicon switching characteristics 53 4.4.3 Radiation-damaged GaAs 54 4.4.4 Low-temperature-grown GaAs and In.s5Ga.15As/GaAs superlattice 55 5 Experimental equipment, design, and procedure 60 5.1 Overview 60 5.2 Visible short-pulse generation equipment 60 5.2.1 Nd:YAG oscillator 62 5.2.2 Pulse compressor 63 5.2.3 Dye-laser oscillator 63 5.2.4 Nd:YAG regenerative amplifier 63 5.2.5 Dye amplifier 64 5.3 Principles of autocorrelation 65 5.4 Visible-pulse autocorrelator 71 5.5 Transversely-excited lasers 72 5.6 CO2 hybrid laser 73 5.6.1 Low-pressure section 75 5.6.2 Mechanical details 76 5.6.3 Electrical details 77 5.6.4 Operational details 77 5.7 Multiatmospheric-pressure amplifier 81 iv 5.7.1 Laser body 81 5.7.2 Electrical details 81 .5.7.3 Operational details 83 5.7.4 Optical details 83 5.7.5 Pulse injection 87 5.7.6 Pulse switch out 88 5.8 Timing 89 5.9 Obtaining high contrast ratio amplified pulses 91 5.10 Infrared detectors 94 5.10.1 Cu:Ge detector 94 5.10.2 HgCdTe detectors 94 5.11 Spectral measurements 94 5.12 Infrared autocorrelator 95 6 Experimental results 100 6.1 Pulse injection 100 6.1.1 Single-switch pulse injection 101 6.1.2 Double-switch pulse injection 102 6.2 Amplifier operation 103 6.2.1 Modelling pulse amplification 107 6.2.2 Effects of timing jitter on pulse amplification 114 6.2.3 Effects of semiconductor damage on pulse amplification 119 6.2.4 Limits to pulse amplification caused by damage to win-dows and mirrors and by other mechanisms 124 6.2.5 Unstable resonator 125 6.3 Spectral results 126 6.4 Pulse-duration analysis . 129 6.4.1 Autocorrelator data analysis 129 6.5 Pulse switch out 138 7 Conclusions 144 7.1 Pulse injection 144 7.2 Pulse amplification 146 7.3 Cavity dumping 147 7.4 Conclusions and suggestions for future work 147 Bibliography 149 List of Tables 3.1 Ratios of peak intensities in pulse train for various values of a0L assuming no saturation effects. The main pulse is labelled 0 37 6.1 Best-fit model parameters and modelling results 109 6.2 Best-fit model parameters and modelling results with consid-eration of the first sequence band 115 vi List of Figures 2.1 Pockel's-cell switch: The half-wave voltage applied to the Pockel's cell will rotate the beam polarization so that it will be reflected from the second polarizer. Both polarizers are at the Brewster's angle 12 3.1 CO2 vibrational modes 19 3.2 Normalized population of the rotational-levels of the regular-band upper laser level (00° 1) thermally populated at T = 400 K 24 3.3 Important energy levels of the regular-band CO2-N2 laser sys-tem 25 3.4 C 0 2 small-signal-gain spectrum for the P-branch transition of (00°1) -> (I): (a) 0.4 MPa, (b) 0.8 tMPa, (c) 1.2 M P a 26 3.5 The pulse-train evolution after transmission through the res-onant gain medium, neglecting saturation. 36 4.1 Illustration of the thin-film-model parameters 43 4.2 Calculated reflection from a uniform thin plasma as a function of carrier density 45 4.3 Reflection-transmission cross correlation set-up 48 4.4 Reflected intensity as a function of pump-beam fluence for a single GaAs switch 50 4.5 Sample cross-correlation signal for GaAs 51 4.6 Differentiated cross-correlation signal for GaAs which shows the actual pulse shape 52 4.7 Pulse widths for different H + dosages in GaAs 55 4.8 The reflection-transmission correlation signal for low-temper-ature-grown GaAs 57 4.9 The reflection-transmission correlation signal for a superlat-tice of In 8 5 Ga . i 5 As 58 vn 4.10 Logarithm of the reflection-transmission correlation signal for a superlattice of In.g5Ga.15As showing two different character-istic decay times 59 5.1 Overview of multiatmospheric-pressure amplifier system. . . . 61 5.2 Visible short-pulse laser system 62 5.3 Additional dye amplifier 66 5.4 Visible-pulse-width autocorrelator 67 5.5 Input trial autocorrelation functions: (a) f(t) — {exp[—t/(l — i T A)] + exp[i/(l + ,4)]}- 2, A = 3/4 (b) sech2, (c) Gaussian. . . . 69 5.6 Autocorrelation of trial functions shown in figure 5.5 70 5.7 L - C inversion circuits 74 5.8 The hybrid laser 75 5.9 Low-pressure C W lasing section 76 5.10 Complete electronic schematic diagram of hybrid pressure sec-tion 78 5.11 Hybrid pressure section (end view) 79 5.12 The intensity-evolution of the hybrid laser. The small pulse ~100 ns before the centre line is a timing reference 80 5.13 Multiatmospheric-pressure-amplifier body: end view 82 5.14 Multiatmospheric-pressure laser: Complete electrical schematic diagram 84 5.15 The amplifier small-signal gain for the 9.4-/^m transition and 1.2-MPa pressure 85 5.16 A schematic drawing of the electronic timing and synchroniza-tion for the complete experimental system 90 5.17 Trigger signal variable-delay circuit based on two multivibrators. 91 5.18 Laser-trigger-pulse pushbutton-synchronization unit 92 5.19 Diagram of spectrometer setup 96 5.20 The infrared autocorrelator 97 6.1 Two possibilities for the injection-switch arrangement 102 6.2 A pulse train reflected from the K C l window 104 6.3 Pulse injection and the first-few round trips with RD-GaAs + GaAs double injection 106 6.4 Flow chart for program used to calculate pulse-energy evolu-tion as a function of laser transition 109 6.5 Modelling results fitting parameters to data of table 6.1. . . .110 viii 6.6 Mode temperatures corresponding to figure 6.5 and table 6.1. . I l l 6.7 Modelling results from fitting parameters to data of table 6.2 and considering the first sequence band 115 6.8 Mode temperatures corresponding to figure 6.7 and table 6.2. Note that T i ~ T 2 and considering the first sequence band. . 116 6.9 Effect of timing jitter on the terms corresponding to the four round trips following injection in the denominator of equation 5.7. The round-trip loss is (a) 2/3, (b) 1/3 118 6.10 Effect of timing jitter on the terms corresponding to the four round trips preceding injection in the denominator of equation 5.7. The round-trip loss is (a) 2/3, (b) 1/3 118 6.11 Amplifier operation with silicon cavity-dumping switch 120 6.12 Injection and first-few unamplified round trips with new wafers in cavity. The height of the pulse at the centre line is 2.5 div. The reading is with channel 2 which has a sensitivity of -10 mV/div, 10 ns/div 122 6.13 Injection and first few round trips after wafers damaged. Com-parison with figure 6.12 shows the effect on the pulse trans-mission. The active channel is channel 2 with -10 mV/div and the timescale is 10 ns/div 123 6.14 A sample signal from the spectrometer 127 6.15 Pulse spectrum for GaAs + GaAs injection switching 128 6.16 A sample signal from the autocorrelator. . 130 6.17 Sample data: autocorrelator signal (o) and reference data (o) and fits (solid lines) and their uncertainties (dotted lines) for a delay corresponding to -4 ps. The fits were used so that a second harmonic voltage level could be extrapolated from a given reference signal voltage 133 6.18 The complete autocorrelation ( V 2 w for a reference voltage (V w ) of 450 mV 134 6.19 Description of autocorrelation fit variables. V* — Vi/(V2nai) and V2* = V2/{V2na2). . . . . 135 6.20 Calculated autocorrelation signal for an unsaturated C 0 2 med-ium with aoL = 29.4 and a 4-ps Gaussian injected pulse. . . . 136 6.21 Confidence region for voltages for 450-mV data. The scales are in mV 137 6.22 Confidence region for a values for 450-mV data. The scales are in ps 138 ix 6.23 Autocorrelator pulse-shape evolution for differing reference voltages 139 6.24 Pulse train with GaAs cavity dumping 141 6.25 Pulse switched out using a GaAs switch. 142 x Chapter 1 Introduction Since the first demonstration of laser operation with a pulsed ruby system in 1960 [1], there has been a continuing trend of laser development towards shorter pulses which allow access to new areas of science on shorter time scales. New areas are also opened up when sources are developed in new wavelength regions [2, 3] and at higher intensities. In fact, the production of shorter pulses facilitates the production of higher intensities. The intensity is proportional to the pulse energy divided by the pulse width. For many systems, the pulse energy generated can remain fairly constant as shorter pulses are induced thereby leading to higher peak intensities. In the visible-wavelength region, ultrashort pulses are routinely avail-able through techniques known as mode locking or pulse compression of a spectrally broadened pulse. However, in the mid-infrared-wavelength re-gion, such techniques are less effective largely due to the limitations of the materials transparent in the mid-infrared and of the available lasing media. While the generation of short, intense pulses in the mid-infrared is dif-ficult, such pulses are very desirable since many physical phenomena scale with a term IX2: intensity x (wavelength)2. Comparing a short pulse at a CO2 wavelength ~10 pm, to one in the neodymium range, ~1 /im, the IX2 parameter is 100 x larger. This makes intense, short-pulse C 0 2 lasers useful in many areas such as the rapidly developing studies of relativistic Thompson scattering, above-threshold and tunelling ionization, and laser-acceleration techniques. Applications will be further discussed in section 2.5. This work details the development of a multi-atmospheric-pressure CO2 transversely-excited amplifier to amplify picosecond CO2 pulses generated with optical semiconductor switching. As is the case in other wavelength re-1 gions, it uses ultrafast, visible-laser pulses to generate short C0 2-wavelength pulses. This has the advantage of the C 0 2 pulse being inherently synchro-nized with a visible laser. This is important for many pump-probe type experiments. There are many competing technologies for the generation of short pulses in the mid-infrared. These include techniques which are based on C 0 2 lasers: active and passive mode locking of C 0 2 lasers, optical free-induction decay in hot C 0 2 (and other gases). Also, there are the techniques on which this work is based: semiconductor switching and injection-locked amplification of short pulses. There are also a number of techniques which are not based on C 0 2 sys-tems. These include frequency down-conversion, quantum cascade lasers, and free-electron lasers. Of these, only free-electron lasers and frequency down-conversion have demonstrated pulses < 10 ps. A l l these methods will be discussed in more detail in the next chapter. This study relies on a few areas of development. Firstly, the development of high-pressure C 0 2 lasers. The first operation of the C 0 2 laser was ob-served by C. K . N . Patel [4, 5]. It was quickly realized that a way of increasing the gain in the gas was to increase the molecular density by increasing the gas pressure. In 1971, N . G. Basov et al. operated a 15x atmospheric-pressure electron-beam-pumped pulsed laser in order to take advantage of this higher gain. At the time, they also realized that pressure broadening could lead to picosecond pulses [6]. A C 0 2 laser can operate on many closely-spaced combined rotational-vibrational transitions. At pressures below a few atmospheres a laser will normally operate on only one of these transitions. While the gain envelope of the manifold of transitions has a bandwidth of ~(1.5 p s ) - 1 , each individual line cannot support a pulse shorter than ~25 ps. Above ten atmospheres, the collision frequency becomes large enough that transition levels become broad enough to support pulses shorter than ten picoseconds. Once a system has been created which can amplify short pulses, a method must be found to generate the pulses. The use of mode locking in a laser cavity has been very successful in the visible regime. In the mid-infrared, it has not been as successful. This study utilizes the very closely related injection-locking technique which is discussed in section 2.4.2. The injection locking is accomplished through the use of an intra-cavity semiconductor switch. Semiconductor switching is now a well established technique and has been 2 used to generate pulses as short as 130 fs [7]. However, the development of intra-cavity switching has only been demonstrated in the far infrared. This study investigates its use for injection locking pulses short enough to take advantage of the pressure-broadened spectrum of a 1.24 M P a CO2 gain medium. This thesis is arranged as follows. Chapter 2 discusses the various means and limitations of generating and amplifying short pulses at CO2 wave-lengths. As well it discusses the applications of such pulses. Chapter 3 investigates the physics of C 0 2 laser operation with emphasis on the am-plification of short pulses. Chapter 4 discusses the field of semiconductor switching of mid-infrared pulses. Chapter 5 outlines the apparatus used in this experiment. Chapter 6 presents the experimental results and chapter 7 presents conclusions. 3 Chapter 2 Mid—infrared short—pulse generation: Practice and applications 2.1 Introduction C 0 2 lasers were first demonstrated in 1964 [4]. They are widely used in research and industry due to their possible high efficiencies and powers. They are of interest in fields such as plasma physics due to the high ponderomotive potentials and forces made accessible by their long wavelengths and possible high intensities. While high average power pulses are possible, their use has been limited by the general inability to produce short (< 10 ps) intense pulses as has been possible at shorter wavelengths. This chapter will discuss the methods for creating short pulses at mid-infrared wavelengths which do not use C 0 2 lasers. This will be followed by a discussion of previous work on the generation of short pulses using C 0 2 lasers. Lastly, applications of short intense C 0 2 pulses will be briefly discussed. The mechanics of C 0 2 laser operation and amplification will be addressed in the following chapter. 4 2.2 Short—pulse generation at CO2 wave-lengths Possible methods for short-pulse generation at CO2 wavelengths, but without using CO2 lasers, are frequency down-conversion, free-electron lasing, and quantum cascade lasing. In this work the term, 'short pulse', shall refer to the region between 1 and 100 ps though the region of the most interest is that less than 10 ps. The term 'ultrafast' is normally reserved for the subpicosecond region. 2.2.1 Frequency down-conversion The generation of short pulses at CO2 wavelengths using frequency mixing in non-linear crystals is an established technique. In general, these systems employ short-pulse, visible or near-infrared, lasers which produce two fre-quencies, and LL>2- Additional frequencies, including oj\ — C J 2 = cu3, can be produced. With a suitable choice of wavelengths, crystals, and optical setup, Us can be in the mid-infrared. Many systems have been demonstrated which produce subpicosecond mid-infrared pulses using difference frequency generation [8]. Most of these systems are based on commonly available, short-pulse visible and near-infrared laser systems and produce very low energies: femto- to picojoules per pulse. Recently some work has been done using amplified pump lasers to produce pulses of in the nano- to microjoule range. One example is a system which mixes 120-fs, 815-nm pulses with pulses from a dye laser and amplifier in a AgGaS2 crystal to produce pulses as short as 400 fs in the range of 4.5 to 11.5 fim at a repetition rate up to 1 kHz and with pulse energies up to 10 nJ. The 815 nm pulses are produced in a titanium-doped sapphire (Ti:sapphire) laser and amplifier. A portion of the Ti:sapphire output is used to pump the dye laser and amplifier [9]. Another example is a system which produces pulses with energies in the microjoule range. This is based upon a neodymium-doped glass (Nd:glass) laser system [10]. A portion of the 2-ps pulse at 1-Hz repetition rate pumps a dye laser and amplifier to produce microjoule pulses centred at 1.1 or 1.4 /im. The Nd:glass and dye laser pulses are mixed in a GaSe crystal to produce picosecond pulses through the CO2 range. In general, these systems have the advantage of being tunable over a large 5 wavelength range and the possible advantage of having a high repetition rate. However, thus far, the power levels have remained low and it is not envisioned that such systems will ever be able to compete in the energy range investigated by the present work. 2.2.2 Free-electron lasers Free-electron lasers (FEL), are capable of producing pulses over a very wide wavelength range with variable-duration pulses, often in the femtosecond range. Free-electron lasers are different from all other lasers in that they are not operated on a fixed atomic, molecular or electronic transition but rather by a transfer of the kinetic energy from relativistic electrons. Short-pulse free-electron lasers require short pulses of relativistic elec-trons. These interact, within the optical cavity, with a periodic magnetic field in a device descriptively called an undulator. The Lorentz force causes a transverse motion of the electron bunches which thereby exchange energy with the cavity E M field. This field initially starts from spontaneous emis-sion. Generally, FEL ' s work as synchronously-mode-locked lasers. That is, the round-trip period of the short cavity light pulses are synchronous with the electron bunches. What is different from most mode-locked lasers is that cavity lengths are usually quite long such that an optical pulse is not pumped by successive electron pulses. For instance the Free-Electron Laser for Infrared experiments (FELIX) facility [11] circulates 40 light pulses in the cavity so that each one is pumped by every 40th electron bunch. There are now many FEL's which can operate in the C O 2 range. Two which can produce short pulses are F E L I X and CLIO [12]. The F E L I X facility is tunable in the range of 5 to 110 /xm and produces micro joule pulses in the range of 2 to 20 ps. the CLIO facility can produce pulses as short as 200 fs tunable in the range 3 to 50 fj,m with peak pulse energies up to the microjoule range. It operates using a 50 to 80 Aelectron beam at energies up to 58 MeV. The disadvantage of FEL's is mainly the cost to build such a system which requires a powerful electron accelerator. 6 2.2.3 Quantum cascade lasers Quantum cascade lasers are based on tunnelling transitions between adjacent quantum wells. The differences in the allowed states between the two are such that the transition is in the wavelength region of interest. Quantum wells are formed in semiconductors when thin layers of lower bandgap material are epitaxially grown between semiconductor layers with higher bandgaps in such a way that the carriers can become confined in the low-bandgap layer. This confinement allows only discrete momentum states in the growth direction. The energy levels can be easily varied by adjusting the structure widths and semiconductor-alloy fractions. Quantum cascade lasers have their energy differences between adjacent wells carefully tailored such that photons will be emitted in the wavelength region of interest. As well, other structures are added which act to fill the upper level and empty the lower level to promote efficient lasing. These devices are called cascade lasers because a sequence of wells can be built so that an electron passes through a large number of similar structures, dropping in energy through stimulated photon emission at each. The recent progress in this area has been dramatic. First, gain-switched operation was shown producing 200-ps pulses [13], then mode-locked op-eration was demonstrated with approximately 5-ps pulses [14], and, most interestingly, self-mode locking has yielded pulses less than 5 ps [15]. In this case however, even though the pulses were extremely short, the peak power was only in the order of 1 W. While these experiments were not carried out at CO2 wavelengths, it appears that the wavelength of operation can be set by selection of appro-priate quantum-well parameters to be throughout the infrared. Currently the disadvantages with this approach are very low power and the need for cryogenically-cooled operation. However, it is expected that there will soon be further progress in this area. 2.3 Short—pulse generation with CO2 lasers The primary techniques for producing short pulses with CO2 lasers are optical free-induction decay, mode locking, and ultrafast switching. A good review of the development in this field prior to 1980 was given by A. J. Alcock and P. Corkum [16]. 7 2.3.1 Optical free-induction decay Optical free-induction decay (OFID) was one of the first techniques used for generating sub-nanosecond CO2 pulses. This technique was first demon-strated by E. Yablonovitch and J. Goldhar [17] and has been used to generate pulses as short as 30 ps [18, 19]. Short-pulse generation by this method re-quires two parts: first a continuous-wave (CW) or long-pulse beam is sharply truncated by some sort of switch, thereby creating new optical frequencies; secondly, the incident laser frequency is filtered out. This will leave a short pulse. In practice, this technique uses a plasma shutter to sharply cut off a pulsed CO2 beam. The truncated beam is passed through a spectral filter which removes the original spectral line but leaves the sideband radiation. Free induction decay is a term borrowed from nuclear magnetic reso-nance (NMR). In N M R , nuclear spins are coherently excited, then allowed to precess freely in a magnetic field. A radio frequency signal, generated by the collective precession, can be detected. The signal power decays due to relaxation. This is analogous to the absorption of a coherent optical beam which is abruptly terminated [20]. Before the cutoff, the effect of the absorbing medium is to radiate a beam n/2 out of phase from the excitation beam. The net effect is that destructive interference leads to zero electric field and therefore no transmission of the incident beam. However, when the incident beam is abruptly terminated, the medium will still radiate. The pulse is short lived because the population of the upper laser level quickly decays and loses coherence leading to a short pulse. The plasma shutter is generally used in the following manner. The CO2 beam is sharply focussed within a gas cell. A plasma initiated at the focus of the beam will quickly expand and cut off transmission through the cell both by absorption and reflection. The plasma can be initiated through optically-induced dielectric breakdown or, more commonly, by an electrically-triggered spark, or a surface plasma generated by a split-off part of the main C 0 2 beam [19]. While there are a few possibilities for spectral filters, hot C 0 2 has proven to be nearly ideal. Normally, the absorption of C 0 2 radiation in C 0 2 gas is small because the population of the lower level of the transition is small. However, if the gas is heated, the level can have a significant thermal popula-tion. Naturally, the absorption arising will be spectrally matched to the C 0 2 laser emission. The pulse durations can be varied somewhat by varying the 8 relaxation time of the hot molecules through varying the cell pressure. Typ-ical values for the cell parameters are temperatures of 600-800 K , pressures of 50-1200 Pa, and lengths up to a few meters. The shortest pulses generated by this technique have been approximately 30 ps long. In their paper [18], H. S. Kwok and E. Yablonovitch have stated that shorter pulses were not achievable due to a decrease in pulse-generation efficiency and the finite (~10 ps) cutoff time of their plasma switch. 2.3.2 Mode locking Mode locking is used in a wide variety of systems to produce short pulses. This technique is used to create fast and ultrafast pulses in Tiisapphire and Nd:YAG which are the most widely used visible short-pulse laser systems. Mode locking can be simply described as the fixing of the available phases in the oscillating laser cavity such that a maximum of all the modes simulta-neously occurs at one place. This can also be thought of as one short pulse circulating in the cavity. Modes can be locked together either by amplitude or frequency modulation: losses or phase shifts are periodically introduced within the laser cavity such that only mode oscillations with the desired phase are amplified. The techniques and theory of mode locking in C O 2 lasers are covered in detail in reference [21, chapters 7 and 8]; here these shall only be summarized. An optical cavity will only allow modes which fit an integral number of wavelengths into the cavity to be coherently amplified. These are separated by the frequency: v — cj(2L). Normally, in a homogeneously broadened gain medium, such as low-pressure C 0 2 operating at threshold, only one mode will persist. However, if an amplitude or frequency modulator is placed within the cavity, oscillating at the cavity-round-trip frequency, u, side bands will be generated at the same frequencies as the natural cavity modes. It is the locking together of these modes which permits short-pulse generation through mode locking. As will be discussed in section 3.3, the shorter the pulse desired, the greater the number of phase-locked modes necessary to create it. The number of modes possible is limited by the gain bandwidth of the medium. In a C O 2 system this is controlled by pressure. In C 0 2 lasers, both active and passive mode locking have been put into practice. Active mode locking is the actively-induced modulation of the transmission properties of an intra-cavity component by an applied signal. This can be done by amplitude modulation (AM) through acousto-optic mod-9 ulation (Bragg reflection) in a semiconductor such as germanium, or by fre-quency modulation (FM) through the electro-optic effect in semiconductors such as GaAs or CdTe. In order to get short pulses from this technique; suf-ficient gain bandwidth is required. To get pulses below approximately 2 ns it is necessary to use a pressurized laser and therefore a pulsed discharge. This was first done with an actively mode-locked system which produced pulses approximately 900 ps long [22]. These were generated with a germa-nium acousto-optic modulator placed within a laser cavity with electrical-discharge section filled with 1.2 MPa of C0 2 :N 2 :He : : l : l : 8 . The pulses which start to circulate in the cavity as the lasing threshold is crossed are not short. It can take thousands of round trips for a pulse to become bandwidth limited [23]. However, as the pressure is increased, the gain lifetime also decreases. At 1.2 MPa, the gain lifetime could only accommodate approximately 75 roundtrips: far short of what was required. Furthermore, the size of the mode-locking element limits the shortness of the pulses possible. Normally, the mode locker is placed as close as possible to one of the end mirrors. The pulse duration can be expected to approach the time it takes for a pulse to enter the mode-locking element, reflect off the end mirror, pass through the element, and exit. With the mode-locking element placed at the Brewster angle within the cavity, this transition time can be hundreds of picoseconds. This has been improved by a system employing a travelling-wave modu-lator. Travelling-wave modulation is a technique which increases the speed of electro-optic elements by including the element as part of an electrical transmission line. In that way, a short voltage pulse can propagate along the element with the optical pulse. Since the entire element does not have to be charged to the appropriate voltage this effectively shortens the switching time. The improved system used GaAs Pockel's cells (electro-optic polariza-tion rotators) to mode lock pulses in the same amplifier module that is used in this study. It was pressurized to 1 M P a and produced pulses as short as 500 fs [24]. Passive, rather than active, mode locking has proved to be more successful in terms of generating short pulses. For passive mode locking, an element is inserted into the cavity near one of the mirrors whose transmission is inversely related to the intensity. Such an element is known as a saturable absorber. This has been done with the gases S F 6 [25, 26] and hot C 0 2 [27]. However, the best material appears to be p-doped germanium [28]. This material operates as a two level system for which the upper level lifetime is very short: its relaxation time is only a few picoseconds when doped with gallium or 10 indium to approximately 1 cm. Nearly bandwidth-limited pulses have been generated at 82 kPa [29]. An attempt was made to generate short pulses in a multi-atmosphere C O 2 transverse-electric-discharge, atmospheric-pressure (TEA) laser and pulses as short as 150 ps were realized [22] using a 1 mm thick piece of p-Ge. As with active mode locking, there are the same difficulties in achieving bandwidth-limited pulses from high-pressure lasers: namely the reduced gain lifetime greatly limits the number of round trips possible. 2.3.3 Ultrafast switching The third way to generate ultrafast pulses of C 0 2 laser radiation is by 'slicing' out short pulses from C W or pulsed beams. The simplest approach to slicing pulses would be to use conventional electro-optic switches such as a Mach-Zehnder interference device or a Poc-kel's cell. Pockel's cells are widely used in infrared- and visible-laser systems. They utilize the electro-optic effect to rotate the polarization of a beam passing through them. The degree of rotation is dependent on the voltage applied. Such a cell placed between two polarizers can act as an optical switch as shown in figure 2.1. A Mach-Zehnder device is one in which an incident beam is equally divided through two waveguides and later recombined. In one of the waveguides is placed an electro-optic element which is capable of modulating the phase under the influence of an applied voltage. Interference of the recombined waves determines the transmission of the switch. Both of these devices can be designed to be quite fast, especially if a traveling wave arrangement is used. This is a area of intense development in the near-infrared because of telecommunications applications. However, the fastest modulation frequencies that have been achieved commercially are 40 GHz which corresponds to 25 ps pulses. It is not expected that modulators will be developed soon in the C 0 2 region that will be able to produce pulses < 10 ps. Semiconductor switching involves the use of above-bandgap pump pulses to modulate the reflectivity of normally infrared-transparent semiconductors through the production of an electron-hole plasma. Semiconductor switches can be very fast because the pulses can be switched-on in the same time scale as ultrafast visible pulses and switched off on the time scale of ultrafast carrier recombination in specially engineered semiconductors. The mid-infrared wavelength of C 0 2 lasers makes them ideally suited to semiconductor switching. The shorter the wavelength being switched, the 11 Reflected Beam E © E Polarizer 1 Pockel's Cell Polarizer 2 Figure 2.1: Pockel's-cell switch: The half-wave voltage applied to the Pockel's cell will rotate the beam polarization so that it will be reflected from the second polarizer. Both polarizers are at the Brewster's angle. more pump-pulse energy is required which eventually leads to problems with switch damage. The first demonstration of the semiconductor switching of a CC*2 beam resulted in ~2 ns pulses produced from polycrystalline germanium pumped with ~2-ns pulses from a ruby laser [30]. This was followed by the generation of ~100-ps pulses using ~6-ps pulses from a Nd:glass laser and single crystal of germanium as a switch [31]. It was quickly realized that these switching elements could be used as both reflection and transmission devices and operating them in series could make for faster switches, especially since the reflective state of germanium, an indirect-gap semiconductor which was first used, is quite long but its reflective risetime is quite short. A pulse with a fast risetime could be easily generated and it could be rapidly truncated with a transmission switch. The first to use this technique were S. A . Jamison and A. V . Nurmikko in 1978 [32]. They used a germanium flat first to reflect a pulse which was later truncated by the same flat. The control pulses were provided by a picosecond Nd:glass laser at 1.06 ^m. It should be noted that the pulses produced by this experiment had a significant C W background. In fact, they reduced this through the use of a hot-CC^ filter. The fastest pulses produced to date have been ~130 fs long created through the use of a triple switch arrangement [7]. These switches were pumped with 70-fs, 620-nm pulses from a dye laser and amplifier. The first two elements were polycrystalline CdTe reflection switches and the last was a silicon cut-off switch. These switches were used to 'slice' the pulses from a C 0 2 T E A laser. 12 More recently, work has been done to use 'ultrafast' semiconductors to slice the shortest possible pulses out of a longer pulse or a C W beam. As will be discussed in detail in the following chapter, this has been done with low-temperature-grown GaAs [33], radiation damaged GaAs [34], and a superlat-tice of alternating GaAs and Ino.85Gao.15As layers [35] which have produced pulses as short as 1 ps, 600 fs, and 2.5 ps respectively. It should be noted that, to our knowledge, an intra-cavity semiconductor switch has not been used to inject pulses into a laser cavity. However, there has been some use of such switches to cavity dump far-infrared (FIR) lasers. Cavity dumping is a technique used to maximize the energy output of a laser by using an intra-cavity switching element to 'cavity dump' all of the circulating pulse energy within a cavity. This is in contrast to output coupling through a partially reflective mirror which can only reflect a portion of the circulating energy. In the FIR regime, this was first done with a 5-mm-thick GaAs slab pumped by a 2-W Nd:YAG laser to produce ~10 ns pulses from ~90 to ~500 /im depending on the choice of the lasing medium [36]. This has also been done with a FIR free-electron laser to switch out a ~50 ns pulse from a silicon switch pumped by a Q-switched Nd :YAG laser [37]. 2.4 Short—pulse amplification in multiatmo-spheric-pressure CO2 None of the methods mentioned in sections 2.2.1 to 2.3.3 produce short pulses of the desired intensity; therefore, there is a need to amplify short pulses to the desired intensity. This will be discussed in this section. 2.4.1 Power and pulsewidth limitations of methods for generating fast mid-infrared pulses While all the previously mentioned techniques are capable of producing fast and ultrafast pulses at CO2 wavelengths, none of them are currently capable of directly producing < 10-ps pulses in the millijoule range. Frequency down-conversion: 400-fs, 10-nJ pulses have been produced as well as picosecond, microjoule pulses. Therefore the limitation here is energy. These systems are based on visible-laser systems which, through suitable amplification, could deliver pulses powerful enough 13 to generate high-energy infrared pulses if they could be converted effi-ciently. However, these crystals are expensive and susceptible to optical damage. In order to generate more powerful pulses, thin wide-aperture crystals would have to be used. This may be possible but has not been done. Free-electron lasers: The primary limitation here is cost. The two systems mentioned [11, 12] in section 2.2.2 are very large multiuser facilities. While the pulses generated from them are very short, the pulse energies generated are in the microjoule range. The costs of scaling up these powers would be prohibitive. Quantum cascade lasers: This is a rapidly developing technology. Currently the energy produced is probably too low to seed a C 0 2 amplifier. That is, the spontaneous emission from the amplifier would compete for gain with the seeding pulses leading to a highly unreliable system. Optical free induction decay: It seems that while high-energy pulses may be possible with this system, the pulse-length limitations have can not be easily overcome. Some engineering may speed up the truncation process in the plasma switch; however, the decrease in efficiencies may make pulses < 10 ps impossible. Mode locking: Again, in this instance the limitation seems to be in pulse width. At the multiatmospheric pressures necessary to support a pi-cosecond bandwidth, the amplification time available for mode locking is not short enough to generate bandwidth-limited pulses. Ultrafast switching: This technique can provide short and ultrashort pulses easily but again, the pulse energy is low. It is possible to slice short pulses out of mega- or gigawatt laser pulses, but this is a tremendously inefficient process. Therefore, in order to produce pulses in the desired < 10 ps, mJ range, it is necessary to amplify short pulses from lower-energy sources. Of the above sources, frequency down-conversion, FEL's , and ultrafast switching can produce pulses short enough for our needs. We are concentrating on ultrafast switching. One reason for this is that these pulses can be efficiently coupled into the amplifier cavity through the placement of the switches within 14 the cavity. The only technology suitable for the amplification of short mid-infrared pulses to the desired energy level is that of multiatmosphere CO2 lasers. 2.4.2 Previous work on injection—locked C O 2 lasers In 1975, P. A . Belanger and J. Boivin first demonstrated injection lock-ing, also known as regenerative amplification [38, 39]. Injection locking is the technique whereby pulses are injected into a laser cavity soon after the threshold for gain is crossed. In this case, a mode-locked, nanosecond pulse, selected by a Pockel's cell was injected through a saturable absorber and through a hole in the amplifier end mirror. In this way the pulse could be reliably amplified. This work was followed by A. J. Alcock et al. who used a multiatmo-spheric-pressure (0.8 MPa), transverse-electric-discharge (TE) section to amplify nanosecond pulses up to energies of ~ 1 J [40]. P. Corkum [41] continued this work by demonstrating that shorter pulses could be amplified. High-contrast pulses created using two reflection switches and then a transmission cut-off switch were reflected from a NaCl window into an amplifier which utilized a gas mixture up to 10 atm (~1 MPa). The injected pulses were amplified up to energies of ~15 mJ and had pulse durations as short as 2 ps. Interesting effects were seen such as additional pulses generated due to a residual modulation in the gain spectrum as well as pulse compression due to plasma effects; these shall be discussed in the chapters following. While these results are interesting, as a practical system, they can be improved: the pulses can be more effectively switched into the system by placing a semiconductor switch within the cavity itself and the energy can be efficiently extracted by also placing a cavity-dumping switch within the cavity. 2.5 Applications Applications for high-intensity CO2 lasers include studies of intraband tran-sitions in semiconductors, vibrational excitation of molecular levels, and laser chemistry [42]. These may require a fast, high-power laser to study fast pro-cesses with low cross sections. Many other potential applications involve the creation of and interaction 15 with laser plasmas. This is a field with many areas of study (as seen in recent conference proceedings [43]). The ones that have been of interest most recently involve non-linear physics which requires high fields. These include high-harmonic generation [44], hot-electron production, laser self-focusing, relativistic Thomson scattering, avalanche and tunnelling ionization [45], and various laser-acceleration techniques [46]. Some of these areas relate to inertial-confinement fusion which has been a primary driving force in the field of laser-plasma physics. Many of these areas benefit from the use of high-intensity, long-wavelength sources. In these areas, it is usually the high ponderomotive potential energy or force accessible with these lasers which makes their use advantageous. This potential is the energy that a charged particle will acquire in the electric - e2B2X2 field of a laser, averaged over an optical cycle: Up = 4 ( 2 7 r ) 2 m c 2 • Where E0 is the laser electric field. The ponderomotive force pushes charged particles out of regions with high average electric fields: F oc X2VE2. In its most simple application, this energy means that charged particle in a laser field will be ejected from the beam with energies up to Up [47]. For an example relevant to this experiment, a 100-mJ, 5-ps C 0 2 pulse can generate an average ponderomotive energy of 120 keV in an approximately diffraction limited spot of diameter A = 10.6 /xm. An equal intensity Nd:YAG pulse would have an average ponderomotive energy of only 1 keV. However, it should be noted that the shorter wavelength Nd: Y A G pulse can be focussed to a much smaller diffraction-limited size. Commonly available, short-pulse, moderately high-power lasers have much shorter wavelengths. Ti:sapphire operates in the range 740 to 850 nm, neo-dymium-doped Y A G and glass operate at 1.06 pm and dye lasers can be made tunable efficiently up to ~900 nm [48]. Therefore, a C 0 2 laser of sim-ilar intensity will produce ponderomotive potentials greater than or equal to one hundred times than these other laser types. Just a few of the more interesting potential applications will be briefly discussed. The first of these is particle acceleration. This is the motivation that has led to the construction of a large semiconductor switched C 0 2 laser at the Brookhaven National Laboratory Accelerator Test Facility [49]. Very high fields are accessible with focussed laser beams and in an al-ready ionized plasma, electrical breakdown is not the problem that it is with conventional accelerator schemes. The difficulty in using the large fields for acceleration is that the fields for E M waves are transverse and therefore the 16 acceleration time is limited. Many of the acceleration concepts involve the production of large amplitude plasmon waves on which electrons can be ac-celerated. Laser-wakefield acceleration was first proposed by T. Tajima and J. M . Dawson in 1979 [50]. In this scheme a short, intense pulse is put through an underdense (mostly transparent) plasma. The ponderomotive force pushes electrons out of the beam path. When the pulse has passed, electron motion sets up a strong plasma wave which can be used as an ac-celerator. One scheme which utilizes the transverse field to excite a plasma wave is called the grating LIN A C . This involves a pulsed laser, not necessar-ily CO2, cylindrically focussed on a metallic grating to produce a periodic plasma. A CO2 beam focussed from the side onto the plasma can create a plasma wave which will accelerate particles [51]. Other accelerator possibilities are the inverse-Cerenkov and inverse free-electron laser both of which do not require a plasma [52]. Another interesting application which benefits from high-intensity in-frared pulses is above-threshold ionization [45]. In this process, electrons which are ejected from atoms through multiphoton ionization can absorb further photons. The atomic and continuum levels in this process are shifted by the Stark shift which is given as Up. Tunnelling of electrons from atoms in electric field is known as the Keldysh effect. The rate of tunnelling is deter-mined by the Keldysh parameter, 7: 7 = yj2u>Ip/I, where Ip is the ionization potential. When 7 is small, tunnelling dynamics will dominate. Obviously, the wavelength dependence of these parameters facilitate the study of these effects in the mid-infrared. 17 Chapter 3 The CO2 laser system It is necessary to delve into some details of the CO2 laser system such that an understanding can be developed of the evolution of short pulses in the pressure-broadened gain medium. Fortunately, the CO2 system has been studied extensively; however some development is made in this study in the understanding of the effects of vibrational redistribution on the amplified short pulses. The energy levels and corresponding gain spectrum will be investigated followed by the kinetics of the laser-level excitation in an electrical discharge. The effects of multiatmospheric- pressure broadening on the gain, the gain lifetime, and spectral width will be discussed. The 'temperature model' will then be outlined as a tool for performing calculations on the system and this will be related to the amplification of short pulses. 3.1 CO2 regular—band energy levels CO2 lasers employ combined rotational and vibrational transitions. For low levels of excitation, the rotational dynamics can be treated separately from the vibrational dynamics. CO2 is a linear molecule with only four vibrational degrees of freedom. These are manifest as a symmetric stretch, an asymmet-ric stretch and a twofold degenerate bending mode as shown in figure 3.1. Conventionally, the vibrational state of the molecule is denoted (V1V2V3). The excitation of the symmetric stretch is denoted by v\, the bending mode by i>2, and the asymmetric stretch by v3. The degeneracy of the bending mode is removed by a Coriolis effect [53, pg. 377]. Different arrangements of the 18 < • Symmetric Stretch Bend V2 M + M o - # - o Asymmetric Stretch Figure 3.1: C 0 2 vibrational modes quanta in these bending modes have slightly different energies. We therefore need to assign I, a new quantum number. If v2 is even, I can have the values v2, v2 — 2, v2 — 4 . . . 0 and if v2 is odd, I can have the values v2, v2 — 2, v2 — 4 . . . 1. Therefore, the levels of the C 0 2 system can be simply, and conventionally, described by the notation (viVl2v3). Coincidentally, the energy of the (02°0) mode is very close to the (10°0) mode. The anharmonic coupling between these two modes of the same sym-metry species leads to a perturbation of these levels. This was first recognized by E. Fermi [54]. The actual energy levels were calculated by second-order perturbation theory by A. Adel and D. M . Dennison [55]. The energy dif-ference between these levels increases to 12.7 meV from the unperturbed difference of only 0.8 meV. The states are [21, pg. 18]: (I) = 0.73(10°0) - 0.68(02°0) (3.1) (//) = 0.68(10°0) + 0.73(02°0) (3.2) While other transitions are possible, the strongest transitions, and ones that are usually used are those between the (00° 1) level and the (I) and (II) levels. The spectra corresponding to these are known as the regular bands. 19 Each vibrational level has associated with it many rotational levels. For these bands, the transitions involve a change in both the vibrational and rotational quantum numbers. The rotational-transition selection rule is j —> j dz 1. Again, by convention, the transitions are labelled by the j of the lower level. The j + 1 —>• j transitions are called R branch transitions and the j — 1 —> j transitions are called P branch transitions. Due to symmetry considerations, odd-jf transitions are missing [53, pg. 16]. The CO2 system can be a very efficient lasing medium in part because it is relatively easy to establish a population inversion. For a laser to operate an inversion must be established in order that photons in resonance with a lasing transition will tend to induce stimulated emission rather than be absorbed. This will be facilitated if the upper laser level is long lived in relation to the lower laser level. This is the case here as will be seen in following sections. 3.2 Discharge kinetics For CO2 lasers, the most common methods for creating an inversion are with an electric discharge or with an electron beam. A l l the lasers in this study are electric-discharge lasers. For discharge lasers, C 0 2 is mixed with other molecules in order to fa-cilitate efficient excitation of the upper laser energy levels and discriminate against the excitation of the lower laser levels. A l l the molecular vibrations can be excited through inelastic collisions with the electrons and with each other. In addition, electron collisions can lead to other processes such as dissociation. The probabilities for different processes are determined by the electron-energy distribution function which is a function of the ratio of the electric field to the gas density, E / N [56]. The gas mix and E / N are chosen to optimize the excitation of the population inversion. Almost exclusively, C 0 2 discharge lasers are a combination of three pri-mary gases: C 0 2 , N 2 , and helium. N 2 is added because its v = 1 level is closely resonant to the (00° 1) C 0 2 transition and therefore it very efficiently transfers energy to the upper laser level. The difference in energy is only 2.2 meV. This level is very efficiently excited by an electric discharge. Fur-thermore it is long lived since its radiative decay is forbidden, therefore, most of the molecules in this level can eventually transfer their energy to the C 0 2 level. Favourable electron-energy distributions will only be seen in what is 20 known as a glow discharge; this is in contrast to an arc discharge. In this regime, the current density can be relatively even over a large area and the electron temperature will be low enough that the desired excitations will occur preferentially. In order to get a good glow discharge, it is necessary to add helium to the laser mix. Helium is is a light atom therefore it can exchange energy collisionally with electrons relatively efficiently. Therefore, the electron distribution of the discharge can be cooled which promotes a glow discharge. For a C W laser, helium acts to cool the whole gas as well. Its thermal conductivity is approximately six times that of CO2 or N 2 [21, pg. 74]. This is important in ensuring that the lower laser levels remain thermally unpopulated. 3.3 CO2 laser—gain spectrum The most important parameter for optical short-pulse amplification is the bandwidth of the gain medium. To understand the bandwidth requirements, the spectral components of short pulses must be understood. If a single frequency, UQ, electromagnetic wave is modulated with an envelope function, f(t), to produce a short pulse, £(t) = £0f(t)eluot. It can be shown that new frequencies are produced by looking at the Fourier transform, £{u) = £of{u — w o), where f(ui) is the Fourier transform of f(t). The shorter the pulse that must be amplified, the wider the bandwidth must be; the more narrow f(t) is the wider /(cv) must be. For pulses which have a Gaussian temporal profile, the bandwidth-pulse-duration relation is AvAt = 0.44. To find the bandwidth that can be supported by the C 0 2 system, we can start by examining the stimulated-transition rate.1 W21 is stimulated-transition rate between two levels, designated 1 and 2. SnhunHspont where S(u) is the lineshape function, I(u) is the intensity of the field at frequency v and tspont is the spontaneous lifetime. This can be related to a 1The stimulated-emission rate can be derived, either through the classical Einstein B coefficient [57, pg. 171] or through quantum-mechanical considerations [57, pg. 74]. The details of these derivations is not important for this work. 21 gain coefficient a(u) where the change in intensity with propagation distance, di/dz is a(u)I{u,z) = N2-^Nr W2i, (3.4) (3.5) where Ni and N2 are the densities of the respective states. Of course, if there is more than one possible transition at a given frequency, a summation over all possible transitions has to be made. Above a pressure of ~10 kPa, the C 0 2 spectrum is homogeneously broad-ened; that is, the molecules are indistinguishable and effects such as Doppler broadening become insignificant. At atmospheric pressures the lineshape is determined by the collision frequency. The lineshape is Lorentzian and given Here v>12 is the centre frequency of the transition of interest and AuP is the full width at half maximum of S. Increasing the gas pressure increases the collision frequency and there-fore increases the transition line width. It is used to merge the lines of the rotational spectrum so that a wide, continuous spectrum emerges. When this occurs, the spectrum is again better described as being inhomogeneous since the molecules are not indistinguishable; molecules in different rotational states have different transition frequencies and these rotational states can be accessed independently. This was first demonstrated by N . G. Basov et al. in 1971 [6] to take advantage of the higher power densities available due to the increased densities of excited molecules at higher pressures. He also was the first to realize that the pressure broadening of the gain spectrum could lead to the generation of picosecond pulses in C 0 2 . Also it should be noted that, early on, it was realized that the pressure broadening would be useful to build widely tunable C 0 2 oscillators or amplifiers [58]. The gain bandwidth, at 300 K , of a lasing transition is given by Aup = 56.9(ipco2 + 0.73^TV2 + 0.64t/>#e)P MHz where ip is the gas fraction, and P is the pressure in kPa [59]. The entire manifold of the R-branch or P-branch rotational transitions corresponding to a vibrational transition has a spectral width of (~1.5 p s ) - 1 . At low pressures, the spectrum comprises a number of by (3.6) 22 essentially discrete lines separated by ~55 GHz. At high pressures, the line width becomes comparable to the line separation and can then begin to be considered as being continuous. The equilibrium populations of the rotational lines can be easily cal-culated from the Maxwell-Boltzmann distribution function. For a linear molecule such as C 0 2 the distribution is usually written as where Nj is the population of a rotational level, N is the number of molecules, Q is the partition function, gj is the degeneracy, and F(j)hc is the energy of the level, g, = 2j + 1 and F(j) = B(j + 1) - Dj2(j + l ) 2 . B is known as the rotational constant [53, pg. 505]. D is much smaller than B and therefore the second term is often ignored. B and D change slightly with vibrational level; the values of B and D are tabulated in reference [21, pg. 23]. Population-density calculations for T = 400 K are made from equation 3.7 and shown in figure 3.2. A diagram of the energy levels involved in the regular-band transitions is shown in figure 3.3. The regular-band small-signal-gain spectrum, as calculated from equa-tions 3.3 to 3.6 and 3.7, is shown in figure 3.4 for three pressures. The gain spectrum becomes continuous as the pressure is increased. At 0.4 MPa, which is four-times-atmospheric pressure, the gain minimum between the peaks drops to approximately 15% of the peak value. However, at 1.2 MPa, which is the operational pressure for this experiment, the minimum is ap-proximately 75% of the peak value. The regular bands are not the only lasing transitions possible. The most common additional ones form the 'hot' bands (Ol 1!) —> (1110) and 'sequence' bands (00°^) (10(v3 - 1)) or (02°(i>3 - 1)) for v3 > 1. Usually the populations of these levels are assumed to be small. However, in discharge lasers when attempts are made to maximize gain, the gain from these other bands can become significant. This issue will be further discussed in section It should be briefly mentioned that some systems in operation use a mult i-isotopic mix in order to get a broad spectrum without resorting to pressures > 1 M P a [60, 52]. Adding molecules of 1 2 C 1 8 0 2 in addition to the usual C 1 6 0 2 will change the vibration frequencies to add additional lines to the spectrum. Adding molecules of 1 8 0 1 2 C 1 6 0 will also remove a symmetry and therefore (3.7) 3.4.2. 23 20 40 Rotational Transition (j) 60 Figure 3.2: Normalized population of the rotational-levels of the regular-band upper laser level (00° 1) thermally populated at T = 400 K 24 300 Relaxation Ground State (0 0 0) ^Ground State Figure 3.3: Important energy levels of the regular-band CO2-N2 laser system. The excitation of the long-lived asymmetric-stretch and N 2 modes is by electric discharge. The lower levels are quickly depopulated, in part due to the close resonance between the levels (I) and (II). • 25 Rotational Transition (j) Figure 3.4: C 0 2 small-signal-gain spectrum for the P-branch transition of (00°1) -> (I): (a) 0.4 MPa, (b) 0.8 MPa, (c) 1.2 MPa. 2G odd-j transitions will be seen as well as the slightly different frequencies due to the different masses. 3.4 Modelling the CO2 system In order to simultaneously model the intensity of the pulse and the popula-tions of the laser levels we must keep track of not just those levels directly involved in the laser transition, but also all the levels that have significant populations. The higher levels of the three primary vibrational modes and the N 2 level can store significant energy which is rapidly redistributed to those levels which are directly involved. To obviate the need to track the popu-lations of each of these levels individually, it is convenient to approximate each of the populations with the Boltzmann distribution which is specified by a thermodynamic temperature. This is the first approximation that will be made and is known as the five-temperature model [61, 62, 63]. 3.4.1 Five-temperature model In this model, each vibrational mode is assigned a thermodynamic temper-ature which determines an assumed Boltzmann distribution. The labelling scheme is the same as for the vibrations; therefore Ti corresponds to the symmetric stretch, T 2 the bend, and T 3 the asymmetric stretch. Similarly, the N 2 molecule is assigned T 4 and the rotational levels, which efficiently exchange energy with translation, are assigned the same temperature (T) as the gas. This approximation is possible because of the low relaxation rates between the C 0 2 vibrational modes and with the other gas species, relative to that within modes. For a 1.2-MPa 3:3:94::C0 2:N 2:He system, the in-tramode relaxation time is approximately 15 ps [21]; whereas the intermode relaxation times are all larger than a nanosecond. This means that the rate of collisional redistribution amongst molecules sharing the same mode is suf-ficient that their populations will rapidly equilibrate and can therefore be accurately described by a thermodynamic temperature. The time to reach equilibrium for molecules with differing modes is much longer such that such a distribution will only be established after hundreds of nanoseconds. The energy relaxation rates can be specified, in general, by dEa E(Ta)-E(Ta,) (3.8) dt a' 27 where the transfer is from the mode a to a', r is the rate constant and E(T) is the mode energy calculated for that particular temperature. The raai values are temperature dependent. For r 2 (a' is the ground state) the temperature dependence can be described as ,rp . 1/2 r cx ( ^ J exp [ A E (1/ftT - 1/fcTo)]. ' (3.9) where T 0 = 300.K" and AE is the energy difference of the transition. For r 2 i and r 4 3 , (3.10) The relaxation rates at room temperature are r 4 3 = 185 ns, r2o = 35.4 ns, Ti2 = 2.47 ns, and r 3 = 2.7 fjs [63]. While the relevant temperatures are often calculated from a knowledge of the detailed time evolution of the discharge parameters, in this study the phenomena of interest take place long after the current through the gas is finished. Therefore, the initial temperatures can be assumed and fits done to the real data. The initial temperatures can then be checked for consistency with knowledge of the mode-excitation efficiencies. This shall be discussed in more detail in section 6.2.1. 3.4.2 Hot and sequence bands Now that vibrational temperatures have been defined, the populations of the levels responsible for the hot and sequence bands can be calculated. Given that in lasing mixes, the gain is increased by increasing T 3 while keeping Ti and T 2 low, T3 values of ~ 3000 K are desirable and fairly com-mon. At these temperatures, the hot- and sequence-band gains can become significant. The population of the 'mixed' levels can be calculated by NCo2 f-vihujA (-v2hu2\ f-v3hui3\ N m = -Q- exp j (v2 + 1) exp j exp j . (3.11) Most calculations have been of the small-signal gain of these transitions and assume that the lower levels are completely unpopulated and do not take into account any saturation effects. It is difficult to incorporate these bands into a short-pulse temperature model because it is unclear how the relaxation of the lower level to the states involved in the regular band affects 28 the gain of the regular band. This issue is not resolved from a survey of the literature [29, 64, 65, 66, 67, 68, 69]. In addition to increasing the small-signal gain of the CO2 laser, the hot and sequence bands make the spectrum smoother since their transition fre-quencies are offset from those of the regular bands. This is discussed further in section 6.4.1. 3.5 Short—pulse amplification To model the short-pulse amplification, we would like to calculate the pulse parameters after each round trip rather than recalculating the parameters at a large number of points within the gain medium. A procedure to accomplish this will be developed in this section. In modelling this system, consideration must be made of the change to the laser-level populations by spontaneous and stimulated emission and by collisional population changes. With short pulses, the modelling of the level dynamics can be considerably simplified if the laser-level collisional repop-ulation is insignificant on the time scale of the pulse. For a CO2 laser this assumption can be made if the product of the pulse duration and pressure is less than 5 x IG 1 - 5 Pa [21, pg. 270]. At the 1.2 MPa operational pressure of the amplifier under consideration, this condition is satisfied if the pulse length is less than 400 ps; this condition is easily met. However, the colli-sional repopulation will have to be considered when the pulse passes through the gain medium more than once. Under these conditions, the system can be modelled by two levels. The system under consideration is really more like a manifold of independent (in-homogeneously broadened) two-level systems. A modification to this simpler theory will be made in the following section. The levels in this model are also considered to be infinitely narrow. This obviates the need to integrate over wavelength. This is a reasonable assump-tion because we are mainly concerned with saturation effects. Therefore, once accounting for level populations is done, then shape of the gain spectrum can be calculated. A further simplification can be made by considering the beam and gain profiles to be uniform in the transverse direction which leads to a one-dimensional model. This basic analysis was first done by L. M . Frantz and 29 J . S. Nodvik [70]. In such a system, the governing equations are (9/ dt 9 1 T c— = cap! ox (3.12) and dp l i (3.13) where I is the intensity, p is the difference in densities of the upper and lower states, which is also known as the inversion, and a is the stimulated-emission cross section which can be calculated from equation 3.3. Of great interest in this work is the effect of gain saturation on the pulse energy. After passing through a gain medium of length L , with small- signal gain a 0 = °~Po, where p 0 is the inversion as the pulse enters the cavity, the ratio of the output fluence, E ^ , to the saturation fluence, E s = hu/2a, can be found by solving the previous two equations. It can be seen that if E 0 <C E s and a^L -C 1 then EL/ES tends to exp(aoL). Note that fluence is the time-integrated intensity. Qualitatively these equations describe the effects of depletion of the pop-ulation inversion. Because this is a two-level system, atoms in the upper level that have been stimulated to emit a photon will be transferred to the lower level where they are available for absorption. Intense pulses will trans-fer enough atoms to the lower level that the gain will change significantly during their passage. When the leading edge of a pulse experiences more gain than the trailing-edge distortion of the pulse shape will occur. If this were the only effect, the pulse would generally become shorter. However, pulses cannot become arbitrarily short as they are constrained by the gain bandwidth. 3.5.1 Accounting for redistributions While the Frantz-Nodvik equations adequately account for very short pulses at time scales shorter than relaxation times, the equations can be adapted to more complex situations where the system is not a single two-level system but a series of them and also a situation where the pulse passes through the EL ln[l + eaoL(eEo/E° - 1)]. (3.14) 30 gain medium a number of times with the time in between passages longer than energy redistribution times. If the pulse is short enough that the corresponding spectrum is wide enough to straddle several gain transitions, equations 3.12 to 3.14 still apply; however, the pulse must be spectrally partitioned and the equations applied to each level then a summation made. In multipass and regenerative amplifiers, the pulse being amplified passes through the gain medium more than once. Therefore, the equations also apply for each transition through the medium but before the pulse enters the medium on each successive round trip, the a0 and E0 terms have to be recalculated using equation 3.8 with the appropriate relaxation times and taking into account the optical losses due to the elements in the amplifier cavity. The computer program used to calculate the amplification will be dis-cussed in chapter 6. 3.5.2 Coherent effects in pulse amplification One of the more interesting effects seen with short-pulse amplification in a CO2 medium is the formation of a train of pulses following the initial pulses at intervals of 18 ps. From the perspective of the E M wave, the presence of resonant transitions in the gain medium leads to frequency dependent phase changes which then lead to energy from the initial pulse being transferred to a train of pulses separated by the 1/(55 GHz) = 18 ps separation between the rotational transitions. Another way of thinking of this is that the electric field of the short pulse excites the molecular polarizations which then oscillate at their resonance frequencies. These will then form beating modes which produce trailing pulses at the inverse of the difference frequencies. The magnitude of the gain calculated by equation 3.5 is correct but must be modified by imaginary terms. Whereas the real part of the gain could be derived from classical physics following the Einstein derivation mentioned in section 3.3, this problem requires a semi-classical approach.2 We start by again considering a two-level system with energy levels Ei and E2 and a resonant frequency huj0 = E2-E1. (3.15) 2This derivation largely follows those of A. Yariv [57] and R. W. Boyd [71] 31 We will be using the interaction picture where the Hamiltonian, H = H° + H1 is divided into a part, H°, for which the solution is known and with eigenvalues E\ and E2, and a perturbation H1 which modifies the eigenfunc-tions of the solution. Here H1 = -p£(t), (3.16) where fj, is the dipole operator, r n „ 1 (3.17) 0 / i n 0 The objective here is to find the induced polarization and therefore sus-ceptibility caused by the electric field. This will be done by finding the ensemble average through use of the density operator, p? (fj)=Tr(pix) = fi{p12 + P2i). (3.18) The polarization is given by P = N(tx), (3.19) where N is the density of atoms. The density operator obeys the commutation relationship, | 4 [ P , H ] . (3.20) We can now identify the elements of the density matrix: iJi = iJt = -s[("° + "') ,P] (3.2i) = - ^ [ ( f f 2 i ( P n - P 2 2 ) + ( £ 2 - £ i W ] . (3.22) Using equations 3.15 and 3.16, we get = -iuj0p2i + ij^£(t)(pn - P22) (3.23) 3More detail on this technique can be found in the references [72, pg. 331], [2, pg. 104], and [57]. 32 and ^ - = -i^£(t)(P21-p*21). (3.24) Since the occupation of the upper and lower levels must sum to one, (pn + P22) = 1, j t (pii - P22) = 2i^£{t) (p21 - p*21). (3.25) The polarization term in equation 3.23 oscillates with frequency coo with no applied field. Therefore it is this term which leads to the beating modes when these polarizations are excited. These equations need to be modified to account for population changes due to collisions. There are two types of collisions which are important. Firstly there are the phase-changing collisions which have the effect of broad-ening the laser transition; this is characterised by the time T2. Also, r is the characteristic time of the population-inversion decay rate. Equation 3.23 then becomes = -iu0p21 + ijr£(t)(pu - p22) - jf-, (3.26) and equation 3.25 becomes d ( n n \ o , - ^ p ^ w „ n* \ (Pn ~ P22) - (pn - P22)rj , o 0 7 A -jt (P11 - P22) = 2i-£{t) (p2l - p 2 1) , (3.27) where N(pn — p22)o is the equilibrium inversion. As noted previously, the solutions are dominated by terms oscillating at ±u>o. Therefore, we would like to consider solutions which oscillate near this frequency and exclude terms which are far from the resonance and which do not contribute when time averaged. These terms can be simplified by introducing a frequency cu w coo- Since we are interested in resonance effects between the system and the incident electric field, we shall introduce an electric field which oscillates at this frequency: 5(t) = ^(e i w * + e- < w t). (3.28) It will also be useful to introduce a''precession' frequency: f2 = p£§J2h~. Since P21 and P12 are expected to oscillate near —LO and co respectively, and the 33 population inversion only decays slowly with time, to solve these equations making a steady-state approximation, it is useful to introduce new variables cr21 = a*12 = p21eiut. (3.29) Substituting this and equation 3.28 into 3.26, we get ^ = - io2i (w - uQ) + ij~{t){pxi - P22) - j r , (3.30) where we have neglected the rapidly oscillating e2luJt term obtained when multiplying both sides by elut. Similarly, equation 3.27 becomes d, v p£(t) , (pn - P22) - (pii - £22)0 , „ _ n v j t (P11 - P22) = 2 % f t — ^ 2 1 ~ a2i) • ( 3- 3 1) Since we are looking for a steady-state solution, we can set 3.30 and 3.31 to be zero. Doing so leads to, ( \ ( \ 1 + (w - w 0 ) 2 T 2 (Pll - P22) = (Pll - P22)07—7 \2T2 , AC,2rr (3>32^ 1 + (ui — uio) i 2 + A\V12T And using equations 3.18 and 3.19, n _ y2AN0T2 c ( smut + (LJ0-UJ)T2 cosut\ , . r ~ h t 0 [l + (co0 - cu)*T2 + 4WT2r) > ^ j where AATo = N(pu — p22)o which is the zero field population difference. The definition of the electric displacement vector is D = e0£ + P = e(cu)£. It is desirable to split e(u>) into e, a frequency-independent component, and a field-induced component which can be written with the susceptibility. D 1 + (3.34) Therefore, the polarization can be identified as P = eoX(cu)£. (3.35) From equation 3.33, the terms of the susceptibility, X = x' ~ ?x" c a n be found: , = p,2AN0T2 (u0 - u)T2 X e0h 1 + (coQ - u)2T2 + 4Q2T2T [ } = »2AN0T2 1 X e0h 1 + (UJ0-OJ)2TZ + 4WT2T' { ' 34 The 4tt2T2T term in the denominator leads to saturation effects. Without this term, %' and x" can be compared to equation 3.6, which is the Lorentzian lineshape function. The linewidth AuP of equation 3.6 is related to T2 by (T2 AuP) = 1/TT. 4 To see how this affects the propagating wave, we can identify the wavenum-ber k(u>) = OJ\Jixe(uo) =>k(uj) « + (3-38) where k = LOyTjIe. An E M wave will propagate through the medium as £ = £0e%(-ut~k((VW. Obviously, the real part of the exponent represents the gain and the imaginary part is the phase. The small-signal gain, a0 can be identified as -kLe0 „ . . a0 = x • (3-39) e This is a useful quantity since the total amount of unsaturated gain in the medium is usually quoted as a0L and this is the same quantity that was used in equation 3.14. We are interested in calculating a transfer function, g(oo), where £ L(CO>) = g(uj)£t)(uj) and £Q(OJ) and £ L ( C < J ) are the fields at z = 0 and L respectively. We can then identify g(co) = e x p { - i H , [ l + - ix")}}- (3.40) However, the situation is a bit more complex than this. We are dealing with a manifold of transitions. The real susceptibilities have to be summed over all of these weighted by the factor calculated by equation 3.7. This has been done, neglecting saturation. The procedure used was to take an input pulse, here assumed to be a 3-ps (FWHM) Gaussian for con-venience, take the Fourier transform to find £( n , then to multiply this by g(co) for various lengths. The lower level was assumed to be unpopulated and the electric field is low enough for the gain to be unsaturated. The re-sults are shown in figure 3.5. It can be clearly seen that the resonant gain spectrum quickly leads to a trailing pulse train which continues to increase in amplitude. The ratios of the peak values are tabulated in Table 3.1. 4The equations obtained in this section are very similar to the Bloch equations of magnetic resonance. The similarity is discussed by A. Yariv [57]. 35 Time (ps) Figure 3.5: Pulse-train evolution after transmission through the resonant gain medium, neglecting saturation, (a) injected pulse, (b) a0L = 1, (c) a0L = 2, (d) aoL = 5, and (e) a0L — 10. arj is taken to be the maximum value. Pressure is 1.24 MPa, S7 —> 0, and T = 400 K . 36 a0L h/h h/h 0 oo -1 8.43 7.96 2 4.22 5.41 5 1.68 2.75 10 0.84 1.51 Table 3.1: Ratios of peak intensities in pulse train for various values of a0L assuming no saturation effects. The main pulse is labelled 0. It is interesting to note that without the imaginary part of the suscep-tibility, this formulism leads to a completely symmetric pulse train, with pulses preceding and following the central pulse. Since this pulse travels at nearly the speed of light, such a result is clearly non-physical; however, the total amplification is the same for both methods. This is very important when considering the Frantz-Nodvik equations (3.12 to 3.14): the calculated energies will be correct but the pulse shapes will not be. Therefore for cal-culations where only the total gain is important such as in calculations of the energy-level redistributions discussed in the previous section, the more complicated calculations mentioned here are not necessary. Only when one is interested in calculating the relative energies of pulses in the pulse train or the pulse shapes would the calculations discussed in this chapter become necessary. Using the approach here, the saturation was ignored; to take it into ac-count greatly complicates the solutions. It is then no longer possible to integrate a solution on a round-trip basis. It is then necessary to numeri-cally solve Maxwell's equations and the density-matrix equations throughout the gain medium. This is beyond the scope of this work. However, similar calculations have been performed by V . T. Platonenko and V . D. Taranukhin [73]. They simultaneously found solutions to differential equations represent-ing Maxwell's equations, equations 3.26, and 3.27 for short pulses propagat-ing in CO2 media up to 1.0 MPa. Of most interest for comparison to these results were their results of amplification of 3-ps pulses. They found that at a0L = 10 the first trailing pulse was approximately half the height of the main pulse. However, after that, the relative energy of the first trailing pulse started to decrease until it nearly disappeared at aoL = 30. Their results indicated that the pulses increased until the saturation regime was entered. 37 In this regime, the trailing pulses would be absorbed. They also showed that the length of the initial pulse did not significantly increase in length. Their calculations did not take into account any energy-level redistribution or non-regular-band transitions. However, the inclusion of these should not change the qualitative results. The apparent decrease of trailing pulses in the train has also been described for an experiment [41]. Therefore, these more exact calculations largely agree with the calcula-tions which lead to figure 3.5 in the unsaturated regime. 38 Chapter 4 Ultrafast semiconductor—switching materials 4.1 Introduction Semiconductor switching is the use of optically-induced, transient, metal-like electron-hole plasmas in semiconductors to convert the material from being transparent, at mid-infrared wavelengths, to being temporarily reflective. Most semiconductors are essentially transparent in the mid-infrared due to their electronic-band structure. Radiation in this wavelength region has photon energies below the bandgap energy and thereby avoids absorption caused by the production of electron-hole pairs. Most of the interaction of an optical beam with the semiconductor is through free carriers which are generated either thermally or optically. At low densities, these effects in-clude free-carrier, interband, and impurity absorption. For our study, the interband- and impurity-absorption mechanisms should be unimportant be-cause we are dealing with semi-insulating semiconductors and therefore the number of available states should be small. For alloy semiconductors with a permanent dipole moment such as GaAs, it is possible for mid-infrared radiation to also excite phonons through cou-pling with the electric field. For GaAs this occurs at wavelengths longer than those of the the CO2 regular bands. However, it is possible for a second or-der effect to occur such that an EM-field-induced dipole moment will lead 39 to lattice excitations in homogeneous semiconductors such as silicon [74]. However, this is a small effect for thin wafers. At higher densities, collective effects become important. The calculation of the reflectivity and absorption due to an excitation of carriers can be treated as a change in the dielectric permittivity of the semiconductor. When the real part of the dielectric permittivity approaches zero, the material will become reflective. The carrier density corresponding to this transition is known as the critical density. The excitation of the switch can take place on time scales as fast as or faster than the laser pump pulse: ~250 fs. The speed of the switch is governed by the duration of the transient, dense, electron-hole plasma which is determined by the speed of the carrier recombination and therefore by the choice of switch material. Intrinsic semiconductors all have recombination times in the picosecond to nanosecond scale for low levels of excitation. However, the introduction of impurities and defects which act as recombination centres can speed up the recombination process. This chapter will first detail the processes of carrier excitation and re-combination, then outline the electro-magnetic theory of reflection from a semiconductor plasma, and discuss our experimental findings for semicon-ductor plasma-reflection in various materials. 4.2 Carrier excitation and recombination In the semiconductor materials we have used, the primary excitation mech-anism is a direct absorption of above-bandgap-energy photons by electrons in the valance band. This promotes the electrons to states with nearly the same k value in the conduction band. As the photon energy is above the minimum bandgap energy, hot electrons are produced. These rapidly de-cay [75] through phonon emission to the bottom of the band. This effect is essentially instantaneous. Of course absorption-depth effects have to be taken into account as well. The depth profile of the e-h concentration can be assumed to be e~Sz where 8'1 is the absorption depth. Once the reflective plasma is created, various effects determine the decay of the plasma density and thereby the switch-off time of the switch. Firstly, there are many decay mechanisms. The most important are direct recom-bination, Auger recombination, surface recombination, and defect trapping. Secondly, diffusion plays an important role in reducing the carrier density. Typically, the injected plasma has a maximum density of 5 to 50 times 40 the critical density. The carrier density cannot be arbitrarily increased as at some point surface damage through melting will occur. Direct recombination, that is, the radiative two-body recombination of electrons and holes such that k is preserved, is proportional to the product of the carrier densities. This is limited by the relatively low number of carriers in the appropriate k states. Auger recombination is a three-body effect. A n electron and hole will recombine but the energy and momentum are conserved by transfer to an additional electron (or hole). This effect is, of course, proportional to the product of densities of the three species involved (two being the same). This effect can be radiative or not. Since the injected-carrier density is much higher than any dopant density, the carrier concentrations can all be taken to be equal for modelling. Surface recombination involves the discontinuity at the surface of the semiconductor. The band structure is interrupted in such a way that elec-trons and holes can rapidly recombine in a non-radiative manner. Similar to this is recombination at imperfections in the lattice. Recombinations at imperfections is especially important for this work since this can be largely controlled by density and type of imperfections introduced into a lattice. 4.3 Modelling a semiconductor switch The first part to modelling the semiconductor switch is to model the reflection as a function of density. The second is to model the density due to pump-pulse excitation and decay due to recombination and diffusion. Modelling semiconductor switches can be quite complicated. Models could take into account the non-uniformity in CO2 and pump beams, the detailed variations of carrier density with depth, the different types of carrier-recombination mechanisms, and discontinuities that arise out of the Maxwell equations. We will start with a simple thin-film model of a semiconductor switch. The switch will be assumed to be at Brewster's angle with respect to the CO2 beam and the electron-hole plasma will be assumed to be of uniform distribution in a layer the thickness of the inverse absorption depth of the pump beam. Figure 4.1 shows the basic details. The beam enters the thin plasma slab at the bulk Brewster angle (#1), the beam then passes through to the bulk semiconductor: marked 3 in the diagram. The dielectric permittivity, e, is 41 described by 1 ,z < 0 e(cu) = { e 6 (l - n/n c(w)) , 0 < z < r (4.1) e6 , z > r where is the bulk static dielectric function, n is the effective plasma density, nc(io) is the critical plasma density as a function of the light frequency, defined as uj2m*e/q2 and r is the thin-film thickness. The form of the density-dependent dielectric function will be discussed in the following section. The reflected field is the summation of many components. The electric-field reflection of the wave going from 1 to 2 shall be denoted r 1 2 and that of the wave travelling from 2 to 1 shall be denoted r 2 i . Similar notation shall be adopted for the transmission: t i 2 and t 2 i respectively. Given a wave of the form Ei = £ 0expi(u;£ — kx), £r/£i, which is the ratio of the reflected wave to the incident wave, is the sum of an infinite series of terms. To calculate £r/£i knowledge of all the reflected amplitudes and phases is needed. Two distances determine the relative phase, one, the distance the ray passes between entering the plasma and leaving, and the second, the distance that the first reflected ray must pass to reach a point perpendicular to the exiting second round trip. Let the first distance be A s i and the second A s 2 - Let j3 be A;(Asi — A s 2 ) . Therefore, if each successive term in the summation is an additional reflection, Sr/£i = ra + h2r23t21eip + t12r223r21t21e2i? + t12r323r22le3^ + ... (4.2) Using the equation that S^Lo 3 -" = V ( l — x) 1 0 1 \x\ < 1) — = f l 2 + TT— JgT. (4.3) £i r21 (1 + ri2r23elP) From the form of the Fresnel equations, we know that ti2t2i + r 1 2 r 2 1 = 1 and also that r 2 i = — r i 2 . This equation then becomes £r r 1 2 + r a 3 e* ( 4 4 ) £% 1 + r12r23ei0' Also from the Fresnel equation for reflection of an electric field polarized in the plane of the surface normal and the wave vector, the first reflection is cos 62 — A / C ^ I — n/n c ) cos 9i ri2 = i • (4.5) cos#2 -(- Je^l — n/nc) cost^ 42 Figure 4.1: Illustration of the thin-film-model parameters. The thin film is defined by the absorption depth, The total reflection from the film is determined by the summation of the electric field amplitudes and phases. The amplitudes can be calculated using the Fresnel equations. 43 Using the Brewster's angle condition, tan(n t/n;) = ##, Snell's Law and a trigonometric identity, (1 -n/nc){l + eb) (4.6) (4.7) (4.8) Which gives, y/Fb{l - n/nc)~ Jeb(l - n/nc) - n/nc rii = , = (4.9) V ^ l - n/nc) + yjeb(l - n/nc) - n/nc and r 2 3 = - r 1 2 (4.10) Using equations 4.4 and 4.9, the reflectivity of the thin film can be easily calculated. Figure 4.2 shows the reflectivity as a function of the ratio of the carrier density to the critical density for the case of a C 0 2 beam at 10.6 /im, a GaAs switch, and 616 nm excitation radiation. The graph shows that there is a very narrow reflectivity peak at n/nc = 1 and a steadily-rising reflectivity after that. The peak has a full width at half maximum of only 0.04. This simple model agrees well with other more complicated models [76]. For instance, if instead of a single layer, the plasma volume it taken to be a stack of such layers, the result is more realistic but very similar, ne difference is that the peak at n/nc = 1 is not as high. 4.3.1 Refractive index as a function of carrier density For our purposes, the basic properties of the semiconductor switch are ade-quately modelled by the Drude theory [77] which was developed to discuss conductivity and reflectivity in metals. In this theory, collisions between free carriers and the lattice are treated as instantaneous events and the probabil-ity of collisions is considered to be equal for all carriers. 44 1.0 0.8 0.6 h •2 0.4 0.2 0.0 0 2 4 6 8 Carrier density/critical density 10 Figure 4.2: Calculated reflection from a uniform thin plasma as a function of carrier density. The reflection behaviour of a switch can be approximated knowing that a carrier density will be photo-injected into the switch. Know-ing that the density will monotonically decay, the reflectivity trace can be estimated by following the curve to the origin from the position determined from the injected intensity. This curve is calculated using parameters match-ing a 616-nm wavelength pump pulse incident on GaAs 45 The relevant equation of motion, for a free carrier driven by an electric field E and with a collisional-damping term, written in velocity terms, is qE v = m* —, (4.11) rc dt where r c is the mean collision time and m* is the effective mass. Making a harmonic approximation: dv/dt — icov. This is easily solved as <S <1—LY\ (4.12) This is of interest because, the current density, J = aE = nqv, (4.13) where n is the carrier density. In order to find the frequency-dependent dielectric permittivity, e(u), it is necessary to examine Maxwell's equations. With a harmonic approximation, the relevant equations become: V x E = -iuB (4.14) VxH = J + itoD. (4.15) Using J = oE and the electric displacement, D = eE, where e is the static permittivity, then V x f f = iue (l - E. (4.16) We would like to include the term in parentheses in a frequency dependent permittivity, e(W) = e ( l - ^) . (4.17) Inserting equations 4.12 and 4.13, e(w) = e where C0Z \ LIT, (4.18) = — (4-19) 2 46 defines the plasma frequency. Using the critical density defined with equation It can be seen that the imaginary component can be ignored to give equation 4.1 when OJTC 1. This is not strictly true but the results of the modelling of the previous section are not significantly changed. 4.4 Experimental investigation of switch ma-terials It is known that the carrier recombination times of intrinsic and doped semi-conductors is quite long [74]. GaAs, one of the best semiconductors for switching, reliably produces pulses ~25 ps long [78]. This is not short enough to match the full bandwidth created by pressure broadening the CO2 gain medium. While placing a number of semiconductor switches in series can produce shorter pulses, this greatly increases the complexity of the injection arrangement. Therefore, we invested considerable effort to pro-duce and study 'engineered' semiconductors such as low-temperature-grown GaAs (LT-GaAs), radiation-damaged GaAs (RD-GaAs), and a superlattice of GaAs and In. 8 5 Ga . i 5 As in addition to the silicon and GaAs switches which were also used in this experiment. These materials were investigated using cross correlation which is illus-trated in figure 4.3. GaAs was also investigated by reflection-reflection cor-relation; those results are not relevant for this study and therefore will not be discussed here. Cross correlation involves the use of two switches. The first is oriented at Brewster's angle in the C W - C 0 2 beam. The pump beam is split in two: the first is directly incident on the first switch and the second passes through a variable-delay line before being directed onto the second switch. The energy reaching the detector is dependent on the time delay of the pump pulse on the second switch. At zero delay, where the delay path length is equal to the pulse path length, no energy should get through. I(T) OC / 0 ° ° I(t)T(t + r)dt where I(t) is the intensity of the pulse reflected from the first switch and T is the transmission of the second switch. The results from this are complimentary to autocorrelation since a much better idea of the actual pulse shape can be found. Another advantage of cross 4.1 (4.20) 47 From CO 2 . \ " ' " " " | , : - - T o r r g y meter ^ Detector SW#2 Transmission SW#1 Reflection Figure 4.3: Reflection-transmission cross correlation set-up. The energy-measured by the detector is measured as a function of the delay between the pump pulses to the two switches. The actual pulse shape can be inferred by differentiating the resultant function. correlation is that it can be performed with much lower pulse energies than is possible for autocorrelation. 4.4.1 GaAs switching characteristics GaAs was studied in detail both experimentally and by modelling [78]. The results will be briefly reviewed in this section. GaAs is a direct-bandgap ma-terial with a bandgap energy of 1.4 eV. The excitation pulses have a photon energy of 2.0 eV. At this energy, electrons are excited into the conduction band only in the T (|A;| near zero) valley. Silicon was used as the gating switch as the cutoff time has been found to be as short as 0.24 ps with a 0.49-fs pump pulse [79]. From a graph of the total energy reflected as a function of the pump-pulse energy (figure 4.4), much useful information was derived. Firstly the orange (616 nm) energy measured with a photodetector was correlated to the carrier density in the material. This was done by fitting a line to the linear portion of the curve (that below / = /yF/(hu>nc) = 4). The energy absorbed in the switch is 7 F 1 since F is the pump-pulse fluence which is 48 absorbed in the depth 7 - 1 (assuming uniform beam intensity). The fluence is defined as total absorbed pulse energy area density. Assuming a unit quantum efficiency, / is the multiple of the critical density induced by the pump pulse. Figure 4.2 suggests that there will be a sharp onset of the pulse when the critical density is reached. Where this fit line crosses the abscissa of figure 4.4 is where critical density is reached. Such a measurement was performed before every run of the experiment such that the density could be accurately calibrated. Cross-correlation measurements were made for various pump-beam in-tensities. Some of these are shown in figure 4.5. Figure 4.6 shows the pulse shape derived by differentiating the data from figure 4.5. One can predict the pulse behaviour of a real switch by examining the modelling results described in figure 4.2. A fast pump pulse will mean that the reflectivity will be rapidly determined by / , the normalized density of photo-injected carriers, on the abscissa. The carrier density will then mono-tonically decay. Therefore, the predicted reflectivity can be determined by following the curve backwards to the zero density point while tracing the reflectivity on the ordinate. One would therefore expect the pulse reflected from the switch to show a sudden onset, to decay until the density approaches one, then to show a sudden spike before disappearing. Indeed this is what is seen. Figure 4.6 shows this. The / = 3 and 15 values correspond most closely to the values that are used in the amplification experiment. As there is very little difference between the two (on the normalized scale) all the results for / between these two values should be approximately the same. The pulse shows a large increase in reflectivity which lasts for 3 ps followed by a drop to less than half the peak value. There is a local minimum 15 ps after the start of the pulse. Then the reflected intensity increases to about 70% of the initial peak value before decreasing to zero at +25 ps from the beginning of the pulse. tc can be defined as the time it takes for the excited density to decay to the critical density. It can be identified on the graph (4.6) as the time from the initial peak to the second peak. Information on the diffusion rates and recombination mechanisms and rates could be obtained from these graphs. Previous results show that surface-recombination rates are small compared to diffusion and Auger re-combination. Assuming that the diffusion and Auger co-efficients are D = 20 cm 2 /s [80] and A = (7 ± 4 ) x 10" 3 1 cm 6 /s [81] respectively, above the critical density, diffusion should dominate. Therefore it shall be initially assumed 49 Figure 4.4: Reflected intensity as a function of pump-beam fluence for a single GaAs switch. / = ^F/(hionc) is the injected density normalized to the critical density. / = 1 can be found by fitting a line to the data in the linear range (/ < 4 here); where the line crosses the abscissa is the critical density. 50 Figure 4.5: Sample cross-correlation signal for GaAs. Due to the long re-sponse time of the detector, this is the total (integrated) pulse energy as a function of the cross-correlator delay, r. Empty circles are / = 3; solid circles are / = 15. 51 Time (ps) Figure 4.6: Differentiated cross-correlation signal for GaAs which shows the actual pulse shape. The dashed line is / = 2; the dash-dot line is /=3; and the solid line is / = 15. 52 that diffusion alone explains the behaviour [82, 83]. By assuming that the density profile rapidly begins to resemble a Gaussian curve with depth, a calculation can be made of the time, tc, needed to reach critical density after the pulse is injected [78]: Knowing that for 3 < / < 15 the time-averaged reflectivity, (R), is approximately constant, one would expect the curve to resemble (R)tc and therefore have a f2 dependence. It does not. The other possibility is to look at Auger recombination. From A, given above, the critical time would be expected to be This process is too slow to explain the results and an additional fast recom-bination mechanism is required. Therefore, while there is a short pulse at the beginning, the whole pulse is at least 25 ps in length. To model this, it is necessary to invoke a recom-bination rate of T = 1.9 x 10" 2 8 cm 6/s. Using this rate and modelling the system as a stack of thin plasma films, the switch behaviour as seen in figure 4.6 was adequately modelled. As this modelling is not very relevant to this study, details will not be reproduced here. 4.4.2 Silicon switching characteristics Silicon has been studied extensively for its use as a transmission-cutoff switch [79]. It is ideal for this because its reflectivity risetime is relatively fast and, at hundreds of nanoseconds, the duration of the reflectivity is very much longer than that of the other materials investigated. Of course part of the reason for this is that silicon is an indirect-bandgap semiconductor and therefore the components of the electron-hole plasma will not directly recombine. Furthermore, the absorption depth of the 616-nm pump beam is a relatively large 3 //m. Therefore, the switching efficiency should also be relatively large. The results of the work on silicon [79] can be summarized as follows: 1. The switch-cutoff time can be very short: on the order of the pump-pulse duration. t c = 6 . 1 7 ( / 2 - l ) p s . (4.21) tc = 1 4 ( l - / - 2 ) n s . (4.22) 53 2. The critical plasma density of n-type material was found to be larger than that for p-type material: n c(n-type) = (1.7 ± 0.5)nc(p-type). 3. The slope of reflection as a function of absorbed pump radiation was steeper for p-type material than for n-type material. For these reasons and the fact that free-carrier absorption is lower in p-type material than n-type, p-type silicon should make a better semiconductor switch than n-type. However, there was some concern that some short-pulse effects such as those which make p-type germanium a saturable absorber led us to try both n - and p-type silicon; no difference was seen between the two when used as an intra-cavity elements. 4.4.3 Radiation-damaged GaAs Radiation-damaged GaAs has also been used as an ultrafast switch [34, 76]. It is a particularly attractive material because the length of the pulse has been found to be somewhat adjustable through variations in the dosage. The material we used was created by irradiating GaAs wafers with 180-keV protons at dosages of 10 1 2 , 10 1 4, and 10 1 6 c m - 2 . In characterizing this material, it was found that the damage was confined to a depth of ~3 pm for the 10 1 4 and 1 0 1 6 - c m - 2 samples. This was adequate for our purposes as the absorption depth of the 616-nm pump beam was only ~0.2 /zm. A concern when introducing damage such as this to a semi-conductor is that the semiconducting properties may change. To investigate this, ellipsometric measurements were performed to infer the dielectric func-tion: only very small changes were found. However, one significant change was that the fraction of the C W beam that was reflected at Brewster's angle increased to ~0.2% from ~0.1%. Measurements of the pulse duration were done through the cross-correl-ation technique. An excitation of ~ 2 x l 0 1 9 c m - 3 was induced by the pump beam. Figure 4.7 shows the results for the three different samples. It can be seen that pulse width decreases with a slope of -0.4 on the logarithmically-scaled graph. If the damage mechanism were linear, one would expect a slope of -1. The most likely explanation for the slope seen is that there is some saturation inherent to the damage mechanism. However, it can be seen that pulses as short as (600±200) fs are produced by the 1 0 1 6 - c m - 2 material. It is not known if even shorter pulses could be 54 H + Dosage (cm 2) Figure 4.7: Pulse widths for different H + dosages in GaAs. produced as the measurements are limited by the duration of the ~500-fs pump pulses. 4.4.4 Low—temperature-grown GaAs and In.85Ga.15As/GaAs superlattice Experiments were also performed on low-temperature-grown GaAs (LT-GaAs) and a In .85Ga.15As /GaAs superlattice: both epitaxially grown on GaAs substrates. These experiments will be briefly discussed but mainly to discuss why these materials were not used even though they are capable of producing ultrashort pulses. Both these techniques are just additional methods of introducing a high density of recombination centres into the ma-terials. The LT-GaAs was grown by molecular-beam epitaxy on a semi-insulat-ing-GaAs substrate. First a 2-/j,m GaAs buffer layer was grown at the stan-dard temperature of 600°C. Next the temperature was ramped down to 320°C in six minutes while a further 100 nm of GaAs was grown. At this point, the AS2 to Ga flux ratio was increased to 3:1 while 200 nm was grown at this low 55 temperature. The sample was then annealed for 6 min at 550°C in an As 2 flux. The result of this was to promote the formation of ~200-nm arsenic precipitates in the material which acted as effective recombination centres. From the sample cross-correlation signal of figure 4.8 it can be seen that the pulse width is ~1 ps. However, there is also a long tail at the end of the pulse which makes makes this material somewhat unsuitable for short-pulse semiconductor switching. Since the low-temperature-grown layer is only approximately as thick as the absorption depth, some of the reflective e-h plasma must be injected into the regular GaAs substrate which has a much longer recombination time. The plasma in the substrate explains the longer recombination time. The superlattice consisted of 20 layers of alternating 84 to 126 A-thick In 8 5 G a . i 5 A s and 210 A-thick GaAs, to make a layer 310 nm thick. This ma-terial is effective because it is a relaxed superstructure. The indium fraction is large enough that the lattice spacings are mismatched by ~6%. Above a few monolayers, the overlying lattice cannot elastically deform to match the underlying lattice spacing and defects will be incorporated into the structure to compensate. Again, these defects act as fast recombination centres. A correlation signal is shown in figure 4.9. While there is again a short pulse which decays at (2.6±0.3) ps there is a much longer tail which decays with a time constant of (10.0±0.3) ps. This is easily seen in figure 4.10. 56 1.0 •a s 0.5 d " O cb o-l-O cb 0 - J 0 0 0 - r . 0 0 0-0.0 0 o o o o o 0 10 Time delay (ps) 15 0" 1 1 20 Figure 4.8: The reflection-transmission correlation signal for low-temper-ature-grown GaAs. 57 4 6 Time delay (ps) 10 Figure 4.9: The reflection-transmission correlation signal for a superlattice of I n . 8 5 G a . 1 5 A s . 58 Figure 4.10: Logarithm of the reflection-transmission correlation signal for a superlattice of In.s5Ga.15As showing two different characteristic decay times. 59 Chapter 5 Experimental equipment, design, and procedure 5.1 Overview This experiment is centred about a multiatmospheric-pressure C 0 2 laser amplifier (figure 5.1). Short laser pulses are switched into the amplifier using two semiconductor switches in series. Pulses are regeneratively amplified then switched out with another semiconductor switch placed within the cavity. The switch-in (injection) switches 'chop' picosecond slices from a 'hybrid' C 0 2 laser. These switches are controlled by sub-picosecond optical pump pulses that are produced by a dye-laser amplifier. Pulses are switched out of the laser cavity using another visible (5.32-nm) pulse from a Nd:YAG regenerative amplifier. • This chapter describes the multiatmospheric-pressure C 0 2 amplifier, the 'hybrid' C 0 2 laser, the control lasers, the associated timing electronics and the pulse-detection and analysis apparatus. 5.2 Visible short-pulse generation equipment The pump pulses for this experiment are provided by a system based on a Nd:YAG mode locked oscillator (figure 5.2). Most of the beam from this laser is injected into a pulse compressor which in turn pumps an ultrashort dye-laser oscillator operating at a wavelength of 616 nm. This beam is then amplified by a dye amplifier which produces the pump pulses for the 60 Figure 5.1: Overview of multiatmospheric-pressure amplifier system. The hybrid laser produces ~ 120 kW single-mode pulses incident on the first semiconductor switch which is normally transparent to the C 0 2 beam. The ~500 fs visible pulse from the dye laser excites the semiconductor switches in series such that a short pulse is injected into the amplifier cavity. The pulse is amplified and can be monitored with a reflection from the amplifier window and switched out using a second intra-cavity semiconductor switch. 61 Nd:YAG oscillator 1.064)xm wavelength 11 W average Power 70 ps pulses 82 MHz repetition 5% Split-Off Pulse compressor and Frequency doubler 532 nm, 750 mW, 5 ps |Regenerative amplifier 532 nm, 70 ps 25% Split-off To Switch-out 5% Split-off Dye oscillator 616 nm, 300 mW, 500 fs Dye Amplifier #1 Energies up to 300|xJ (Dye Amplifier #2 Energies up to 1 mJ To pulse-injection \ system Figure 5.2: The visible short-pulse laser system. The Nd:YAG oscillator generates 70-ps pulses which are compressed and doubled to 5-ps, 532-nm pulses by the pulse-compressor unit. This in turn pumps the dye-laser oscil-lator to produce 500-fs pulses at 616 nm. These are amplified in a dye-laser amplifier which is optically pumped with a Nd:YAG regenerative amplifier. injection semiconductor switches. The switch-out switch as well as two dye-laser amplifiers are pumped by a frequency-doubled Nd :YAG regenerative amplifier. 5.2.1 N d : Y A G oscillator A Spectra Physics Model 3800 Nd:YAG laser is the basis for the pump-laser system. The laser medium is an arc lamp pumped rod of yttrium aluminum garnet, doped with N d 3 + atoms. Pulses of 70-ps duration, 1.064-fj,m wavelength , and 82-MHz repetition rate are produced by a mode locker in the cavity. The average power emitted is approximately 11 W. The quartz, acousto-optic mode locker is driven by a sinusoidal 41-MHz frequency-stabilized voltage. Bragg diffraction within the crystal introduces losses within the oscillator cavity which disappear at the zero crossings of the acoustic field. The frequency is fine tuned to produce pulses as short as possible near the resonant frequency of the crystal. A cavity-length adjust-ment is necessary to fine-tune the pulse round-trip time to the modulator frequency. The output pulse is monitored by a nanosecond-response-time 62 diode which is placed under a quartz beam splitter directly after the output coupler. 5.2.2 Pulse compressor The 70-ps pulses from the oscillator are compressed to approximately 5 ps in the Spectra Physics Model 3695 Pulse Compressor. Self-phase modula-tion in a single-mode optical fibre increases the spectral bandwidth of the pulse which allows for a shorter pulse. At the same time the group velocity dependence on wavelength introduces a frequency chirp to the pulses. These pulses are then compressed using a grating and prism arrangement. A K T P (potasium titanyl phosphate) crystal is then used to frequency double these pulses to a wavelength of 532 nm. They are also reduced in duration to less than 3.5 ps. The average power produced by this system varied from 600 to 900 mW. 5.2.3 Dye-laser oscillator A Spectra Physics Model 3500 synchronously-pumped dye oscillator is used. As mentioned previously, this is pumped with the 532-nm pulses from the pulse compressor. The dye used is Rhodamine 6G dissolved in ethylene glycol. A thin dye jet is produced by pumping the dye mixture through a sapphire nozzle at 800 kPa. This makes it possible to generate pulses of less than 500-fs duration at the same 82-MHz frequency of the pump laser. While the frequency is tunable over a 80-nm spectral range, the system was always tuned to 616 nm. The average power from this laser is 200 to 300 mW. 5.2.4 N d : Y A G regenerative amplifier Approximately 5% of the pulse train from the Nd:YAG oscillator is fed into the regenerative amplifier from a dielectric beam splitter. A regenerative amplifier is so-called because it switches in pulses and amplifies them in a stable cavity mode before switching them out again. The amplifier is a Continuum Model R G A 60. It is optically isolated from the oscillator with a Faraday polarization rotator placed in between two polarizers. A K D P (potassium dihydrogen phosphate) Pockel's cell and polarizer selects single pulses to switch into the cavity. These are amplified in a 6-mm diameter Nd:YAG flashlamp pumped rod and then switched out 63 using a second Pockel's cell. These pulses are then further amplified by a single pass through a 9-mm Nd:YAG rod to an energy of approximately 200 mJ. The amplified pulses are passed through a K D P frequency doubling unit to produce pulses of energies between 85 and 95 mJ with a wavelength of 532 nm. The repetition rate of the pulses can be varied by varying the rates of the Pockel's cells and the flashlamps. The maximum rate is 10 Hz but it was normally operated at 2 Hz. At least three times during the course of this experiment, one of the Pockel's cells became damaged due to the high intensities present within the cavity. The K D P crystals were hand repolished and new electrodes were fashioned from conductive paint. The optical quality was somewhat degraded which led to a slightly decreased energy output from the dye-laser amplifier which will be discussed in the next section. However, the second-harmonic conversion efficiency only decreased slightly which implied that the pulse was not significantly lengthened. 5.2.5 Dye amplifier A Continuum Model P T A 60 dye amplifier is used to amplify the pulses from the dye-laser oscillator. Further amplification is obtained through the use of an amplification module built in the lab. The P T A 60 has three amplification stages. One quarter of the 532 nm beam is allowed to pass through a dielectric beamsplitter and into the am-plifier. Since the dye-laser level lifetime is less than 300 ps, the path lengths within the amplifier have to be carefully adjusted. For this reason, each dye cell has its own delaying prism arrangement. It is found in practice that the path lengths have to be adjusted to within 2 cm for optimum power. The first two dye cells are each pumped with 8% of the beam in the amplifier and the third cell is pumped with the remainder. As well, the beam diameter in-creases with each successive cell: 1 mm in the first, 2.5 mm in the second, and 6 mm in the third. The dye used is Sulforhodamine 640 dissolved in water. The dye is circulated in series through the first and second cells. A separate dye pump was used for the third cell. With this system, amplification of up to one million times can be obtained, giving energies 200 to 300 / /J . Damage to the regenerative amplifier resulted in a reduction to the energy available at this stage. Further amplification is achieved using an additional amplifier. The dye cell body was machined from half-inch thick aluminum and 3-mm-thick 64 Pyrex flats were epoxied on to create the cell as shown in figure 5.3. The dye is supplied from the output of the third dye cell. Optical pumping is obtained by directing ~60 mJ from the regenerative amplifier, through an adjustable prism delay line, through a steering prism and onto the dye cell. Amplification of approximately 5 times is achievable with this setup and energies of 750 to 1000 / i J . Pulse energies were measured with a Molectron Model J3 Pyroelectric joulemeter. 5.3 Principles of autocorrelation Since photo-detection devices capable of measuring ultrashort pulses in the visible range and short pulses in the infrared do not exist or are prohibitively expensive, autocorrelation was developed as a technique to indirectly esti-mate the duration of such pulses. Autocorrelation refers to the practice of splitting a pulse, delaying one part with respect to the other, and recom-bining them in a non-linear crystal in such a way that the pulse duration can be inferred from the integrated second-harmonic signal by use of the mathematical autocorrelation function. In this section, the principles of autocorrelation will be discussed. Two autocorrelators are used for this experiment: the pulses from the dye-laser oscillator and the dye amplifier are measured by the visible autocorrelator which will be discussed in the following section. The fast pulses generated by the multiatmospheric-pressure amplifier are measured by the infrared autocorrelator which will be discussed in section 5.12. Figure 5.4 shows the visible autocorrelator and will be used to discuss the essentials of what is known as a zero background autocorrelator [84]. The short pulse is first divided at a beamsplitter. One half (B) is delayed by a time delay, r, with respect to the other, (A). Here the time delay is provided by the turntable in a manner which will be described in the next section. The two are recombined in a second-harmonic crystal with a small angle between them. The second-harmonic intensity as a function of delay can be analysed to give the pulse width. The process of second-harmonic generation involves the exchange of en-ergy between waves at frequency co and those at 2co. If there is not phase matching such that the second-harmonic beam stays in phase with the fun-damental beams, the second-harmonic intensity will stay very small as the energy will be converted back to the fundamental beams. In negative uniax-65 Tapped hole for polyflo pipe fitting o >/-> CS l~ i ; J . Dye Flow 0.725 0.875 1.500 Dimensions in inches Tapped hole for l/4"-20 bolt Glass At approx. 45 degrees from vertical Tapped hole for l/4"-20 bolt 532 nm beam Amplified Beam (a) Dye Cell Body Aluminum Plate 616 nm beam Steering Prism (b) Top View Optical Layout Figure 5.3: Additional dye amplifier. This cell was constructed to provide an additional 5x amplification to bring the total energy of the ultrashort dye-laser pulses to ~1 mJ. 66 Dye laser pul: Figure 5.4: The visible-pulse-width autocorrelator. The pulses are di-vided by the beam splitter (B. S.). Pulse A is horizontally displaced on a micrometer-driven delay stage. Pulse B is delayed by mirrors on a rotating table. The pulses are recombined in a second-harmonic-generating crystal (KDP) . The fundamental frequency is filtered out and the second-harmonic signal is measured. The intensity is proportional to the autocorrelation func-tion, equation 5.2. 67 ial crystals, such as the ones used in these autocorrelators, it is possible to match the waves such that efficient second-harmonic generation is possible. Furthermore, by offsetting one fundamental wave with respect to the other it is possible to greatly reduce the background signal. In such crystals, the index of refraction can be varied depending on the angle the wave vector makes with the optic axis. If 7 is the half angle between each fundamental wave vector and the second-harmonic wave vector, it is possible to match the condition such that 2kucosy = The background is much smaller than if the beams were coaxial because neither of the beams by itself matches the phase matching condition. Crystals such as K D P (potassium dihydrogen phosphate) and AgGaSe 2 , which are used as autocorrelation elements in the visible and infrared re-spectively, have to be carefully cut and aligned. Usually, these crystals are cut such that the second-harmonic beam will emerge perpendicular to the surface. If the intensity of one of the pulses is given by Iu(t), the intensity of the delayed pulse will be described as Iw(t — r) . The intensity of the second-harmonic signal will then be described as / ^ o c J U t ) x / „ , ( * - r ) . (5.1) Of course, this signal occurs on a very fast time scale whereas the detectors operate on nanosecond time-scales. The signals are therefore integrated. The signal seen is proportional to the second-order autocorrelation function: n, i(t)i(t - r)dt G2(T) - r.j'M* • { ] This signal is always symmetrical with respect to r and it is fairly insen-sitive to the input pulse shape. The autocorrelation function has. the effect of smoothing out many details of the pulse shape. To illustrate this, we can examine three pulse shapes: a Gaussian, a sech2 pulse, and an asymmetric one given by f(t) = {exp[-r / ( l - A)} + exp[r/(l + A)}}~2 where A = 3/4 here. These are illustrated in figure 5.5. The sech2 and Gaussian functions have been chosen because they are often used as standard pulse shapes [2]. The asymmetric function is shown because it is the pulses generated by the semiconductor switching are expected to have a much shorter rise-time than fall time. The asymmetry here is ~ 2.5x. A l l three of the pulses are scaled to have a F W H M of 2. 68 0.0 -4.0 -2.0 0.0 2.0 4.0 Scaled time Figure 5.5: Input trial autocorrelation functions: (a) f(t) = {exp[—t/(l — A)] + exp[i/(l + -4)]}"2, A = 3/4 (b) seen2, (c) Gaussian. The autocorrelations are shown in figure 5.6. It can be seen that they are all very similar; it is very difficult to experimentally differentiate between them. To determine the pulse widths from autocorrelation signals, it is nec-essary to guess a pulse shape, then to scale the width of the autocorrelation signal appropriately: A i = Atautocorr / ^correction, where At is the actual pulse width (FWHM), A i a u t o c o r r is the measured F W H M of the autocorrelator sig-nal, and ^correction l s the correction factor, ^correction is 1-543 for a sech 2-shaped pulse and 1.414 for a Gaussian. For f(t) ^correction is 1.712. With a single-channel detector for a autocorrelator, each laser pulse pro-duces a value for only one value of G2(r), it is necessary to determine the pulse widths through the analysis of many pulses. This is done in a different way for each of the autocorrelators and will be discussed in sections 5.4 and 5.12. It is possible to measure the pulse width on a single-shot basis but this involves the use of multichannel detectors which were not available for this experiment. 69 -4 -2 0 2 Scaled Width 4 Figure 5.6: Autocorrelation of trial functions shown in figure 5.5. This demonstrates the relative insensitivity of the autocorrelation function to the actual pulse shape. 70 5.4 Visible-pulse autocorrelator In order to achieve pulses from the dye laser as short as the manufacturer's specifications of ~500 fs, it is necessary to fine tune the dye-oscillator cav-ity length using an autocorrelator. This device was constructed in the lab [76] and set up as part of the work characterizing short-pulse generation by semiconductor switches. Again, figure 5.4 depicts the visible autocorrelator. The beam enters through an alignment aperture and is split by a 50/50 beamsplitter. One half goes through path A and is laterally displaced by a corner mirror adjustment. The other half is retroreflected from a fixed mirror after being reflected in each direction from two parallel mirrors mounted on a turntable. The beams pass again through the beamsplitter, one with a lateral displacement, and are focussed onto the second-harmonic crystal by a short focal length lens. In the crystal, a beam of one half the wavelength is generated at the bisector of the the two fundamental beams. This passes through a small aperture and discrimination filter and is detected by a photomultiplier. In this setup, the variable delay can be set on either path for use in different situations. The path with the micrometer adjustment can be used for instrument calibration and also for low repetition rate pulses. The arm with the rotating mirrors can be used for a high repetition rate pulse train. The turntable rotates at 25 Hz. Over the short range in each cycle during which the arm reflects the beam back, the delay can be considered to vary linearly with time. The oscilloscope is triggered once every cycle. The pulses are separated by only 12 ns so that for a scan of ~25 / i s , the oscilloscope will trace out more than a thousand pulses. The time axis can be related to the delay time once appropriate calibration is done. This is simply done by adjusting the micrometer on the other arm and observing the temporal change in the peak of the oscilloscope signal. For the slow, < 10 Hz, pulses from the dye amplifier, the turntable is fixed and the peak voltages are recorded as a function of the delay set by the micrometer. The K D P crystal used in this device is only 1/2 mm thick. The time resolution of the autocorrelator is limited by the dispersion in this crystal. The resolution has been calculated to be less than 50 fs. 71 5.5 Transversely—excited lasers Two transversely-excited (TE) C O 2 laser sections are used in this experi-ment: the atmospheric-pressure section of the hybrid laser and the multiatmospheric-pressure amplifier. Some common details of the two will be discussed before the individual systems are described. In order to efficiently populate the upper laser level through an electric discharge, it is necessary to establish a glow discharge as discussed in section 3.2. Such a discharge is characterized by relatively low electron temperatures which can be stable over a wide area. This is desirable because the whole lasing volume will be excited uniformly. A glow discharge occurs naturally at low gas pressures (< 7 kPa). At higher pressures, pulsed operation is nec-essary. The three requirements for the establishment of a glow discharge are a short discharge duration, good preionization, and the proper gas mixture. Discharges can be characterized by a critical time after which, on average, a glow discharge will become an arc. An arc forms when regions become more conductive. This leads to a feedback which draws more current which in turn increases the ionization which further lowers the resistance [85]. In an arc, filamentary regions of high current flow dominate the discharge. These are unsuitable for exciting the laser transition. As the gas pressure increases, the critical time decreases. Careful consideration of the circuit design must be taken in order that the discharge time will be short enough. In general, the product of the inductance and the capacitance must be made as small as possible [86]. The circuits used in this experiment are L-C inversion circuits. They are so-called because the closing of the spark-gap switch in each circuit excites an L R C circuit. This effectively inverts the voltage seen across the storage capacitors in the circuit leading to the electrical breakdown of the C O 2 laser gas mixture. This process is known as vector inversion [87]. For the L -C inversion circuit this results in a doubling of the charging voltage and for the fourfold circuit used in the multi-atmospheric-pressure amplifier a quadrupling. Figure 5.7 shows the two types of L-C circuits used: what is known as an L-C inversion circuit used in the hybrid laser and the slightly more complicated fourfold L-C inversion circuit. Indicated on each figure are two current loops, the first, A , is the inversion loop which is excited when the spark gap is triggered, the second, B, is the low-inductance main discharge loop which effects the transfer of most of the stored energy to the gas plasma 72 (the circuits are symmetric). The operation of the circuits is described for the hybrid section; the operation of the fourfold-inversion circuit is similar. First the spark gap is triggered which initiates a ringing type current in the inversion loop. The inductance in all these circuits is simply the loop plus switch inductance. The resistance is the very small conductor resistance plus the near short circuit of the spark gap. After half a cycle, the voltage seen across the capacitors is inverted, in figure 5.7(c). This stacks the voltages of all the capacitors which quickly induces a breakdown in the main loop. As previously mentioned, the main loop has a low inductance, much lower than the inductance of the inversion loop. Furthermore, the parameters are chosen such that the current is nearly critically damped. The energy from the capacitors is thus deposited into the laser mix. An initial concentration of electrons is established in the mix just prior to the application of the electric field to the main discharge electrodes. This is done by U V photo-ionization. The ultra-violet photons are created, in this case, from electrical sparks initiated on either side of the discharge volume. It is necessary that a fairly uniform concentration of electrons, 104 < 108 c m - 3 , be created [21, page 139]. The third requirement is a proper gas mixture. For our lasers, a mix of equal parts CO2 and N 2 with a majority part helium were used. The pro-portion of helium is increased with increasing pressure. Helium encourages the formation of a glow discharge because it effectively slows down electrons through elastic collisions, being by far the lightest gas species present. For the hybrid laser pressure section, a mixture of C0 2:N 2:He::6:6:88 was used, and for the multiatmospheric-pressure section, a C0 2:N 2:He::3:3:94 was used. In addition, for the multiatmospheric-pressure section, a small amount of tripropylamine was added. It has been shown that tripropylamine reduces the propensity for arcing [88]. As a low-ionization-threshold gas, it greatly enhances the electron-density production and lifetime at preionization [89]. 5.6 C 0 2 hybrid laser This laser is called a hybrid laser because it contains both a C W (continuous wave) section and a pulsed discharge section within the same optical cavity (see figure 5.8). This arrangement facilitates the operation of the laser in a single mode, characteristic of C W lasers, while allowing one to obtain the high powers associated with pulsed lasers. The availability of a C W beam 73 v0 A '^1 0 IL (a) A (c) (b) Figure 5.7: L - C inversion circuits, (a) L - C inversion before excitation, (b) fourfold L-C inversion before inversion, (c) circuit in (a) after spark gap triggered. A indicates the preionization-current loop and B indicates the main current loop after the main discharge breaks down. The L-C inversion circuit doubles the charging voltage and the fourfold circuit quadruples it. 74 KC1 windows at Brewster's angle J ) Germanium Etelon Atmospheric Pressure Section Low Pressure Section (CW) Figure 5.8: The hybrid laser. The low-pressure C W section provides a single mode. When the atmospheric-pressure section is discharged, single-mode powers are generated up to 120 kW. The temperature-controlled germanium etelon is used to select the lasing transition. also facilitates the beam alignment procedure. The C W section alone will produce up to 20 W on the P20 line while the peak power of the hybrid is approximately 120 kW. The laser cavity is defined by a 6-m radius of curvature gold on silicon mirror at one end of the low-pressure section and an uncoated, 3-mm-thick germanium-flat output coupler at the other end. The separation between the two is 2.1 m. The flat is used to select the laser line through an etalon effect. The germanium is temperature controlled to approximately 1/2 K . The index of refraction of germanium is quite large (~4.2) and has a relatively large dependence on temperature. Lasing will occur on the transition with the highest cavity round-trip gain: the one with the highest total of gain less losses caused by scattering, reflection, and losses through the output coupler. The germanium flat will reflect approximately 35% from each face; however, the reflections will interfere with each other. The reflection and transmission is therefore dependent on the wavelength and the optical path length of the flat (thickness x index of refraction). In this way a narrow line corresponding to a single transition can be selected. 5.6.1 Low-pressure section The CO2 laser transition is electrically excited by creating a glow discharge in a low pressure gas. In this case, the gas used is a mixture of C0 2:N 2:He::8:8:84. When operated at a pressure of 5 torr [670 Pa] and a voltage of 5 kV this produces approximately 6 W of power on the P(20) line. 75 Figure 5.9: The low-pressure C W lasing section. The gas mix is electrically excited by a current flowing between the brass electrodes placed at the ends of the water-cooled Pyrex tube. At the left is shown the bellows mirror adjustment and at the right is shown the Brewster's angle K C l flat. This mixture flows through a 103 cm long, 12 mm inside diameter Pyrex tube. The thin tube section brass electrodes are partially inserted into the ends of the Pyrex tube as shown in figure 5.9. The gas discharge is cooled by water flowing through a 45-mm-inside-diameter Lucite tube co-axial with the Pyrex tube. At one end of the laser is attached a flange which holds a 5-mm-thick K C l flat at the Brewster angle of 55°. The other, grounded, end has a bellows arrangement such that the cavity mirror can easily be adjusted. 5.6.2 Mechanical details The atmospheric pressure section consists of a laser body adapted from use as an excimer laser. This laser body has been used previously and more detail on its construction can be found in previous work [90, 91]. The glow discharge takes place between two parallel brass electrodes with a modified Chang profile [92]. They are 35 cm long and separated by 1.5 cm. The gas is photo-preionized by two rows of spark preionizers, placed half way between and to the sides of the two electrodes. The preionizers were made by fitting 17, 2.5 cm long stainless steel tubes on a 5 mm diameter 76 glass tube. The ends of these stainless steel tubes are spaced 1.0 mm apart so that when a large potential difference was applied to the ends, sparks would appear at each of the gaps. The K C l windows were set to allow light polarized horizontally to pass through at the Brewster angle. The windows were 5-mm-thick flats of 50-mm diameter. The laser was enclosed in a fine copper-mesh to reduce radio-frequency interference produced by the discharges. 5.6.3 E l e c t r i c a l d e t a i l s The complete electronic circuit, including the preionization circuit, is shown in figure 5.10. To minimize the main circuit inductance, the 24, 2.7 nF doorknob capac-itors are divided into four equal groups and placed close to the electrodes as possible as shown in figure 5.11. The high voltage sides are connected to two large brass plates (21.1 cm x 33.2 cm x 0.65 cm). The inversion circuit inductance has been found to be 220 nH while the main circuit inductance is 27 nH. The spark gap electrodes are made of brass and mounted in a Lucite chamber. The discharge s triggered by a -10 k V trigger pulse to a triggering pin located at the centre of the cathode. This pulse is formed by a 4:1 step-up transformer and a E G & G Krytron unit. Pressurized dry air flows through the spark gaps to control the breakdown voltage and to remove ozone. The air pressures and flow rates are controlled by manipulation of the air bottle regulators and small valves. The preionizers fire approximately 100 ns before the main discharge starts. Each preionizer has its own bank of six capacitors arrayed immediately beside the spark gap. When the spark gap fires, the voltage is almost immediately applied across the gaps: the time is just limited by a small inductance. 5.6.4 O p e r a t i o n a l d e t a i l s This laser was operated at 70 kPa and 30 kV. It is possible to operate at higher pressure and voltages but it was found that, over time, optical dam-age to the K C l windows would occur: most likely caused by high optical intensities. The gas mix was flowed through the hybrid body at a rate such 77 50 MQ 10.8 nF -lOkV "LT 16.2 nF 10.8 nF 16.2 nF +UWJ\/\f^, 50 MQ. .(b) Ir 16.2 nF 4:1 (c) 16.2 nF 50 MQ Figure 5.10: Complete electronic schematic diagram of hybrid pressure sec-tion: (a) preionizer spark gap; (b) main discharge; (c) preionizers. When the spark gap is triggered by the -10 k V pulse, vector inversion is initiated such that the main discharge electrically breaks down at close to double the charging voltage. 78 Figure 5.11: Hybrid pressure section (end view). Not shown are the spark-gap and preionizer capacitors. 79 Figure 5.12: The intensity-evolution of the hybrid laser. The small pulse ~100 ns before the centre line is a timing reference. that the gas would be replaced approximately every two minutes. With these parameters it was possible to reliably fire the laser every 15 seconds. The intensity of the hybrid laser is shown in figure 5.12. It can be seen that the full width at half maximum for the pulse is 210 ns. The variation in the temporal position of the peak, known as the timing jitter, of the laser could not be improved to better than ±25ns. More typically, the laser would operate with a jitter of 50 ns. The reasons for such a large jitter could be room temperature changes leading to pressure changes in the spark gap and temperature changes for the etalon also even though the hybrid power supply was attached to a Sola Electric CVS Constant Voltage Transformer, the voltage on the hybrid still varied by approximately 2%. 80 5.7 Multiatmospheric-pressure amplifier As with the hybrid laser, the multiatmospheric-pressure laser amplifier com-prised many components. The physical arrangement consisted of the laser body, end mirrors, an optical window, and the injection and switch out semi-conductor switches. Arrangements had to be made to deliver the pump and CO2 beams to the injection switch and another visible beam to the switch-out switch. As well, precise electronic timing had to be maintained. 5.7.1 Laser body The gas is contained in a 40-cm-long P V C tube of 5.7-cm inside diameter. The electrodes are constructed of aluminum. The effective discharge volume is 1.5 cm by 1.5 cm by 35 cm. Lucite flanges are connected to the P V C body with 12 nylon bolts each. One flange holds a K C l window angled at 10° from the vertical and the other holds a 3-m radius of curvature mirror. An arrangement exists such that the angle of the mirror can easily be adjusted from outside the laser. More details about the construction of this laser can be found in references [93] and [94]. The low inductance arrangement can be seen in figure 5.13. The capac-itors are placed as close as possible to the electrodes so as to minimize the cross sectional area of the current loop during discharge. The electrodes are each connected to aluminum plates through the P V C tube with twelve brass fittings individually sealed with o-rings. This arrangement uses the same 40 kV capacitors that are used for the hybrid laser. These are put in eight groups of 11 capacitors each. U V preionizers were constructed in a similar fashion to those in the hybrid pressure section. The only difference is that a slightly larger gap of 1.2 mm was necessary to adequately preionize the mix. The preionizer electrical connections passed through the flange containing the K C l window and were supported by blind holes in the rear flange. This laser body was also enclosed in a fine copper-mesh Faraday cage fitted over a Plexiglas box in order to reduce radio-frequency interference. 5.7.2 Electrical details The complete electrical schematic diagram can be seen in figure 5.14. The inductance of the main loop has been calculated to be 47 nH, the capacitance 81 Preionizer Cable ; Gas : Inlet < ® V Aluminum plate 2 in Figure 5.13: Multiatmospheric-pressure-amplifier body: end view. The spark gap and preionizer capacitors are not shown. 82 is 240 nF and the resistance of the discharge has been measured to be 3.4 tt at the time of peak current in a gas mix of C0 2:N 2:He::6:6:88 [94]. This is reasonably close to the ideal, critically damped, resistance of 2.5 fi. The triggering arrangements are again similar to the hybrid section. A 4:1 transformer amplifies a -lOkV pulse from a krytron unit. This pulse is applied to the spark gap trigger pin. The discharge hold-off voltage of the spark gap can be controlled by varying the pressure of the dry air flowing through it up to 700 kPa. 5.7.3 Operational details This amplifier was operated at a pressure of 1.24 MPa. The voltage had to be often tuned to achieve the best discharge. This was normally near 28.5 kV. Raising the voltage higher would cause large arcs between components fa-cilitated by a large corona discharge. Approximately (l/6)th of the gas was replaced after each shot. This laser could only be reliably fired once every minute. The small-signal gain was measured by G. C. Stuart [93] and is plotted in figure 5.15. While this measurement is of the 9.4 /um transition, the results in terms of gain duration and risetime are expected to be similar. 5.7.4 Optical details The laser cavity is 1.735 m long. The cavity is defined by a 3 m radius of curvature mirror placed within the pressurized section and a 10-m radius mirror at the other end. Both mirrors are gold on copper to maximize the reflection and power handling capability. The intra-cavity semiconductor injection switch is placed at the waist of the cavity in order to minimize the visible laser energy necessary to switch a pulse into the cavity. It was found that there was substantial, up to 1%, C 0 2 radiation reflected into the cavity of the wrong polarization. While this was not necessarily a problem for amplification as repeated passes through the injection switch at the Brewster's angle would eliminate this, it was often desirable to minimize this so that the injected pulse of the proper polarization could be observed. This could be simply done by inserting a second GaAs or silicon wafer within the cavity to cut off this radiation. This issue will be further discussed in the following section. 83 -lOkV Spark Gap - 1 r~ Trigger U -HV 24.3 nF 24.3 nF 29.7 nF ipwv4 4:1 24.3 nF E L ^ CJP 24.3 nF Preionizer Spark Gap 29.7 nF' 29.7 nF Main |. Discharge 29.7 nF 29.7 nF 29.7 nF Figure 5.14: Multiatmospheric pressure laser: Complete electrical schematic diagram. A l l resistors are 1 Mfi. . 84 500 time (ns) 1000 Figure 5.15: The amplifier small-signal gain for the 9.4-/im transition and 1.2-MPa pressure (from G. Stuart [93]). 85 This wafer is also used as a switch-out switch which can be controlled by ~3% of the 60-ps, 532-nm pulses generated by the regenerative amplifier. In order to align the amplifier, low-power HeNe laser beams were initially used. First, a beam was reflected off an intra-cavity pellicle beamsplitter and through intra-cavity alignment apertures, off the 10 m mirror, back through the cavity and through the laser body onto the 3 m mirror. Adjustments could be made to the end mirror positions until the beam coincided with itself on the second pulse. The pellicle would then be removed. After that, the injection semiconductor wafer was installed and a HeNe beam coincident with the CO2 beam from the hybrid was passed along the same beam path. The intra-cavity apertures were also used to control the allowed stable modes of the cavity and further to introduce losses to limit optical damage to the mirrors, window, and wafers. In a cavity defined by spherical mirrors, Gaussian-beam modes of the form w(z) \w{z) J \w{z) J (5.3) are allowed. A is a constant, x and y are the transverse dimensions and z is the longitudinal. HN are the Hermite polynomials and w(z) = WQ^JI + (z/z0)2 cj) = kz — (m + n + 1) ta.n~l(z/zo), ZQ = TTWI/X and WQ known as the waist. It is desired to allow only the smallest (mn = 00) mode to be amplified. To do that, the apertures, which are placed at the waist ±10 cm, can be adjusted to approximately 7 mm in diameter. In this mode, this equation reduces to A 0—id>(z) E m ( r } z ) = A e eikr>,2BWe-r*/«W\ (5.4) >/i + (*Ao)2 where r is the distance from the axis. For this cavity, the waist is 0.225 cm and the size on the 3-m mirror is 0.32 cm. To limit the round-trip gain, the laser was operated with the apertures as small as 4 mm in diameter. While a Gaussian beam would be attenuated by approximately 80% by such an aperture in this cavity, the beam becomes distorted due to diffraction effects and therefore this amount of loss is not expected on each round trip. The actual beam profile and round-trip losses can be calculated in an analysis similar to that first done by A. G. Fox and T. L i [95]. This issue will be discussed further in chapter 6. 86 5.7.5 Pulse injection Many different configurations were used in attempts to get short pulse injec-tion into the cavity with good contrast ratio. Configurations with single and double injection switches were used. However, the most successful experi-ments were done with the first injection switch outside the cavity supplying a pulse to the intra-cavity injection switch. In order to obtain efficient amplification of the switched C 0 2 pulse, the beam parameters had to be accurately matched to the amplifier cavity pa-rameters. This was done through accurate placement of two small gold-on-copper mirrors of radius of curvature 27.0 cm and 19.8 cm in the beam line before the semiconductor wafers. The angle of incidence on these mirrors was made as small as possible in order to minimize astigmatism effects. To amplify the picosecond pulse without having any noticeable amplifi-cation of the background C W beam some precautions had to be taken. The semiconductor wafers were accurately tuned to Brewster's angle by passing approximately 10 W C W through them and tuning the angle until a minimum of reflection was measured. The best that could be done with each wafer was 0.1% for the GaAs wafer and 0.2% for the radiation damaged GaAs wafer. While this is good, it was believed at many points in the experiment that the injected C W was too great. It was for this reason that two switches in series were employed. It is believed that some reflection is inevitable due to surface or other imperfections in the semiconductor wafers. Furthermore, in order to get contrast ratios that high, the beam had to be passed through another wafer at Brewster's angle. Without these other wafers, the background was approximately 10 times higher. This implied that the beam polarization was not perfect. Improvements could not be made by adjusting the orientations of the Brewster's angle windows in the C W CO2 laser nor by adjusting the po-larizing germanium flat in the C W beam path, therefore, the off-polarization component must arise from scattering in the beam-delivery mirrors. This component is not problematic as it cannot be amplified in the cavity due to the necessary repeated passes through the injection semiconductor switch. For the experiments discussed in this thesis, the first switch was either GaAs damaged with a dose of 10 1 4cm~ 2 of 180 keV protons or a nominally undoped GaAs wafer. The second switch was nominally undoped GaAs. The visible pulses were focussed to a waist size of approximately 2.5 mm using lenses in an inverted telescope arrangement. The pulses were split using a dielectric on glass beamsplitter. The beam splitter was mounted on 87 a micrometer adjustable translation stage so that the control pulse would reach the second switch at exactly the same time as the CO2 pulse from the first switch. The timing could be finely adjusted by maximizing the measured pulse energy from the two switches in series. The alignment was also optimized by maximizing the power. Using just the commercial dye-laser amplifier, pulses up to 300 fiJ were available to pump the switching. When a further amplifier was built, pulses up to 1 mJ were possible. For a single switch with the 300 fiJ pulses, densities up to 5 x n c could be induced in the switch for the 1 mJ pulses, densities up to 16nc and for the double-switch configuration, densities up to 8n c could be induced. 5.7.6 Pulse switch out An arrangement was built to delay the 532-nm, 60-ps pulses from the Nd:YAG regenerative amplifier by ~160 ns to pump a semiconductor switch within the cavity. This corresponds to a length of almost 50 m. Assuming a fast switch-out switch and that the desired timing accuracy would be ±10 ps in order to deliver the peak of the pulse energy at the desired time, the adjustable delay mirror had to be placed within ±1.5 mm. In order to accomplish this, the beam first had to be expanded by about four times with a diverging-converging lens setup to avoid an electrical break-down due to the high optical fields, accurately collimated and reflected from eight, 50 mm diameter, silver on glass, delay mirrors placed ~ 8m apart. The beam had to be then focussed down onto the switch-out switch. At different times, silicon and GaAs switches were used, placed at the Brewster's Angle within the cavity. To some extent the switching efficiency could be optimized by the placement of the lens before the wafer. There was plenty of excess energy within the 532 nm beam. However, great care had to be taken not to damage the surface of the wafer with the high intensities. One of the mirrors in the delay line was placed on an optical rail such that fine adjustment to the path length was possible. Initial path length adjustment was done by comparing the signal from a diode placed near the switch with the infrared signal reflected from the amplifier window. Fine tuning was done by max-imizing the pulse reflected from the switch-out switch while adjusting the delay length. 88 5.8 Timing Circuits had to be built to accurately synchronize the hybrid and multi-atmosphere lasers firing with the injection pulses created by the visible lasers. Extensive precautions had to be taken to ensure that the timing did not change due to the large amount of electrical noise created by the discharge of one of the gas lasers or their spark gaps. It should be noted that much of the detection and timing electronics are placed inside an electrically screened room to avoid interference. This large room is a large Faraday cage. There are two conducting layers which are connected to each other at only one point to avoid noise generating ground loops. Electrical power is provided through a noise filter. There are pass-throughs for eight B N C cables, these are grounded near the connecting point. The conducting layers consists of copper sheet on the walls, door, and floor and fine copper mesh on the roof. A l l the timing systems originate with the 41 MHz sinusoidal signal which drives the Nd:YAG oscillator mode locker fig. 5.16. This signal is then sent to a electronic delay box designed and built by the Electronics Shop at the Department of Physics at U B C . This device is necessary because the T E CO2 amplifier units needed up to 2 ps to adequately be preionized and for gain to build up in the gas. The maximum delay that can be provided by the regenerative-amplifier control unit is approximately 24 ns. Furthermore, while it is possible to control the charging and firing of the regenerative am-plifier Pockel's cells and flashlamps more easily through an external control interface, this has been found to greatly reduce power from the regenerative amplifier. The delay unit operates by acting as an interface between the Nd :YAG regenerative amplifier control unit and its flashlamps and Pockel's cells. The delay unit can provide two channels which independently deliver T T L signals from 0-3 ps in steps of 24 ns. In addition, there is a third T T L signal provided at the maximum delay of 3 ps. The details of the circuitry are outlined in the M . Sc. thesis of A. Elezzabi [90, pg. 227]. A l l three delay signals are sent to devices inside an electrically screened room. The dO signal is sent to a multivibrator based delay unit which trig-gers the oscilloscope. A schematic diagram of this circuit is shown in figure 5.17. The d l and d2 signals are sent to a trigger synchronization unit. This unit passes through the d l and d2 signals when a pushbutton is pressed. A schematic diagram of this circuit is shown in figure 5.18. It was found 89 N d : Y A G Mode Locker Frequency Generator 41 M H z 3V P-P N d : Y A G Regenerative Amplifier Delay Generator T T L Output d2 dl dO —3 \is -750ns -750ns N d : Y A G Regenerative Amplifier Pockel's Cells Delay Unit Pushbutton Synchronization Unit Osilloscope Trigger Hybrid Trigger Multi-atmosphere Laser Trigger Pushbutton Figure 5.16: A schematic drawing of the electronic timing and synchroniza-tion for the complete experimental system. The timing is based on the 41 MHz signal from the Nd:YAG mode locker. This is converted to a T T L signal by a unit which controls the Nd:YAG regenerative amplifier and pro-vides three delayed signal channels which are used to trigger the scope and synchronously fire the hybrid laser and multiatmospheric-pressure amplifier with a push-button switch. 90 dOJL* CLR Oscilloscope Trigger t-450R e x t <p,s> R e x t in Figure 5.17: Trigger signal variable-delay circuit based on two multivibra-tors. The width of the output pulse can be varied through adjustment of the external resistor. that both the delay and trigger synchronization units were very susceptible to electrical interference. The two circuits had to be separated in differ-ent metal boxes with separate power supplies. Furthermore, relatively large buffer capacitances had to be added to the chip 5-V power line. To avoid interference of the output signal, the output signal was ganged up to ensure that the voltage levels did not drop due to current drain. 5.9 Obtaining high contrast ratio amplified pulses Belanger and Boivin outlined the conditions necessary for the amplification of an injection seeded pulse when that pulse was competing against ampli-fied spontaneous emission for gain in the cavity [38]. They indicated that for the pulse to be amplified, there was a period of time during which the pulse should be injected. This was around the time the medium crossed the threshold from being absorbing to being amplifying. If the pulse was injected too early, it would be absorbed; and if were injected too late the spontaneous emission in the cavity would self seed the laser. It was later pointed out by Alcock et al. that the injection time interval became shorter the higher the 91 5V 470& lOuF 5V WV 450 MQ, pushbutton J L 20^is To hybrid laser trigger Figure 5.18: Laser-trigger-pulse pushbutton-synchronization unit. This uses a multivibrator circuit to produce a T T L output pulse when both channels of the input A N D gate are true. The output uses four inverters in parallel to boost the signal current. pressure due to a more rapidly rising gain curve. However, at pressures up to 8 M P a they had few problems with amplified spontaneous emission [40]. Amplified spontaneous emission is not a problem in this experiment ei-ther. When the C W C 0 2 laser is blocked, the self-seeded pulse comes much later (> 100 ns) than the pulse when the C W is incident on the semiconduc-tor switches. The situation here is more complicated. The small background, pulsed-C W , beam reflected from the Brewster's-angle switches is always present and is amplified with the injected pulses. This can become significant because it is not only the background at the time the pulse is injected that is significant; but also the background that has been amplified on previous round trips and the background that will be amplified after the injected pulse. If the hybrid laser fires such that the short pulse intensity is small compared to the background hybrid intensity due to the time evolution of the hybrid pulse, then significant levels of background will be seen. With this in mind and assuming that the gain is varying slowly enough that it can be treated as a constant during a round trip, the pulse, n round 92 trips after injection, becomes n-1 (5.5) k=0 The background level is n n h = B YI h(tjh + kT) 7(t;« + *T) (5.6) 7/j is the hybrid laser intensity, e is the efficiency of the injection switches, B is the fraction of intensity that is reflected from the semiconductor switches at Brewster's angle, j(t) is the round trip gain factor and m is the maximum number of round trip before the injection pulse which are considered, tjh and tja are time constants to take into account the effects of timing jitter. TP is the short pulse length and r^t is the detector integration time. The ratio of these takes into account the apparent reduction in the contrast ratio (of approximately 100 x) resulting from the rise time of the detector being much slower than the pulse duration. The contrast ratio is defined as the ratio of Ip to Ib. Therefore, in terms of optimal injection time, the result is the same as before: the pulse should be injected as near as possible to the threshold between absorption and gain. However, the jitter of the hybrid laser and the amplifier can easily be large enough that the background dominates, especially when the gain is large. When this occurs, the terms of Ib at n ^ 0 become significant. If Ip/h is divided by the the product in Ip, the terms including, preceding, and succeeding the k = 0, Ih(tjh) term are: ... + Ihtjh - 2T7(tja - 2T) + Ih(tjh - T)>y(tja - T) +Ih(tjh) + Ih(tjh + T))/j{tja + T) + Ih(tjh + 2T)h{tia + 2T) + .... (5.7) The worst case would be if the jitter of the hybrid laser and the amplifier cause them to fire early, thereby amplifying the background to significant levels. This issue will be investigated further in chapter 6. 93 5.10 Infrared detectors 5.10.1 Cu:Ge detector In order to maximize the efficiency of the semiconductor switching, it was necessary to use an ultrafast, sensitive copper-doped germanium (Cu:Ge) photoconductive [74, pg. 202] detector. The detector used was a Santa Barbara Research Center Model 9011 Detector. Since the risetime of this detector was in the order of 1 ns while the laser pulses were less than 20 ps long, all the signals were integrated. This meant that the detector was essen-tially measuring pulse energy. The smallest resolvable pulse, using a 34-dB at 1 GHz electronic amplifier was approximately 1 pJ. 5.10.2 HgCdTe detectors Two Boston Electronics, HgCdTe P E M 005 detectors were used to measure the pulse spectra. The response time of these detectors was 200 ns and the responsivity. These detectors use the photomagnetoelectric effect [74, pg. 321] effect. If electronic amplifiers were used which these detectors, they were 10 dB Phillips Scientific Model 6954B 10 Wideband Amplifiers. 5.11 Spectral measurements Given that only single-channel infrared detectors were available, it was not possible to take pulse spectra of single pulses. Instead, a piece of the spectrum would have to be obtained for each shot of the laser and then pieced together. The incident pulses were focussed through a small ( ~ l - m m diameter) aperture and refocused towards the entrance slit of the spectrometer. Ap-proximately 20% of the beam was directed onto a HgCdTe detector using a ZnSe beamsplitter. This provided a reference pulse (see Fig. 5.19). Such a design was relatively insensitive to small deviations of the incident beam in that the pulse levels might change with beam misalignment yet the signal ratios would remain unchanged. The spectrometer used was a Model 82-000, 0.5 m Ebert spectrometer. The original grating was removed and replaced with one which gave higher resolution. The spectrometer was calibrated with the 16th and 17th orders of the 632 nm HeNe line. The entrance slit was 220 fxm wide and the effective exit-slit width was 500 pm defined by the 94 detector placed at the exit. The design of this setup made the measurements quite insensitive to small changes in the beam position. The resolution of the spectrometer is ~5 nm. 5.12 Infrared autocorrelator The infrared autocorrelator was of a similar design to the visible autocorre-lator with two notable changes shown in figure 5.20. There was no need for a device to continuously scan through delays since the pulse repetition rate was less than once a minute; and (2) a CO2 pulse energy reference signal was taken from within the setup. The nonlinear, AgGaSe2, crystal used in this device was chosen for its large conversion efficiency. Its cross-sectional area is 5 x 5 mm 2 and it is 1 mm thick. The crystal is cut such that the optic axis is 64.9° to the surface normal. The phase matching condition was that the half angle between the two pulses was 3.5° within the crystal. A l l mirrors are gold-coated stainless steel. The beamsplitter is KC1: coated on one side in order to split the beam equally. A half-wave plate (TT polarization rotator) is required before the autocorrelator since the beam splitter works on the s-polarization: the polarization for which the electric field vector is perpendicular to the plane of the propagation and surface nor-mal vectors. One mirror is mounted on a translation stage which is accurately positioned with a micrometer adjustment. The mirrors in the other arm are carefully positioned to horizontally displace the reflected beam by 16 mm. The beams are recombined in the AgGaSe 2 crystal by a 6 cm focal length KC1 lens. This separation and focal length give the phase matching condi-tion within the AgGaSe 2 crystal. The fundamental frequency is filtered out with a M g F 2 window and the second-harmonic intensity is measured with a Cu:Ge photoconductive detector. The discrimination of the M g F 2 window is not complete; hence, it is necessary to place a field-stop aperture between the crystal and the detector to block the fundamental beams. The background remaining is measured to be insignificant. As mentioned in section 5.3, it would be preferable to use a detector array behind the AgGaSe2 crystal instead of a single detector. It would then be possible to measure the pulse width of each pulse individually in a single shot instead of the cumbersome method of taking many shots, changing the delay after each. Since the individual shots varied a great deal in energy 95 Spectrometer Figure 5.19: Diagram of spectrometer setup. This setup minimizes the effects of small displacements of the beam from the amplifier by focusing that beam onto an input aperture and splitting off a reference signal. 96 /C\ Cu:Ge detector I I Movable ) \ MgF2 Filter Filters out -10.6 Jim / V KClLens Field Stop _ _ Aperture AgGaSe Gold Mirror Figure 5.20: The infrared autocorrelator. This operates in a similar manner to the visible pulse autocorrelator of figure 5.4. However, this device also incorporates a HgCdTe detector to monitor a reference signal, pulse is divided in two 97 and extensive statistical analysis was limited by the fact that the maximum repetition rate was once a minute, the amount of data necessary could be reduced by measuring a reference pulse energy using a second K C l flat within the cavity. The procedure for data analysis will be discussed in chapter 6. The procedure for operation for each shot was as follows: 1. The CO2 laser was checked to ensure that it was operating on the P20 line. 2. The field-stop aperture was opened and the M g F 2 filter was removed while the hybrid laser was fired to ensure that the injected pulse energy was sufficient. 3. The aperture was closed to a diameter of ~5 mm, the filter was put back in place, and the injected pulse was amplified. The signals from the autocorrelator were photographically recorded from the oscilloscope. 4. If a good pulse train was obtained the dye-laser pulse width was checked to ensure that it was ~200 fs long. 5. The delay line was moved and the procedure was repeated. The procedure for aligning the autocorrelator was complicated enough that it could take several hours. In general, autocorrelator alignment would be done only when necessary; instead, the CO2 beam would be carefully aligned into the autocorrelator with steering mirrors directly before it. As with most other systems in this experiment, the infrared beams had to be initially aligned using a HeNe laser. Very careful alignment was done to ensure that the HeNe-laser beam was collinear with the CO2 beam. Then the 632 nm, HeNe beam was used for alignment as follows. 1. The beam reflected from the beam splitter was observed to ensure that the beam reflected from the corner mirrors is displaced by 1.6 mm. 2. The beam was adjusted until centred on the active element of the HgCdTe detector. 3. The beams were adjusted to be equidistant from the centre of the K C l lens. 98 4. The AgGaSe 2 crystal was replaced with a 200 /im pinhole. Both the pinhole and the crystal had to be carefully placed to ensure that the different focal lengths for the alignment and C 0 2 beams is taken into account. 5. An infrared pulse was generated with a single GaAs semiconductor switch and a 10 W C W C 0 2 beam. The mirror and lens before the Cu:Ge detector were adjusted until the transmission was maximized for the pulses which have travelled on each arm. 6. The crystal was replaced. 99 Chapter 6 Experimental results The goal of this investigation is to create short ~ l - p s C 0 2 pulses by semi-conductor switching, then to amplify these in a multiatmospheric-pressure amplifier without the pulses becoming excessively long and without high am-plitude replicated pulses being generated, and lastly to switch out the am-plified pulses. The results will be presented and evaluated in three sections: pulse injection, amplification, and switch-out. 6.1 Pulse injection As the subject of intra-cavity semiconductor injection switching has been unexplored, this work first involves investigation to find the best injection-switch arrangement. Optical pulse generation by various semiconductors has been well investigated (see section 2.3.3 and chapter 4). As well, the use of up to three switches in series has been explored. However, when semiconductor switches are used in an amplifier cavity, some complications are possible. The unexcited switch material may have unusual absorption or pulse-distortion effects which may make their use unsuitable in an amplifier. Also, there may be phase distortion of the pulses created by unavoidably uneven switch excitation. When investigating switch material, efforts are normally made to make the cross-sectional area of the switched beam as small as possible. When used intra-cavity however, other considerations usually make a larger spot size more desirable. A larger area makes homogeneous switch excitation more difficult. There are many advantages to using only a single injection switch. Firstly 100 such an arrangement is much simpler, each additional switch in series com-plicates the set-up due to the need to time and align the visible and infrared pulses at each switch. Secondly, the lower energy requirements of single in-jection switching is advantageous where pump energy is limited. Thirdly, a single-switch arrangement will minimize any pulse-distortion effects caused by the switching process. Fourthly, given that the switching efficiency is significantly less than 100%, the use of a single switch will maximize the pulse energy injected into the cavity. Lastly, as the switching efficiency is dependent on pump energy and the pump energy is not completely stable, the shot-to-shot variation from a double switch configuration should be much greater than that from a single switch. However, the use of two or more in-jection switches may be desirable to increase the contrast ratio or to reduce the pulse width. Therefore, initially, most of the work involved working with only one injection switch within the laser cavity. The following section will discuss that work before the more successful work on double-injection switching. 6.1.1 Single—switch pulse injection Single-switch pulse injection remains incompletely explored. Attempts were made at using a single GaAs or RD-GaAs injection switch within the am-plifier cavity. Most of these attempts were made with a silicon cavity-dump wafer in the cavity as well. There were many successful shots which demon-strated good pulse amplification with a good contrast ratio. However, these results were very unreliable and a large fraction of them had an unacceptably high background level. While GaAs switching produced good pulse ampli-fication, a single GaAs wafer would not reliably produce pulses as short as necessary for this study. While RD-GaAs will produce much shorter pulses, the Brewster-angle reflection is slightly higher and there are concerns that possibly higher absorption within the material will lead to switch damage. Therefore, while this area could be investigated further, double switch injec-tion should, in general, provide better results if there is enough pump power available. While other fast semiconductor materials were available, such as low-temperature-grown GaAs and a superlattice structure, their use as single injection switches was not investigated due to their long pulse tails. 101 616 nm pump pulse 616 nm pump pulse Figure 6.1: Two possibilities for the injection-switch arrangement: (a) the pump pulse is divided in two, (b) the pump pulse reflected from the first switch is directed onto the second. The configuration chosen was (a). The dashed line is the CO2 beam path. 6.1.2 Double-switch pulse injection A few configurations were attempted for double-switch pulse injection. The primary choice to be made is depicted in figure 6.1. In (a) the pump pulses are split in two halves, each of which pumps a switch. The delay of one of them is adjusted before being directed onto the second switch. In (b) all of the pump energy is directed onto the first switch. Since the reflectivity of the switch is very high for visible light, enough is reflected that it can be appropriately delayed and directed onto the second switch. This has the advantage of being more efficient in terms of pulse energy but has the disadvantage of having a much more complicated set-up. The best arrangements should have the minimum possible spacing be-tween the two injection switches. This eliminates the need for an infrared focusing lens or mirror between the two switches. It was not possible to find an arrangement in which the visible pulses could be collected, appropri-ately delayed and directed onto the second switch in a short enough distance. Therefore, the arrangement shown as (a) was chosen and used in all ampli-fication experiments. As for the choice of switch material, 10 1 4 c m - 2 RD-GaAs was chosen for the first switch and GaAs was chosen for the second. While a GaAs -I- GaAs switch combination would give higher energy injected pulses, this was mainly due to the pulses being longer. The RD-GaAs + GaAs switch combination 102 gave short pulses ~2.4 ps long, with good contrast ratio, measured at greater than 105, which was the detection limit with our equipment. The pulse energy with this arrangement was too low to directly measure the pulse length with the autocorrelator setup. The criteria for good switching can be summarized as good contrast ratio, good switching efficiency, minimum shot-to-shot variation in pulse energy, minimal beam distortion, and minimal passive beam distortion effects within the amplifier. A l l of these will be assessed in section 6.2 as they are most easily analysed in the context of amplifier operation. 6.2 Amplifier operation When pulse amplification was working well, a pulse train would be seen reflected from the front laser window as shown in figure 6.2. This example shows a short pulse amplified after injection by a RD-GaAs + GaAs double-injection switch. It is measured with the HgCdTe detector in the standard autocorrelation setup (figure 5.20). The small background seen is the signal through the autocorrelator when the A/2 waveplate was not in place. In this case, the pulse is injected 200 ns before the centre line of the trace and the energy peak is found at the 23 r d round trip. The peak of the current trace is ~150 ns before the pulse is injected. It is found that the gain is constant from where the pulse is first visible until 30 ns before the centre line at (1.55±0.05)x per round trip; after this gain saturation becomes significant. These results are quite representative. The average gain rates, and peak pulse times vary according to parameters such as aperture size, amplifier voltage, and alignment. A set of results taken for one run showed a peak gain variation of 15% and a variation of the timing of the peak pulse of only 12%. Section 6.2.1 will discuss the modelling of the amplifier in order to get good estimates of the parameters involved. It is also instructive to look more closely at the pulse injection and first few round trips. As might be expected from the Frantz-Nodvik equations (3.12-3.14), the pulse energy should start off growing exponentially before the medium exhibits saturation effects. Figure 6.3 shows the pulse injec-tion and first few round trips of amplification. One interesting result is that the pulse here, and in general, is seen to decrease before increasing. If one takes the second to the sixth pulses, these show a constant round-trip gain of (1.87±0.04)x and thus illustrate exponential growth. Extrapolating back 103 / Figure 6.2: A pulse train reflected from the K C l window with RD-GaAs + GaAs double-injection and the GaAs cavity-dumping switch in place but not pumped. The peak of the current trace is (145±10)ns before the short-pulse injection. The pulse injection is 200 ns before the centerline of the trace. The scale settings are -50 mV/div, 20 mV/div, and 50 ns/div. 104 to the injected pulse, one can calculate that only 30% of the injection pulse is amplified. Figure 6.3 also shows the beginning of background C W am-plification starting just after the centre line of the trace. However, it can be calculated that the contrast ratio is still > 70. There are a few possible explanations for this initial decrease. 1. The pulse is injected too soon, while the gain medium is still in the absorption phase. However, this is unlikely as care was taken to inject the pulses when there was sufficient gain. Furthermore, the pulses immediately following the pulses which show absorption show constant gain. 2. There is a small misalignment in the injected beam. But, these results were quite consistent; just realigning the injection beam path might only effect a small improvement. 3. The focusing mirrors could be incorrectly spaced; however, analysis of the beam equations showed that misalignment by a few millimeters should not cause this large an effect. 4. Diffraction effects at the intra-cavity apertures and end mirrors might be responsible. This is a good possibility as the size of the apertures is such that significant diffraction is expected for pure Gaussian beam modes. It would be expected from a detailed analysis that there would initially be a large amount of attenuation until a stable mode formed within the beam parameters. This result is similar to the results of the analysis first done by Fox and L i [95]. 5. There might be effects caused by the injection-switch arrangement. These might include diffraction caused by the finite size of the reflec-tive area on the switch or phase distortion caused by inhomogeneous excitation of the switches. The intensity decrease is probably caused by some combination of the last two effects. Even when the laser was working at its best, the amplification of pulses was not nearly as reliable as desired. One typical result was out of 150 shots, only 15% resulted in short pulse amplification, 5% showed mixed short and long pulse amplification. Two possible explanations for this behaviour will be considered: the effect of timing jitter and the effect of semiconductor and 105 Figure 6.3: Pulse injection and the first-few round trips with RD-GaAs + GaAs double injection and the silicon cavity-dumping switch in place but not pumped. Some detector-saturation effects are seen towards the end of the trace. The scale settings are 500 mV/div and 20 ns/div. 106 window damage. In section 6.2.2 the cause will first be sought in the effects of timing jitter on contrast ratio. It will be found that this only provides a partial explanation. Secondly, the effects of damage to the semiconductors will be investigated in section 6.2.3. Again, this will only provide a limited explanation. Section 6.2.4 will discuss the optical damage observed on the amplifier windows and mirrors and the effect of that and other mechanisms on the pulse amplification. Section 6.2.5 will briefly discuss some experiments that were attempted to increase the total energy extracted from the amplifier through the use of an 'unstable' resonator. 6.2.1 Modelling pulse amplification Modelling of pulse amplification, based on the discussion of sections 3.4 and 3.5 has been undertaken to better understand the physics of the process as well as to compare the results to theory. Such modelling must take into account the many rotational lines that the amplification occurs on and the energy redistribution that occurs amongst all the C 0 2 and N 2 energy levels. Fortunately, the pulse duration is short enough that energy-level redistribu-tion does not have to be taken into account on the pulse time scale. Therefore, the redistribution only has to be calculated once per round trip. As we are not interested in optimizing the physical set-up of the C 0 2 amplifier, we will not model the entire electrical-discharge process but instead assume that it is finished by the time the pulse is injected into the cavity. This is a valid assumption as the pulse is always injected into the cavity at least 50 ns after the end of the current pulse. Therefore, the initial five temperatures of the temperature model discussed in section 3.4.1 will be assumed and treated as the fit parameters for the model. A Fortran program was written to do these calculations. A flow chart for the algorithm is shown in figure 6.4. Firstly, the injected pulse was as-sumed to have Gaussian temporal profile. The spectral profile was then calculated and divided according to the rotational transition by which it would be amplified. The gain experienced by each spectral component was then calculated using equations 3.3, 3.5, 3.6, and 3.7. The effect of the pulse propagation through the gain medium, off the 3-m mirror and back through the gain medium was calculated by multiplying by the Frantz-Nodvik gain factor, calculated from equation 3.14 which takes into account gain satura-tion. Next, the loss factor was multiplied evenly across the spectrum to the 107 energy. At this point the pulse has completed one round trip and the energy distribution should be calculated before the process is repeated. To calculate this redistribution, first the population transfer from the up-per to the lower laser level was calculated. (EL — E0)/hco is the total number of atoms removed from the upper laser vibrational level and transfered to the lower where EL and E0 are defined by equation 3.14. Also, the change in vibrational populations due to energy relaxation can be calculated on a round-trip basis using equations 3.8 and 3.9. Given the new populations and assuming that the intramode relaxation is fast with respect to the round-trip time, the new temperatures can be calculated from the Maxwell-Boltzmann distribution. The major assumptions made for this calculation are summarized as fol-lows: 1. The pulse was short enough that rotational redistribution did not have to be accounted for in the duration of the pulse. This can be justified if the pulse is much shorter than the rotational redistribution time of ~15 ps. 2. The effect of propagating the pulse back through the gain medium without calculating any redistribution was minimal. 3. The rotational redistribution was complete between round trips. 4. The gas temperature, T, is constant. This should be a reasonable assumption for T E A lasers which have a short discharge time [63]. 5. Initially the gain from the hot and sequence bands is assumed to be insignificant. This will be re-evaluated once the temperature of the upper laser level is determined. The results of the modelling for a 1-ps Gaussian pulse are shown in figures 6.5 and 6.6 and the best-fit parameters are listed in table 6.1. The gas temperature, temperature of the v3 and N 2 modes, loss, and injection fluence were varied until the gain of the pulse in figure 6.2 most closely matched the modelled gain on a least-squares basis; that is, the parameter x2 = — Jmodeij)2/o~2, where a is the uncertainty and is assumed to be constant for all the points and 7 is the round-trip gain. It should be emphasized that the fit was done to the gain and not the relative pulse fluences as this would 108 Initialize mode and gas temperatures, loss and injection fluence Calculate relaxation times as a function of gas temperature Calculate saturation fluence as a function of rotational transition (j) Calculate the spectral distribution of the injected pulse as a function of the pulse width Calculate the Boltzmann distribution factors Reinitialize with perturbed variables E injected (j) Apply round trip loss Roundtrip = 1 to 40 E injected (j) j=2 to 60 Calculate E out (j) based on Franz Nodvik equations j=j+2 Calculate number of molecules transfered from upper to lower laser levels X Calculate intermode relaxations for the round trip Calculate new temperatures and Boltzmann factors (effectively redistributing rotationally) Calculate ^from real gain data Figure 6.4: Flow chart for program used to calculate pulse-energy evolution as a function of laser transition. T (395 ± 40) K T i , T 2 (400 ± 96) K T 3 , T 4 (3960 ± 710) K Round-trip loss (36.5 ± 3.3)% Injected fluence 168 / / J /cm 2 Maximum fluence 0.38 J / cm 2 Maximum small-signal gain 0.013 cm" 1 Table 6.1: Best-fit model parameters and modelling results 109 Figure 6.5: Modelling results fitting parameters to data of table 6.1. 110 4000 3000 u a « Ui a E a H 2000 1000 1 1 1 ~" - ^ ~ -T l T2 T3 T4 X X. x \ \ \ \ -•v - -1 , 1 . 1 10 20 Round Tr ip 30 40 Figure 6.6: Mode temperatures corresponding to figure 6.5 and table 6.1. Note that T i ~ T 2 . The temperatures are defined in section 3.4.1. I l l better model the more important amplifier parameters. The results are quite similar for pulses between 1 and 10 ps long. There were five fit parameters; therefore, in order to find estimates of uncertainties, parameters individually varied until the x2 value increased by 5.89 in order to find the region in which 68.4% of points, normally distributed by their uncertainties, would fall [96]. While it would be more conventional to describe these uncertainties as projections onto subspaces of the full pa-rameter space, for a complicated model such as this, these spaces could not be simply calculated. Therefore, the uncertainties listed in table 6.1 were calculated to include the range which caused the total x2 t ° v a r v by the appropriate amount. It can be seen from figure 6.6 that the upper-level temperature, and therefore population, remains fairly constant until the pulse fluence becomes significant with respect to the saturation fluence. Then the effectiveness of the N 2 molecules as an energy reservoir can be easily seen as T 4 follows T 3 . It can also be seen that the lower level remains quite unpopulated throughout due to its efficient coupling to the (02°0) level. There is only a small increase seen when energy is being rapidly transfered to the circulating pulse. Many of the parameters resulting are in reasonable agreement with the known parameters. An upper limit to the temperature of upper laser level and the N 2 vibration can be calculated with some knowledge of the pumping efficiencies. The analysis of reference [56] calculates the pumping efficiencies as a function of the ratio of the electric field to the gas density. For the current investigation, the E / N is approximately 2.6 x 1 0 - 1 6 V / c m 2 . In a gas mix of l : l :8 : :C0 2 :N 2 :He , which is the closest to the experimental mix for which these parameters have been calculated, the pumping efficiency was found to be 54%. Assuming the same energy deposition of 1.33 J / (cm 3 MPa) which has previously been measured for this amplifier [93], the temperature of the (00^3) and N 2 modes will be 5125 K if the energy is deposited almost equally between them. This is in reasonable agreement with the values found through this calculation. A more accurate calculation cannot be made since it is not clear how the extra helium in the experimental gas mix will affect the pumping efficiency. This result, with T 3 = 3960 K is also in agreement with previous work which has measured upper-level temperatures of ~4000 K and also which noted that the upper level temperature increased with decreasing C 0 2 fraction: this experiment utilizes a very low fraction [66]. However, other previous work has noted that temperatures much above 3000 K are very difficult to obtain: most likely due to a decrease of pumping efficiency 112 at the high temperatures [97]. It is expected that the gas temperature remains under 400 K and that the lower laser level temperatures remain close to this due to their fast relaxation times [98]. Indeed, this is what is observed. Similarly the loss of (36.5±3.3)% per round trip is within the range of what might be expected from observations of pulse decay in the cavity with no gain. The resultant injected-pulse fluence of 168 /^J/cm 2 corresponds to a pulsewidth-intensity product of 27 M W ps when taking into account the beam area. This is substantially larger than what could be expected given that the peak power of the hybrid laser is ~120 kW. One more variable which is not in agreement with previous measurements is the small-signal gain. This analysis finds a peak small-signal gain of 0.013 c m - 1 whereas Stuart [93] has found it to be 0.026 c m - 1 for the same mix at 1.0 M P a with the (00°1) to (II) transition. With the higher pressure and (00°1) to (I) transition, the small-signal gain could be expected to be even higher. The adjustment of parameters such as the upper-level temperatures to produce such gains led to clearly non-physical values. However, both these discrepancies might be accounted for if the hot- and sequence-band transitions are included. These were introduced in section 3.4.1. It is often assumed, as a first approximation, that the small-signal-gain ratios of the sequence and hot bands can be estimated by assuming that the lower levels are unpopulated and the ratio is same as the ratios of the vibrational level populations. This assumption neglects the actual transition frequencies and the fact that at high temperatures the populations may start to deviate from Maxwell-Boltzmann distributions [97]. The gain ratios are for the sequence bands where the quantum number, v3 indicates the upper lasing level, (00°v3). The extra factor of v3 is included to take into account a simple harmonic oscillator model [66, 98]. Similarly, the gain ratios of the hot bands to the regular band can be calculated as (6.1) (6.2) and (6.3) 113 Therefore, taking these equations into account, the small-signal gain could be expected to be up to 2.34x greater with T 3 = 3960 K . This is in much closer agreement with the value of the small-signal gain previously measured for this laser body. Also, the much higher than expected injection fluence can be explained as resulting from a higher initial small-signal gain. Therefore, in an attempt to illustrate how the results might change when the sequence and hot bands were taken into account, some refinement of the model was made. The same program was run, however, the gain was increased by the factor given by equation 6.1 for v3 = 2. In doing this, it was implicitly assumed that the higher sequence bands and the hot bands were unimportant and that the lower levels would relax to the (I) and (II) lower levels of the regular-band transition within a round-trip time. This also neglects the shifted spectrum of the sequence band with respect to the regular band and assumes that the stimulated cross sections are the same. The results of these calculations are summarized in table 6.2. When this was done the injected fluence and upper level temperature becomes more realistic, the small-signal gain is closer to what is expected, and the overall fit becomes better. The other input pa-rameters remain essentially the same apart for the loss: a much larger loss is required. The biggest change is that the maximum calculated fluence is now only 0.129 J /cm 2 . However, this result is likely more accurate than the previously calculated one. The new model energies and temperatures are shown in figures 6.7 and 6.8 respectively. It is expected that these results would match the known parameters even more closely if a more detailed model were taken into consideration; however, in order to do so, more details of the sequence-band saturation behaviour and lower-level relaxation would have to be known. While not all the parameters agree to complete satisfaction, the behaviour in the saturation regime should be correct and therefore this should give a good estimate of the peak intensity. In fact, the peak intensities calculated here are in reasonable agreement with the damage thresholds observed. This will be discussed in section 6.2.3. 6.2.2 Effects of timing jitter on pulse amplification Equations 5.5 and 5.6 define the contrast ratio, Ip/Ib, measured by a finite-integration-time detector and reduced by the effects of timing jitter. An analysis can be made to decide if the observed lack of reliability can be caused 114 T (395 ± 40) K T i , T 2 (395 ± 5 1 ) K T 3 , T 4 (2600 ± 77) K Round trip loss (48.0 ± 2 . 1 ) % Injected fluence 52.6 /LtJ /cm 2 Maximum fluence 0.129 J / c m 2 Maximum small-signal gain 0.016 cm" 1 Table 6.2: Best-fit model parameters and modelling results with considera-tion of the first sequence band Figure 6.7: Modelling results from fitting parameters to data of table 6.2 and considering the first sequence band. 115 3000 2000 h 1000 20 Round Trip Figure 6.8: Mode temperatures corresponding to figure 6.7 and table 6.2. Note that T i ~ T 2 and considering the first sequence band. 116 by this timing jitter. The contrast ratio of the injected pulse is T v t J T i c i B . The contrast ratio of the amplified pulse is reduced from this value by terms in the denominator which correspond to the amplified background injected before the short pulse is injected and that entering the cavity after the short pulse is injected. These terms are expanded in equation 5.7. First, some assumptions have to be made about the shape of the hybrid-laser pulse and the shape of the amplifier-gain curve. Figure 5.12 shows the intensity of the hybrid laser as a function of time. Since it is desired to inject the short pulse at the peak of the hybrid pulse, a fit shall be made to this region. The pulse fits well to a Lorentzian curve: A/((t — to)2 + A) with A = 1.066 x 104 ns 2. The gain of the amplifier can also be fit to a curve. Figure 5.12 shows the small-signal gain. The section between the minimum and the peak fits well to a,(t) = 0.022 ( l - exp cm- . ' (6.4) The round-trip gain is 7 = KI exp(ao(t)L) where is the round-trip loss factor and t0 is chosen such that j(t = 0) = 1. As mentioned in section 5.9, it is necessary to investigate cases where the jitter causes both lasers to fire simultaneously early or late. Where one fires early and the other late, the effects counteract each other so this doesn't have to be investigated. The hybrid laser typically had a jitter, tjh, of ±50 ns and the multi-atmospheric-pressure laser typically had a jitter, tja, of ±20 ns. Since the detrimental effects of the jitter should be greatest when the two lasers both fire at the maximum jitter of their ranges, the effects can be most simply i l -lustrated by reducing the points investigated in the (tja, tjh) parameter space to the line tja = 2/5 x tjh- The terms preceding and following the term at the short-pulse injection can be summed and normalized by the term right at the injection time. These can be plotted as a function of the delay of the hybrid laser. The preceding terms become large when the jitter causes the lasers to fire early and the following terms become large when the discharges fire late. Figures 6.9 and 6.10 show the effects of this timing jitter on the four terms preceding and following the pulse injection term for jitter terms in the denominator. This is done for two values of the round-trip loss, 1/3 and 2/3. Perhaps unexpectedly, the curve for the higher gain starts off lower. This is because the gain curve is shifted such that j t = 0 = 1. If the loss is higher, the slope of the gain curve is lower. For the higher-loss value, curve (a), 117 S3 4> > ct ~ 4 PS 1 1 1 1 1 1 1 (a) - - - - (b) -1 , 1 -100 -80 -60 -40 -20 Pulse injection time relative to peak of hybrid intensity Figure 6.9: Effect of timing jitter on the terms corresponding to the four round trips following injection in the denominator of equation 5.7. The round-trip loss is (a) 2/3, (b) 1/3. 20 40 60 80 Pulse Injection Time After the Peak of Hybrid Intensity 100 Figure 6.10: Effect of timing jitter on the terms corresponding to the four round trips preceding injection in the denominator of equation 5.7. The round-trip loss is (a) 2/3, (b) 1/3. 118 which more closely corresponds to the way the laser is usually operated, a sum of all these terms can be considered. If 10 terms are considered for the lower-loss case, five on either side of the zero term, the total does not exceed 6.5 x the reference value at tjh = ±50 ns, and does not exceed 10 x at tjh = ±100 ns. At greater delays the validity of the sum starts to become questionable due to the simple fits assumed for Ih and a0(t). For the higher-loss case, the results are similar. Therefore, the consideration of all the terms in the denominator cannot lead to a reduction of the contrast ratio by more than a factor of ten even in the worst case scenario and this is not large enough to cause the unreliability seen. The injection contrast ratio, rpe/TdetB, can be estimated experimentally by observing the injected pulse. This term is at least 50, limited by the oscilloscope resolution, and varies somewhat mainly due to the pump-pulse energy. If the maximum reduction is only 10 x then the jitter at the extreme values might cause the few cases of pulse amplification on a background of a long pulse. But it cannot be the only mechanism reducing the contrast ratio as the observed effect is much greater. Further explanation has to be sought. 6.2.3 Effects of semiconductor damage on pulse ampli-fication Initially, most of the experiments were attempted with silicon as the cavity-dumping switch. Silicon had been seen as the ideal material for this applica-tion due to the efficient switching as well as the long duration of the reflective phase which greatly simplifies pulse timing. In fact, very good results were obtained for the switch-out contrast ratio as is seen in figure 6.11. Which is an oscilloscope trace of the pulse train reflected from the K C L amplifier window. The sharp decrease near the centre line is caused by the silicon switch being 'turned on' by the green pump laser. However, as is also evi-dent from figure 6.11, there is insufficient contrast to the pulses themselves: the background intensity is too large leading to a contrast ratio of less than 10. The problem of low contrast ratio for the amplified pulse was eventually attributed to non-visible damage to the silicon wafers tried: both a ultra-thin, 50 - /xm - th ick, sample and regular, 300 - / im - th ick samples. This was a very difficult problem to diagnose as the symptoms seemed to point to insufficient contrast ratios for the injected pulses or poor system alignment: 119 120 amplification of the C W beam was not affected to the same extent, only the amplification of the short pulses. Furthermore, taking steps such as reducing the net gain seemed to increase the chances of pulse amplification; yet the background pulse always was seen at an unacceptable level. In order to conclusively diagnose this problem transmission of the short pulses through the wafers had to be closely examined. It was possible to look at the second and later round trips within the cavity in order to measure the round-trip losses. Figure 6.12 shows such a trace with new wafers and figure 6.13 shows the same measurement after a single shot with short-pulse amplification. Damage has apparently increased the loss by 34%. It should be noted that close examination of the timing of this damage showed that the mechanism appeared to be related to the intense short pulse rather than the long natural pulse. This points to an intensity-dependent mechanism rather than an energy-dependent one. While some damage may have been caused by long pulses of, probably, equivalent energy but lower peak intensity this was not observed and a lack of wafers available for destruction prevented further investigation into this matter. Many possible mechanisms exist for this damage. Investigation of the mechanism is complicated since most theoretical and experimental studies of this problem at this1 wavelength have been done on much longer time scales. Nonetheless, the most likely damage mechanism seems to be avalanche elec-tron multiplication in the intense optical field. The scaling of the damage threshold cannot be exactly determined; yet, for this mechanism, it is pro-portional to the beam size and has an exponential dependence on the pulse length [99]. The effect of this damage would have been to deflect or scat-ter the beam on small scales. This was seen in the apparent disappearance of the short pulse. It is unknown why long pulses would still be amplified. Perhaps the long pulses seen were amplified spontaneous emission operating on a cavity mode other than the lowest order, injected one, which was made possible by a lensing effect caused by the damage such as might be caused by rapid local heating. These traces were very difficult to distinguish from pulses which were simply badly timed. In one study, GaAs had more than three times the damage threshold of silicon: 16.5 G W / c m 2 and 5.0 G W / c m 2 respectively [100]. These values can only be roughly compared as small material differences make a big difference in damage thresholds. These values are comparable to the intensities that have been calculated through the modelling (~32 G W / c m 2 if all the energy is concentrated in a single 4-ps-long pulse). 121 10 ns Figure 6.12: Injection and first-few unamplified round trips with new wafers in cavity. The height of the pulse at the centre line is 2.5 div. The reading is with channel 2 which has a sensitivity of -10 mV/div, 10 ns/div. 122 IO MS Figure 6.13: Injection and first few round trips after wafers damaged. Com-parison with figure 6.12 shows the effect on the pulse transmission. The active channel is channel 2 with -10 mV/div and the timescale is 10 ns/div 123 When the silicon wafers were simply replaced with GaAs, pulse amplifica-tion became readily apparent. However, with a GaAs switch in place, switch-ing out the pulse became very much more difficult due to the increased need for timing accuracy due to the very short switching time. One advantage of using silicon as a cavity-dumping switch is that the relatively long-lasting reflectivity easily extinguishes the pulse within the cavity. The GaAs switch often leaves a residual pulse within the cavity which can still be amplified to levels large enough to cause the window to break. Therefore, care had to be taken to not damage the K C l windows. K C l apparently has a much higher damage threshold than either GaAs or silicon. Yet, when short pulses were amplified, these windows would occasionally visibly crack just beneath the outer surface. The placement of this damage occurred at what was probably the position of maximum-field strength, considering that the pulse exiting the laser would be larger due to amplification and reflection at the surface would make the field strength highest just below the exit surface. 6.2.4 Limits to pulse amplification caused by damage to windows and mirrors and by other mecha-nisms While this laser amplifier stored a lot of energy, ~1.6 J / cm 3 [93], extracting all the energy was impossible due to constraints imposed to limit damage to the optical components. Based on the small-signal gain within the C 0 2 medium, round-trip gains up to 3.1x should have been possible (based on the modelled gains with only one sequence band included. However, the gain was always intentionally diffraction limited to less than 2 x in order to avoid damage. At different times damage was observed on both the end mirrors, all the windows (uncoated ZnSe, anti-reflection-coated ZnSe, and KCl ) , and the silicon and GaAs switching wafers. Some attempts to avoid damage while having higher gain were made. Uncoated and anti-reflection-coated ZnSe were used as amplifier windows due to their high damage thresholds. While both seemed more robust than uncoated K C l , eventually they succumbed to visible laser damage as well. However, the mechanism for this damage may have been different as it was manifest as pitting of the outer surface of the material which appeared quite different from the damage to the K C l windows. However, this may have been due to the polycrystalline nature of the ZnSe as opposed to the single-crystal 124 structure of the KC1. Other effects which limited the reliability of the amplifier operation were as follows. 1. The tendency of the positions of the 3-m mirror and the amplifier window to shift slightly due to the laser firing. This would put the amplifier out of alignment after many shots. 2. The tendency of the KC1 flat to plasticly deform under pressure. This would become evident after a few days of operation even though the flat was only 2.5 cm in diameter and 2.5 cm in thickness. Such damage caused the flat to act as a lens. 3. The interior surfaces of the amplifier, including the mirror and the KC1 flat would become coated with the triproplyamine used as an arc suppressant. This would inhibit pulse amplification. The mirror could be easily cleaned after partial disassembly of the laser body but the window could not be cleaned due to the softness and hygroscopic nature o f K C l . 6.2.5 Unstable resonator Attempts were made to operate the multi-atmospheric-pressure amplifier as an unstable resonator. That is, operate with an arrangement such that an arbitrary ray close to the optic axis will not remain within the cavity after a small number of round trips. The configuration used was with an 8-m mirror at the back of the pressure vessel, and a 1-cm-diameter, -5-m-mirror mounted on a KC1 flat 1.5 m away as the front mirror. This is known as a confocal arrangement. The beam could be extracted from around the -5-m mirror, as a partially reflected beam from the laser-body window, or cavity dumped from an additional switch within the cavity Unstable resonators can have an advantage in that their mode volumes can be very large in comparison with stable-resonator configurations. This means that the total energy extracted can be much greater [101, pg. 523]. It was found, with an unstable resonator, that it was very difficult to align both the cavity end mirrors and the beam going into the cavity. Therefore, the beam exiting the cavity was very unpredictable. As well, there were 'hot spots' in the beam. These caused the amplifier windows to crack, damaged the mirrors, and caused sparks to form on the edges of the -5-m mirror which 125 could impair the beam extraction. In the stable amplifier arrangement, it is possible to increase the round-trip loss by closing down intra-cavity irises. If that were done here the possibility of extraction around the front mirror would be eliminated. Furthermore, it isn't clear that this would solve the problems seen: the same hot spots, close to the optical axis, might still arise. With these problems, it was decided to concentrate on a stable-cavity arrangement. However, if an application were to be found which requires a higher total energy than could be provided with a stable configuration, the unstable resonator could be considered with effective cavity dumping to limit the total gain to non-damaging levels. 6.3 Spectral results Measurements were made of the pulse-width evolution using the spectrome-ter arrangement referred to in section 5.11. This was done with both injection switches as well as the cavity-dumping switch being GaAs. A sample picture is shown in figure 6.14. As with other data, the entire pulse train is seen: a portion of the pulse from each round trip is reflected from the amplifier K C l window. The pulse is injected 15 round trips before the centre line of the oscilloscope picture. A portion of the pulse is reflected from a ZnSe flat before the majority is allowed into the spectrometer. In this picture, the larger, leading part to each pair is the reference signal. It should be noted that the signals from the HgCdTe detectors were electronically amplified. Where the base line starts to dip below the zero voltage line is where some saturation effects are seen. Also, on many traces, a detector artifact can be seen at approximately 15% of the total pulse height. Above ~800 mV, the reference channel detector becomes saturated. Results are shown in figure 6.15. Attempts were made to look for spectral width evolution by grouping the data together by pulse round-trip number. There appears to be no clear trend in this respect on the graph. Further attempts were made to look for such a trend by fitting the data from each round trip to a curve. A Gaussian curve was used for simplicity. The param-eters for all the curves were the same within their uncertainties. Therefore, it was possible to get a good picture of the pulse by grouping together all the data and fitting a curve to that. That curve is seen as the solid line in figure 6.15. The spectral width is calculated to be (11±1) nm. This corresponds to 126 Figure 6.14: A sample signal from spectrometer. The larger signal of each pair is the reference signal. The wavelength is 10.592 pm. The scale settings are: left and right channels: 200 mV/div and 20 ns/div. 127 Figure 6.15: Pulse spectrum for GaAs + GaAs injection switching. There is no appreciable change in the spectrum for different round-trip numbers. A Gaussian fit is made to the data; a Gaussian is chosen mainly for convenience as there is not enough data to construct a more accurate pulse shape. r 128 a bandwidth-limited pulse of 15 ps which is approximately what might be expected from a GaAs + GaAs double injection switch. This implies that the lasing occurs primarily on only one line. 6.4 Pulse—duration analysis As described in section 5.12 the temporal pulse width and, to some extent, the pulse shape can be inferred from the autocorrelator signals. Figure 6.16 is an example of the output from the autocorrelator. The entire pulse train is shown, the pulse injection occurs at approximately 50 ns from the left edge of the picture. This trace shows the superposition of the reference signal (left channel) and the second-harmonic signal (right channel). The reference signal has been cable-length delayed to provide a suitable separation between the two. The second-harmonic signal can be easily identified due to its much higher growth rate. The necessary data consists of a large series of such pictures each taken at a known displacement of the delay arm of the autocorrelator. It can be seen that before the gain is exhausted, the 2co signal increases very rapidly such that only a few round trips can be recorded when working with the desired resolution. Different voltage scales on the oscilloscope could be chosen to record different parts of the pulse train. Many attempts were made to measure the pulse width with a GaAs cavity-dumping switch within the cavity. These measurements were made of the pulse train reflected from the KC1 window on the front of the amplifier body. However, it was found that the position of the KC1 window would often shift slightly after a few shots which would dramatically alter the alignment into the autocorrelator. A KC1 flat was introduced into the cavity to try to get around this problem, however, it was found that with this flat in place, short-pulse amplification would not occur with the GaAs cavity-dumping switch in place. 6.4.1 Autocorrelator data analysis Before discussing the approach taken in analysing the data, further discussion of the data is necessary. From a simple analysis, one would expect, given a constant pulse width, that the round-trip gain of the 5.3 jum pulses (as seen on the oscilloscope) would be the square of the round-trip gain of the 10.6 fim 129 Figure 6.16: A sample signal from the autocorrelator. The more slowly grow-ing pulse train is the reference signal and the other is the second-harmonic, autocorrelator signal. The right channel scale is -100 mV/div , the left is -50 mV/div and the time scale is 50 ns/div. 130 pulses. That is, if the pulse intensity, 7, at round trip n is related to the intensity of the previous round trip by the round trip gain, In(t) = 7 J n_i( i) . And the voltage seen on the oscilloscope Vn oc In(t)In(t—r)dt this implies that Vn oc 7 2 K - i -This is definitely not the case. In fact, the 5.3 pm gain is very consistently much higher than the square of the 10.6 pm gain. This is seen even for back-ground traces: that is, shots taken with one of the arms of the autocorrelator blocked. It is also seen very uniformly across the various delays. The most plausible explanation is that the pulse shape is changing. The shape could change as a result of the gain changing during the pulse transit through the gain medium due to saturation effects. Because this effect is seen, any data analysis must take into account the possibility of the pulse shape changing as a function of intensity. Problems in data analysis first arise from the very limited amount of data that could be obtained. The rate of data collection was painstakingly slow; therefore it was necessary to find an efficient method of data analysis. The V2W(T) signal is a function of many variables: the ones which are easily observable are the round-trip pulse number, the gain, and the pulse height. Since the data is taken on a single-shot basis, a collection of single shots must be extrapolated to a collection of representative shots. At least two approaches could be taken to arranging and then analysing this data. 1. The voltages could be grouped simply as a function of pulse number and binned according to voltage for analysis. 2. The data series for Vu and V2U could be fit to curves then interpolation could be done such that a V-jw could be estimated from any given Vu as a function of r. A V ^ T ) curve could be constructed and the width estimated from that. While the first approach is attractive in terms of simplicity and the lack of a need to rely on imperfect models, there is not enough data available. For many reasons, previously discussed in section 6.2, the gain experienced by a pulse in the cavity varies by a very large amount on a shot-to-shot basis. Since a fairly representative sample of 12 data points with the same round-trip index taken on the same day varied by just over 30%, the corresponding signal could be expected to vary by over 60%. With such large variation, it was not feasible to have enough data in each voltage bin to calculate meaningful results. 131 The more reasonable way to analyse the data is to fit the observed pulse trains to suitable curves. It was found that the reference data fit very well to a straight line while the second-harmonic data fit very well to an exponential curve. This was done for all the data using a least-squares method. This is illustrated in figure 6.17. The data is shown as well as the fits to this data with uncertainties. The vertical scale corresponds to the number of divisions on the oscilloscope screen. Therefore, the range of data seen is approximately the maximum number of points that can be reasonably seen for the autocorrelator signal. In order to investigate earlier or later round trips it was necessary to change the oscilloscope amplification scale. Once the curves were fit, a reference voltage, which was within the range of most of the data, could be chosen and a second-harmonic voltage inter-polated. From this data, a fits could be done with test models. This method also facilitated the calculation of suitable uncertainties. While it might have been possible to fit this data in a more complex manner such as in the analysis of section 3.4, firstly, often not enough data to do this well existed; and secondly, the fits obtained are quite good. Coin-cidentally, the portion of the curve that appeared linear corresponds to the maximum sensitivity of the detector and oscilloscope combination without any electronic amplifiers. As was discussed in section 5.3, autocorrelation traces are quite insensitive to changes in specific pulse shapes: especially when experimental noise is seen on the signal. It is quite usual to just assume a particular pulse shape based on the physics of the situation. For our case where the uncertainties are fairly large, the actual shape doesn't matter too much and a Gaussian shape is easy to work with. Therefore, the modelling is initially done with two Gaussians separated by 18.4 ps on a small background. Figure 6.18 shows data for an arbitrary reference voltage of 450 mV. Referring to figure 6.19 for the variable definitions, this fit corresponds to an energy, Vi , and standard deviation , c r i , of the zero-delay peak equal to (340 ±973) mV and (5.8 ±0 .8 ) ps respectively'and V 2 and a 2 of the, r = 18.4 ps, secondary peak of (168 ± 431) mV and (3.2 ± 0.4) ps respectively. Such a fit was done by minimizing x2 = YlilJi — Vfit,i)2/&2, where are the extrapolated points yfitii are the corresponding fit values, and cr, are the calculated uncertainties. Since these uncertainties are highly correlated, figures 6.21 and 6.22 depict the 68% confidence regions for the parameters projected onto the two parameter planes of interest. It is easily seen that these figures do not provide a very accurate description of the actual shape of the uncertainty region as they 132 8 Relative round t r ip Figure 6.17: Sample data: autocorrelator signal (o) and reference data (o) and fits (solid lines) and their uncertainties (dotted lines) for a delay corre-sponding to -4 ps. The fits were used so that a second harmonic voltage level could be extrapolated from a given reference signal voltage. 133 40 Time Delay (ps) Figure 6.18: The complete autocorrelation ( V 2 w for a reference voltage (V w ) of 450 mV. The second-harmonic signal is interpolated from the data as described in the text. The best fit curve is the sum of two Gaussians separated by 18.4 ps. include unphysical values. The reason for this is that the extent of the elipse is derived from gradient values at the best-fit point. However, they do provide a reasonable estimate of the size of the uncertainties which is sufficient for this work. The fit shows a fairly broad central peak which contains most of the energy and also a large secondary peak with approximately half the energy of the primary. This indicates that a pulse train is fairly well developed. For the 450-mV data, the ratio of the peak voltage of the secondary peak to that of the primary peak is 0.95. In order to get such a high ratio, it is necessary to use a long, well-developed pulse train. A first approximation of what the coherent pulse train might look like was developed in section 3.5.2 and is depicted in figure 3.5. It is very easy to computationally generate the autocorrelation of the pulse-train functions. It was found that the ratio of 134 Figure 6.19: Description of autocorrelation fit variables. Vi* = Vi/(v /27ro'i) and V2* = V2/{V2^o-2). the voltages of the first two pulses in the autocorrelation signal were almost entirely a function of a0L, the logarithm of the total gain experienced by the pulse in the model system since any saturation effects are neglected. The value which matched the data for a reference voltage of 450 mV was a0L = 29.4. The autocorrelation function was found to be extremely sensitive to the input pulse width. Figure 6.20 compares the autocorrelation function for an input pulse 4 ps long to the best fit for the 450-mV data. For longer pulses the individual pulses tend to merge together. It can also be seen that the points are much more scattered in the 18.4-ps peak than in the r = 0 peak. The energy in this peak is related to the energy in the trailing pulses in the pulse train. This analysis was done assuming that the rate of change in pulse shape was solely a function of the pulse intensity. However, the situation is slightly more complicated. A number of processes are capable of changing the pulse shape. The processes underlying the Frantz-Nodvik equations (3.12 and 3.13) tend to shorten pulses as the leading edge of the pulse will experience higher gain under saturation. Of course, this is complicated by the different saturation levels of each of the laser transitions. Also, any shortening of the pulse has to be supported by the gain bandwidth. If the pulse is already near the bandwidth limit then it cannot become shorter unless the bandwidth is expanded. If parameters such as the small-signal gain were fairly constant on a shot-to-shot basis and if the short pulses transversed the gain medium only once then it could 135 -10 0 10 20 Time delay (ps) 30 40 Figure 6.20: Calculated autocorrelation signal for an unsaturated C 0 2 med-ium with a0L — 29A and a 4-ps Gaussian injected pulse, (a) is the calculated pulse-train autocorrelation, (b) is a fit to the data, (c) is the uncorrelated injected pulse shape. 136 Figure 6.21: Confidence region for voltages for 450-mV data. The scales are in mV. be expected that the rate of change in the pulse shape would be a function of intensity (as long as the injected intensity is well below the saturation fluence). However, because the pulse experiences losses when not in the gain medium and because there is significant redistribution among energy levels between cavity round trips the pulse does not have a monotonically increasing E / E s and therefore the dependence of the rate of change of pulse shape is a function of more than just the intensity. This dependence on other variables appears as a large scatter of the experimental point about the fitted line for the T = 18.4-ps peak. Analysis similar to that illustrated in figure 6.18 can be made for other reference voltages. This was done primarily to investigate if the pulse shape was varying with time. Figure 6.23 shows the fits obtained for four different reference voltages normalized to the value at the zero delay position. While there is apparently some difference, all these curves are essentially the same to within experimental uncertainty therefore no conclusions about the pulse-shape evolution can be made from this data. However, at earlier times, the pulse is injected as a single peak; therefore pulse-shape evolution must occur. Furthermore, it is expected that the greatest change in pulse shape will occur at the greatest saturation since the differing levels of saturation of each of the lasing transitions will lead to the greatest changes in the pulse spectrum. There was very little data obtained for this intensity region and therefore no 137 -5 0 2 4 6 8 ° 1 Figure 6.22: Confidence region for a values for 450-mV data. The scales are in ps. conclusions can be made as to whether this occurred. 6.5 Pulse switch out In order to maximize the pulse energy available to applications, it is desirable to completely switch the circulating pulse out of the amplifier cavity. This technique is called cavity dumping. Additionally, it should be possible to improve the contrast ratio of the pulse with respect to trailing pulses. If there are trailing pulses which follow the main pulse in intervals of 18.4 ps, the switching time of a GaAs switch is fast enough that only the pulse desired can be switched out. Furthermore, it should be possible to use an ultrafast semiconductor, such as RD-GaAs, as the switch to actually shorten the pulse as it is being switched out. It was attempted to switch out the pulses with both silicon and regular GaAs. With GaAs it was possible to discriminate against unwanted pulses and with silicon it was possible to extinguish the circulating pulse within the cavity. It was found that, with GaAs, while the switching efficiency was not good enough for complete cavity dumping, it was good enough to switch out pulses. Figure 6.24 shows a pulse train reflected from the K C l window. At one round trip before the centre line, the effect of the cavity-dumping switch can be seen. Almost 50% of the energy is switched out from the pulse circulating within the amplifier. To look at this from another perspective, 138 300 mV 450 mV Delay (ps) Figure 6.23: Autocorrelator pulse-shape evolution for differing reference volt-ages. 139 figure 6.25 shows a reflected pulse from the same wafer. The contrast ratio is very high; however, there is definitely some background. The remainder of the pulse starts to come up four round trips later. It should be noted that the oscilloscope trigger delay timing is slightly different for figures 6.24 and 6.25. It should also be noted that the efficiency of the switch-out might be improved through better alignment and timing. The optimization of the timing would involve the analysis of many pictures such as figure 6.24 with slightly different delay times. The timing could probably be optimized on a scale of less than a millimeter out of a total path length of tens of meters. As mentioned, the use of fast switching could be used to discriminate against the inevitable secondary pulses which follow at 18.4-ps intervals after the main pulse. Unfortunately, the use of a GaAs switch-out switch could not eliminate the high intensities which led to optical damage. Many attempts were made to switch out the optical pulses while their intensity was still below the damage threshold. However, often, enough energy would be left circulating within the cavity such that damage would still occur after these pulses were further amplified. It should also be noted that no attempts were made to switch out the pulses later (after ~25 round trips), when the pulse energies would be higher. This was because this amount of delay (~160 ns) implied a physical delay of ~50 m and the reflection off 10 mirrors. The diffraction effects, beam divergence, and energy loss due to imperfect reflection made switching less efficient with longer delays. While longer delays are definitely possible, this length of delay was good enough for a proof of principle. As discussed in section 6.2.3, in order to try to improve the cavity-dumping efficiency and to avoid optical damage within the amplifier cavity, silicon was used as the cavity dumping switch. With the long reflectivity duration of silicon, the need to accurately time the switch-out was much reduced. Also, it was possible to completely extinguish the pulse within the amplifier. Again, figure 6.11 shows the effect of the switch-out switch very well. Unexpectedly, at just over 50%, the cutoff efficiency of silicon isn't that much greater than that for GaAs. Therefore, the only advantage to using silicon would be that it is possible to extinguish the pulse within the cavity: the reflectivity lasts for more than a single-round-trip time. The second, pulse after the cutoff could be assumed to be ~270 mV if the gain increased at the same rate as before as in the GaAs case. Instead it is less than 30% of this. However, of course, the damage probability makes silicon unsuitable for use 140 SO n< Figure 6.24: Pulse train with GaAs cavity dumping. The cavity-dumping switch is excited one round trip before the centre line: -1 V / d i v and 50 ns/div. The apparent subpulses seen are an artifact of the detector responding to a large signal. 141 $0 H$ Figure 6.25: Pulse switched out using a GaAs switch. The pulse train aris-ing near the centre line shows that the cavity-dumping switch is not 100% efficient and that there is a small residual reflectivity even at the Brewster's angle. The peak of the switched out pulse is ~3 V above the base line. The voltage sensitivity is 500 mV/div and the time scale is 50 ns/div. 142 as a semiconductor switch in a high gain setup. 143 Chapter 7 Conclusions The main objectives of this study were to: • create short pulses by semiconductor switching; • efficiently amplify the pulses in the large-bandwidth, multiatmospheric-pressure C02- laser amplifier; and • use semiconductor switching to cavity dump the picosecond pulse. With respect to these objectives, the study was largely successful. This chapter will summarize the results and discuss them in the context of future experiments. 7.1 Pulse injection Pulse injection was successful in that it was possible to generate short pulses with energies, beam quality, and duration sufficient to be amplified by the multiatmospheric-pressure C O 2 amplifier. The use of a semiconductor injec-tion switch inside an amplifier cavity had not been previously demonstrated. It was mentioned in section 6.1.1 that, for simplicity, it would be desirable to use only a single injection switch. While the feasibility of this has not been completely investigated, it should be remembered that damage to the semiconductor switches was always a concern throughout the experiment and therefore ultrafast-recombination-time semiconductors which have slightly higher absorption might not be entirely suitable since they may be more susceptible to damage. Double switching had a considerable advantage in 144 that the more damage resistant but longer-pulse switch could be placed in the cavity to inject pulses from a faster semiconductor switch. If a laser is operating near the semiconductor damage threshold, this has a significant cost advantage. The expensive, engineered semiconductors are protected from damage; whereas the mass-produced intra-cavity wafers can be cheaply replaced when damaged. The best configuration for double-switch pumping employs a beam split-ter which divides the pump beam in two, as was shown in figure 6.1 (a). It was found that the 300-//J energy produced by the commercial dye amplifier was not enough for efficient switching with a double-switch arrangement. Therefore, a further dye amplifier was constructed with a further 5x ampli-fication. This allowed the switches to operate with an efficiency of ~50% each. Two combinations were tried for the double switch: both employed GaAs as the intra-cavity switch. One also used GaAs as the first switch and the other used radiation-damaged GaAs. It was found that the pulse length of the GaAs 4- GaAs arrangement was not short enough to match the full bandwidth available with the 1.24-MPa CO2 amplifier. The injection switching can also be deemed successful in that the back-ground reflection was low enough (the contrast ratio was high enough) that short pulse-amplification should be expected reliably. Therefore, this work presents an improvement to previous injection ar-rangements. In section 2.4.2 it was mentioned that the first injection scheme employed a hole in the amplifier end mirror through which the pulse was injected [38, 39]. Obviously this is inefficient; there will always be significant losses due to the mode of the injected pulse differing from the cavity mode. The most recent work with CO2 lasers employed pulse injection by reflection from an amplifier pressure-section end window [41]. This is inefficient due to a small coupling efficiency. Furthermore, problems with this technique can be foreseen in that our experiment employed a relatively large aperture at high pressures; it was found that the end window shifted significantly with time due to shock waves in the gas caused by the electrical discharge. While considerable effort was invested to ensure that the mode of the injected pulse would match the lowest-order cavity mode, it was found that the injection efficiency was only ~30%. Some of this low efficiency might be attributed to attenuation at the intra-cavity irises: however, a lot of that must also be attributed to either phase distortion or diffraction effects at the switch. 145 7.2 Pulse amplification The injected pulses were successfully amplified in the multiatmospheric-pressure amplifier. Although the pulse fluence was not successfully mea-sured, it was found through computer modelling that the pulse fluence was ~0.13 J /cm 2 . If the pulses are 4 ps long and have most of the energy concen-trated in the leading pulse, this corresponds to a intensity of ~33 G W / c m 2 . As with many other C O 2 amplifiers [41], optical-damage thresholds limit the amount of amplification possible. It was thus necessary to limit the gain by introducing diffraction losses through the use of intra-cavity irises. Single-shot autocorrelation was performed on a series of pulse trains. It was found that, in a region where the pulse intensity was increasing linearly, the autocorrelation corresponded well to an injected pulse width of ~4 ps with a well- developed coherent pulse train. It did not appear to be changing with time. While it was expected that evidence would be seen for pulse-width evolution due to the fact that the 5.3 pm wavelength round-trip 'gain' was much higher than the 10.6 //m gain, autocorrelation evidence for this was not seen. However, the effect might be more obvious if measurements were performed later in the pulse train. The spectral width of the amplified pulses from a GaAs + GaAs dou-ble reflection switch was found to be (11±1) nm which corresponds to a bandwidth-limited Gaussian pulse ~15 ps long which agrees with the pulse length expected from such an arrangement. Modelling was done of the pulse amplification. This appears to be the first computational study of picosecond-pulse amplification in a multiatmospheric-pressure C 0 2 medium which takes into account rotational and vibrational energy-level redistribution with nanosecond roundtrip times, and sequence-band transitions. It was found that the reliability of the amplification was poor ( 15%). There was a large tendency for the short pulses to appear on a ~0.2 ps background, or for just the background to appear. Analysis was done to check if it was possible if the relatively large timing jitter seen for the C O 2 hybrid laser could cause such an effect. This was found not to be the case in section 6.2.2. The maximum decrease in the contrast ratio caused by the large jitter was calculated to by ~6.5x at the observed jitter. As the injected contrast ratio was at least 50, the effect of the jitter is not large enough to explain the observed effects. The most likely explanation for the the lack of consistent amplification 146 was damage to the semiconductors. Damage to the semiconductor switches was possible when high intensities were present within the cavity, usually during short-pulse amplification. It was also found that silicon was far more likely to be damaged than GaAs. The energies calculated from modelling were close to the damage thresholds for these semiconductors. 7.3 Cavity dumping Attempts were made to switch the amplified pulses from the cavity efficiently. It was found that with both silicon and GaAs, the maximum switching ef-ficiency was only ~50%. This is a surprising result in that it had been expected that the silicon would show a greater efficiency due to its greater absorption depth for the pump-beam wavelength and due to the reduced need for millimeter-scale delay alignment from its long recombination time. Though the efficiency was lower than desired, it is believed that this is still the first demonstration of semiconductor-switch cavity dumping in the mid-infrared. However, while doing experiments to measure the pulse duration, it was not possible to amplify short pulses with the semiconductor cavity-dumping switch in place since it was necessary to insert an extra K C l flat in the cavity. If a single-shot autocorrelator were available, it would be interesting to look at these pulses and see if the main pulse could be adequately separated from the pulse train using a intra-cavity cavity-dumping switch. 7.4 Conclusions and suggestions for future work This work has demonstrated an efficient scheme for injection locking a 1.24-MPa-pressure C O 2 laser amplifier with ~4-ps pulses through semicon-ductor switching. It has also shown that it is possible to switch, out such pulses also using semiconductor switching, perhaps eliminating inevitable trailing pulses in a coherent pulse train in the process. It was found that the limitations to.greater pulse amplification were mainly in optical dam-age: primarily to semiconductor switches and secondarily to K C l and ZnSe windows. 147 Therefore, as the motivation for this work was the generation of high-power short (<10 ps) pulses, the obvious next steps would be to use the knowledge obtained to minimize the possibility of optical damage, and to maximize the energy and reduce the duration of pulses switched out of the cavity with semiconductor switching. If attempts were to be made to select only one pulse in the pulse train, improvements would have to be made to the ultrafast pump-pulse system as currently there is not enough energy in the system to efficiently pump an additional switch. Another route to take would be to attempt to reduce the intensity of the trailing pulses in the pulse train. These pulses should be reduced when the laser is operating more in the saturated regime. 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