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Design, construction, and characterization of an interference-filter stabilized external-cavity diode… Bowden, William; Quentin, Damien; Sun, Jon-Paul Apr 4, 2011

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    Design, Construction, and Characterization of an Interference- Filter Stabilized External-Cavity Diode Laser    William Bowden Damien Quentin Jon-Paul Sun  Project Sponsors: Dr. Kirk Madison Dr. Bruce Kapplauf  Group 1120 Applied Science 459 Engineering Physics Project Laboratory The University of British Columbia April 4, 2011      ii  Executive Summary As scientists understand more about the principles of atomic physics, they need tools which allow them to conduct precise measurements which reveal the fundamental properties of the building blocks of matter. One of the most important of these tools is the laser—a coherent light source with well defined frequency—that is capable of exciting and even cooling atoms. In this report we develop techniques for measuring the linewidth and stability of narrow bandwidth interference filter-stabilized external cavity diode lasers. Based on the characterization of two prototypes lasers, we identified key design parameters affecting laser linewidth and stability. Using these results, we designed a monolithic, hermetically sealable, diode laser using the same interference based feedback system. Using characterization techniques found in literature, such as self-heterodyne and heterodyne interference linewidth measurements, we measured an upper limit for the prototype diode laser linewidth of 10 kHz. This is significantly less than the upper limit of 100 kHz defined in the project proposal. We ensured the output was stable and capable of continuous single mode operation using a Fabry–Pérot interferometer. Precise focal lengths of optical components within the cavity were measured using a conventional knife-edge technique. The effects of misalignment on laser performance were investigated to provide reasonable tolerances for machining and adjustment ranges of components. The optical transmission of a commercial and a custom manufactured interference filter were characterized using variable angle transmission tests. This data was used to determine the tuning range and precision of the optical filters within the cavity to achieve the desired frequency range and sensitivity of hundreds of GHz and 1 GHz respectively. We have demonstrated that the desired performance characteristics can be achieved using interference filter-stabilized diode lasers. Therefore, we recommend a more robust laser should be fabricated whose design is outlined and justified in this report. This monolithic design will have improved stability and increased sensitivity to frequency tuning. This device must be characterized using the methods developed when testing the prototype lasers to ensure it meets its performance specifications. We outline issues with these testing methods and explain why we believe a conventional heterodyne measurement using two lasers would provide more accurate results than the self-heterodyne measurement. However, this will require the implementation of a control system to lock the lasers together to limit drifting of the beat frequency. This drifting is currently preventing accurate linewidth measurements. After completion of the above mentioned experiments and performance goals for the laser are met, multiple laser units can be manufactured for general use for atomic physics applications.      iii   Contents Executive Summary ....................................................................................................................................... ii Introduction .................................................................................................................................................. 1 Discussion...................................................................................................................................................... 3 Theory ....................................................................................................................................................... 3 External Cavity Design ........................................................................................................................... 3 Collimator Lens ..................................................................................................................................... 4 Half-wave Plate ..................................................................................................................................... 4 Beam Splitter......................................................................................................................................... 4 Interference Filters................................................................................................................................ 5 Piezo Controlled Cavity Mirror .............................................................................................................. 6 Laser Housing ........................................................................................................................................ 6 Temperature Control System ................................................................................................................ 7 Applications of Diode Lasers ................................................................................................................. 7 Methods and Testing Protocol .................................................................................................................. 8 Component Alignment .......................................................................................................................... 8 Beam Focus / Profiling .......................................................................................................................... 9 IF Filter Transmission Test................................................................................................................... 10 Fabry-Pérot Interferometers for Single Mode Selection .................................................................... 10 Self-heterodyne Linewidth Measurement .......................................................................................... 11 Two Laser Heterodyne Interference Linewidth Measurement .......................................................... 12 Experimental Equipment ........................................................................................................................ 13 Results ..................................................................................................................................................... 16 Discussion of Results ............................................................................................................................... 20 Knife-Edge Diffraction Test ................................................................................................................. 20 Interference Filter Transmission Test ................................................................................................. 21 Self-Heterodyne Linewidth Measurement ......................................................................................... 22 Sources of Error in the Self Heterodyne measurement ...................................................................... 23 Two Laser Heterodyne Linewidth Measurement ............................................................................... 23 Conclusions ................................................................................................................................................. 24  iv  Project Deliverables .................................................................................................................................... 25 List of Deliverables .................................................................................................................................. 25 Financial Summary .................................................................................................................................. 26 Ongoing Commitments ........................................................................................................................... 27 Recommendations ...................................................................................................................................... 29 Appendices .................................................................................................................................................. 30 Appendix A: Frequency Noise Model ...................................................................................................... 30 Appendix B: Laser Design ........................................................................................................................ 32 Appendix C: Diode Protection Circuit ..................................................................................................... 71 Appendix D: Self-Heterodyne Linewidth Measurements ....................................................................... 72 Appendix E: Python Code for Fitting Self-Heterodyne Linewidths ......................................................... 83 References .................................................................................................................................................. 89     v  Figures Figure 1. Schematic of basic diode laser [1].................................................................................................. 3 Figure 2. Schematic of an external cavity laser............................................................................................. 4 Figure 3. Polarization beam splitter. ............................................................................................................. 5 Figure 4: The two interference filers (IF) are multiplied together and the overlapping area is the transmitted region. ....................................................................................................................................... 6 Figure 5.  Method for aligning the laser beam in the cavity. ........................................................................ 8 Figure 6. Light output of a laser diode as a function of supply current. ....................................................... 9 Figure 7. Knife-edge laser beam profiling. .................................................................................................. 10 Figure 8. Output spectrum of a single mode laser in a Fabry-Pérot cavity. ............................................... 11 Figure 9. Self-heterodyne linewidth measurement. ................................................................................... 12 Figure 10. Experimental setup for the two laser heterodyne linewidth measurement. ............................ 13 Figure 11. Thorlabs LDC 500 laser diode controller .................................................................................... 13 Figure 12. Thorlabs TEC2000 temperature controller. ............................................................................... 13 Figure 13. Thorlabs MDT694A single channel piezo controller. ................................................................. 14 Figure 14. Tektronix TDS 2004 oscilloscope. ............................................................................................... 14 Figure 15. Agilent E4407B spectrum analyzer. ........................................................................................... 14 Figure 16. Ando AQ-6135A optical spectrum analyzer. .............................................................................. 15 Figure 17. Coherent LabMax 10 power meter. ........................................................................................... 15 Figure 18. Protoype laser. ........................................................................................................................... 15 Figure 19. Table top setup of the prototype lasers and optics ................................................................... 16 Figure 20. Gaussian beam waist profile. ..................................................................................................... 17 Figure 21. Focal length vs. cavity length. .................................................................................................... 17 Figure 22. Transmission vs. incident angle for the 3nm interference filter. ............................................... 18 Figure 23. Transmission vs. incident angle for the 0.3 nm interference filter. ........................................... 18 Figure 24. Self-heterodyne linewidth measurement for a 230 mm cavity with simulations. .................... 19 Figure 25. Final design for the cat’s eye lens mount. ................................................................................. 21 Figure 26. Final design for the interference filter mount assembly. .......................................................... 22 Figure 27. Surface mount PCB design of diode protection circuit. ............................................................. 71 Figure 28. Circuit diagram of diode protection circuit. ............................................................................... 71 Figure 29. Spectra from first test of linewidth dependency on cavity length. ........................................... 73 Figure 30. Spectra from second test of linewidth dependency on cavity length. ...................................... 77 Figure 31. Spectra from test of linewidth dependency on feedback ratio. ................................................ 79 Figure 32. Linewidth and threshold current as the feedback ratio is varied. The linewidths attained for this graphs were done by a rough eyeball estimate of the lorentzian peaks of the spectra in Figure 31. . 79 Figure 33. Spectra of 240 mm cavity length as the distance between the mirror and cat’s eye lens is varied. The spectra have been overlaid and offset to make them overlap in the center. ......................... 80 Figure 34. Spectra taken using the Thorlabs LDC 500 current driver as the cavity length is changed. The spectra have been overlaid and offset for easier viewing. ......................................................................... 81  vi  Figure 35. Overlaid spectra of the Thorlabs LDC 500 current driver and the custom current driver. For each cavity length the Thorlabs driver is the darker line. The spectra have been given offsets for easier viewing. ....................................................................................................................................................... 82        1    Introduction This report summarizes a list of recommendations for the UBC QDG Lab that are essential for the use of the external-cavity diode laser (ECDL) for its intended purpose.  A final design for the ECDL has been submitted to the UBC Department of Physics and Astronomy Machine Shop, and the final product will need to be tested and characterized before it can be put into operation.  The ECDL project was started for the purposes of building a low-cost and functionally robust master laser with a very narrow linewidth.  In recent years, atomic physicists have turned to diode lasers as a relatively cheap and effective alternative to conventional coherent light sources for their research. Being both small in size and not requiring elaborate cooling systems, diode lasers can be easily incorporated into most optical systems.  Traditionally, diode lasers could not compare in wavelength coverage and output power to traditional dye lasers, but technological advancements have expanded their potential applications. Furthermore, due to the inherent semiconducting properties of diode lasers, the output amplitude is stable and can be tuned for sensitive absorption or fluorescence measurements [1].  The objectives for this project are to design, construct and characterize an interference-filter stabilized ECDL. The laser housing is to be mechanically robust, such that acoustic vibrations and temperature fluctuations and gradients do not significantly modulate the amplitude or frequency of the emitted laser.  The housing will be portable and mountable to a standard optics table, and will have the ability to be hermetically sealed and evacuated.  The housing will accommodate interchangeable components, namely diode lasers, lenses, interference filters and beam splitters that can easily be mounted without additional parts.  A mirror mounted to a piezoelectric transducer with the ability to be PID controlled will maintain the length of the external cavity.  The diode laser and housing will each be thermally stabilized with Peltier devices.  This monolithic device will contain all the necessary control circuitry, as well as a protection circuit for the laser diode.  The output wavelength of the ECDL should be tunable over nanometers about the native wavelength of the diode laser, which will be in the visible to telecom emission spectrum.  This output should be stable in both frequency and amplitude, with less than 1 part in 105 attributed to noise.  The overall design of the ECDL should result in a laser that can be used for laser cooling applications.  The desired atoms to be cooled and their required laser linewidths are 1 MHz for lithium and rubidium, and 100 kHz for ytterbium.  The power of the laser is dependent on the diode and the application, but will typically range from tens to hundreds of milliwatts.  The fully assembled ECDL will be characterized by its wavelength tuneability, amplitude and frequency stability, and laser linewidth.  The successful product is to be replicated, on the order of 5 to 10 units, for atomic and molecular optics experiments.  This report serves as a detailed description of the development and optimization of experimental techniques necessary for characterizing narrow linewidth diode lasers. These methods were used to 2    characterize the performance of two prototype interference-filter stabilized lasers and investigate key design parameters important for stability and a narrow linewidth. The results of these experiments guided the design of a monolithic, hermetically sealable, diode laser using the same interference-filter feedback system.  Once constructed, this laser’s linewidth and stability must be characterized before being used to ensure it meets the performance requirements necessary for its intended application. The required experimental equipment and optical setups are available in the QDG labs, and the characterization must be completed before multiple units are to be constructed. Due to the limited time-frame of this project, this report does not address specific considerations such as thermal flow analysis and fabrication cost optimization.  The thermal cooling design is based on research into similar external cavity laser designs and was not quantitatively assessed. The design of the laser was driven by optimizing performance and assumed a low reproduction quantity. Therefore industrial design considerations will not be addressed in this report.  This report begins by introducing the background theory of the ECDL, and gives a detailed outline of all the components comprising the laser setup. Specifically, the collimator lens, half-wave plate, beam splitter, and the piezo-controlled mirror. Then, an overview of the methods and testing protocols are presented, such as the alignment of the components, measuring the focal point of the cavity lens, and the use of the Fabry-Pérot interferometer. Results are then presented and discussed detailing data collected from all the experiments, along with sources of error. Conclusions are then drawn from the results of the experiments. Following these discussions, project deliverables are listed as a follow-up of the project proposal, along with a financial summary of the costs associated with the project and ongoing commitments by team members. Finally, the report is concluded with a discussion on project recommendations to outline directions to be taken after the submission of this report.      3    Discussion Theory A typical diode laser operates by sending a current though the active region of a diode sandwiched between two n and p doped layers. This injection current produces free electrons in the conducting band and holes in the valence band. For direct band gap semiconductors, electron-hole recombination leads to a photon being emitted. The wavelength of the light is determined by the energy gap between the bands. Figure 1 shows a schematic of a standard diode laser.  Figure 1. Schematic of basic diode laser [1].  For a device to operate properly, coherent light must be generated through stimulated emission - a process where excited electrons recombine when stimulated by photons with energy matching that of the band gap. This requires two conditions: first a population inversion must be achieved by electrical pumping and secondly, there must be a resonator that keeps photons contained within the device to stimulate further emission. When the losses of the system are overcome by the system’s gain, which occurs when the current reaches the threshold level, the device will lase [2].  External Cavity Design As mentioned above, a resonator keeps emitted photons confined to the device in order for stimulated emission to occur at a substantial rate. Typically, this is achieved by coupling the light to an external 4    cavity with feedback mirrors. The cavity can also control certain spectral properties. Figure 2 shows a basic design for the external cavity.  Figure 2. Schematic of an external cavity laser.   Collimator Lens As a result of the scale of the active region, the emitted laser beam is highly divergent—in some cases up to 90: *2]. Therefore, at the output of the laser a collimator with a high numerical aperture must be placed to collect the emissions. For best results, the collimator should be free of spherical aberration and have a maximum spot size on the order of the dimensions of the active region.  Half-wave Plate The half-wave plate rotates the plane of polarization and thus decouples the polarization from the spatial mode orientation. [4] By controlling the polarization of the beam, the feedback to output ratio of the beam splitter can be set.  Beam Splitter The beam splitter controls the ratio of output power to feedback power. This ratio must be optimized for each device to achieve the necessary feedback to sustain lasing. The output ratio is defined by the polarization vector of the light with respect to the surface of the cube; therefore the wave plate can set the fraction of the beam that is emitted.  By opting for a beam splitter over partial reflective mirrors, this ratio can be easily adjusted without switching components.  Figure 3 shows how a beam splitter cube transmits and reflects light of different polarizations. 5     Figure 3. Polarization beam splitter.   Interference Filters Two of the key properties of lasers for atomic physics are output frequency and linewidth. The laser’s source must be tuned to particular atomic transitions of interest, with a narrow spectral output. A narrow linewidth is important since it maximizes the amount of energy at the desired frequency and thus increases the probability of absorption. Free running diode lasers do not provide the necessary linewidths needed for atomic cooling, and external filters are needed to increase the quality factor of the output. Two interference filters placed at set angles with respect to each other may be used instead of one custom filter due to budget constraints - custom filters can cost up to $10,000. Interference filters have been shown in the literature to work effectively to select the desired wavelengths with narrow linewidths [5]. Wavelength discrimination using an interference filter utilizes multiple reflections within its dielectric coatings and can be modeled as a thin Fabry-Pérot etalon. The transmitted wavelength is given by:                   (1) where λ is the output wavelength, λmax is the wavelength at normal incidence, θ is the angle between the beam path and filter, and neff  is the effective refractive index [5].  The interference filter is a Gaussian band pass filter. Changing the angle of both filters together sets the wavelength, while changing the angle between the two filters sets the linewidth. This can be seen in Figure 4.  6     Figure 4: The two interference filers (IF) are multiplied together and the overlapping area is the transmitted region.  It is clear that the product of two Gaussians is also a Gaussian. Figure 4 illustrates a key point - increased linewidth comes at the cost of output power. The filter also helps to suppress the other modes of the laser. This design was chosen over a diffraction based filter system, such as the Littrow arrangement, because wavelength discrimination and the optical feedback are performed by two independent elements. Also, diffraction arrangements are ultra- sensitive to misalignments due to increased beam width.  Piezo Controlled Cavity Mirror The final optical component within the cavity is the piezo controlled mirror. The mirror reflects the emission back into the laser diode to sustain lasing. The cavity of the laser must be a multiple of the wavelength. Since the laser operates with wavelengths in the visible and infrared regime, the cavity length must be stable with a high degree of precision - hence the need for the piezo control.  Laser Housing The optical components and laser diode must be securely housed in a sealed container. The laser’s housing must be rigid to minimize vibrations, and be able to sustain a vacuum within the cavity so that water does not condense on the laser diode when it is cooled below the dew point. The laser’s design should be modular and allow for the exchange of optical components for various experimental tasks. Fine optical adjustments should be possible during operation without breaking the vacuum seal. This will require external electrical controllers. The device will be mounted to an optical table where real estate is 7    valuable; therefore the device should have a small footprint.  Another design concern is temperature stability. Thermal expansion and contraction of the housing will cause wavelength instability. A temperature control system must be implemented. Finally, the total length of the laser cavity must be considered.  The performance of the laser will be characterized by its Q factor.  The Q factor is a ratio of the energy stored in the system to the energy lost per cycle. Naturally, as the length of the cavity increases the energy lost per cycle decreases since the number of cycles increase. This means that a longer cavity length leads to a better Q factor; however at some point the decreased mechanical rigidity of a longer cavity decreases the Q factor and becomes a hindrance to laser performance.  Additionally, it has been found that when the relaxation oscillation frequency (typically a few GHz for diode lasers) is larger than the axial mode spacing, mode hopping becomes an issue [6][7].   Temperature Control System The optical properties of diode lasers are highly dependent on their operational temperature. A closed- loop feedback control system using Peltier devices and thermistors will be implemented for this laser. The Peltier device is a two terminal semi-conductor device that makes use of the thermoelectric effect. Depending on the current’s direction, the device will either absorb or release heat. The basic principle of the feedback system is to use a thermistor as one of the legs of a balancing bridge, then amplify the voltage across the bridge to power the Peltier device [8]. There will be separate Peltier devices for the laser diode mount and the outer housing.  The laser diode mount will be set to a variety of temperatures that could range from -40 to +80 °C, with the housing acting as a heat sink for the Peltier device controlling the laser diode mount.  The housing will also have a Peltier device regulating the temperature of the housing to roughly ambient temperature.  Applications of Diode Lasers The laser diode system being proposed will be primarily used for laser cooling. An atom will absorb a photon if the photon’s energy matches one of its electronic transitions. In the process the atom will absorb the photon’s momentum. By red shifting the light with respect to the transition of interest, the frequency will be Doppler shifted to the correct transition energy as the atom moves towards the light source, making absorption possible and slowing the atom. By using 6 lasers, two pointing in opposite directions on three orthogonal axes, atoms can be cooled to ultra low temperatures. The final design will be used to cool rubidium, lithium, and ytterbium atoms. This requires the laser to produce a linewidth in the hundred to thousand kHz range, and be free of mode-hopping over a tunable range of hundreds of GHz.   8    Methods and Testing Protocol Component Alignment Preparing the laser to run experiments requires the alignment and setup of various components. It is necessary to align the mirrors, polarizing plates, filters, and beam-splitting cubes as well as the optical fiber-coupling mounts in order to minimize the attenuation of the signal along the tabletop setup. Having a misaligned beam will reduce the transmitted power such that the photodiodes and optical spectrum analyzers will either not able to detect a signal, or the signal to noise ratio will be too low to intelligibly determine the signal characteristics. The process for alignment optimization is carried out in two steps: rough estimation by eye, followed by a precise optimization using a power meter or a photodiode connected to an oscilloscope. The laser beam is aligned in the cavity by adjusting the positioning of the collimator tube so that the beam is centered on the cat’s eye lens.  A piece of transparent plastic is then inserted into the cavity to provide a plane for viewing the incident and reflected beams.  This arrangement can be seen in Figure 5.  Figure 5.  Method for aligning the laser beam in the cavity.  The kinematic mount that the mirror is attached to can then be tilted appropriately so that the two beams overlap on the transparent film.  When the two beams overlap, the intensity of the beam spots on the film will dramatically increase since the laser is being provided with feedback.  This is most easily seen when looking at the transparent film through an infrared scope.  The fine adjustment for the internal cavity alignment is then performed by shining the laser beam onto a photodiode and looking at the signal on an oscilloscope.  The current supplied to the diode is ramped about the threshold by modulating the output of the current driver with a triangle wave from a function generator.  The mirror angle of the mirror is then fine adjusted so that the threshold current for stimulated emission is 9    minimized.  At this point, the laser beam is optimally aligned within the cavity. Figure 6 shows a graph of light output as a function of current.  Figure 6. Light output of a laser diode as a function of supply current.  Most components on the table top are mounted to kinematic mounts, allowing precise control over the orientation and angle of mirrors and lenses. By using an infrared viewing card, coarse alignment can be performed. Fine adjustments can then be made by using a power meter where necessary.  Beam Focus / Profiling A potential variable necessary in the design of the cavity is the focal length of the cat’s eye lens/mirror configuration. Beam diffusion of all laser beams is a Gaussian function of the length of the beam. This means that the focal length of the cat’s eye setup varies with cavity length. Since data relating cavity length to spectral linewidth is required for this project, it was first necessary to determine the focal length at various cavity lengths as well as the linewidth sensitivity to deviations from the optimal focal length. With this data, the effect of cavity length on linewidth can be independently investigated. Data relating cavity length to focal length was obtained using knife-edge diffraction. To do this, a razor blade was attached to a micrometer-adjustable stage. The razor edge was placed perpendicular to the beam and cut partway into it. This setup can be seen in Figure 7. 10     Figure 7. Knife-edge laser beam profiling.  The image of the beam on the other side of the razor was viewed on a piece of paper. When the razor is on the short side of the focus, the image of the beam on the paper is inverted.  When the razor is on the far side of the focus, the image on the paper is non-inverted. By sliding the razor/stage with the micrometer along the axis of the beam and cutting in and out of the beam, location of the focus can be determined.  IF Filter Transmission Test Using a master laser locked at 780 nm, the transmission of the interference filters can be tested by measuring the amount of power transmitted as a function of the filter angle. This is most easily done be determining the angle of the reflected beam and dividing by two.  Fabry-Pérot Interferometers for Single Mode Selection The methods used for measuring linewidth require that the laser is operating in a single mode. To verify this a Fabry-Pérot Interferometer was used. This consists of two highly reflective planar mirrors with slight transparency whose separation cavity distance is swept over a range using a piezoelectric transducer. When a laser is injected into the cavity, it will experience strong constructive interference when the separation distance in a multiple of the half integer wavelength. By monitoring the output of the cavity with a photodiode, multiple modes of that laser that are in resonance with cavity at various piezo voltages can be seen. Figure 8 shows a spectrum of a single mode laser spectrum output from a Fabry-Pérot cavity. A multimode spectrum would consist of a forest of spikes that are periodic. 11      Figure 8. Output spectrum of a single mode laser in a Fabry-Pérot cavity.  Self-heterodyne Linewidth Measurement A common way to obtain a measurement of spectral linewidth is to use a self-heterodyne mixing technique. The beam from the cavity is split in two, and one of the beams is sent through a fiber delay of approximately 5km, presumably longer than the coherence length of the laser. The other beam is sent to an acousto-optical modulator (AOM), which shifts the frequency by 80 MHz. The resulting beat note of the recombined beams is centered about the sum and difference of the frequencies. The photodiode is only fast enough to detect the difference signal at 80 MHz. Figure 9 shows a schematic of the self- heterodyne setup.  12     Figure 9. Self-heterodyne linewidth measurement.  Ideally, this frequency superposition would be Lorentzian, from which the spectral linewidth could easily be discerned.   Two Laser Heterodyne Interference Linewidth Measurement Another technique similar to the self-heterodyne measurement is to use two lasers and mix the two output beams to produce a beat note spectrum centered at the frequency difference, with a linewidth which is the sum of the two individual laser linewidths.  To produce the beat note, the two beams must be co-linear and have the same polarization. The signal is coupled to an optical fiber which can be connected to the input of an optical spectrum analyzer or a receiver optical sub-assembly (ROSA) consisting of a high speed photo diode and filtering electronics. The ROSA is then inputted to a spectrum analyzer. The bandwidth of the ROSA is 10 GHz, therefore the two lasers’ wavelengths must be within 0.02 nm of each other. This was achieved by finding stable modes for both lasers whose wavelengths overlap within the tuning range of the interference filter. Next, while monitoring the optical spectrum analyzer, the wavelengths were tuned to each other to produce a beat note within the bandwidth of the ROSA. Then, the signal is fed via the ROSA to the spectrum analyzer.  This method does not suffer from the beams being correlated, as is the case with the self heterodyne measurement, because they originate from two separate lasers. However, stability of the lasers is critical to ensure the beat note remains centered at a constant frequency. This was not an issue with the self heterodyne measurement since the frequency fluctuations are the same for both beams and the 13    frequency difference is unaffected. Figure 10 shows the schematic for producing a two laser heterodyne linewidth measurement.   Figure 10. Experimental setup for the two laser heterodyne linewidth measurement.  Experimental Equipment   Figure 11. Thorlabs LDC 500 laser diode controller   Figure 12. Thorlabs TEC2000 temperature controller. 14      Figure 13. Thorlabs MDT694A single channel piezo controller.   Figure 14. Tektronix TDS 2004 oscilloscope.   Figure 15. Agilent E4407B spectrum analyzer.  15     Figure 16. Ando AQ-6135A optical spectrum analyzer.   Figure 17. Coherent LabMax 10 power meter.   Figure 18. Protoype laser.  16     Figure 19. Table top setup of the prototype lasers and optics  Prototype laser components: Intellite MLD 780-100S5P diode Thorlabs LT230P-B collimating lens tube Melcor CP1.0-63-08L thermoelectric cooler General Electric RL0503-5820-97-MS thermistor Newport 05D20FR2 mirror Thorlabs zero order halfwave plate, 780 nm Thorlabs BS017 non-polarizing beam splitter cube Research Electro-Optics Inc. 0.3 nm bandwidth 785 nm interference filter Melles-Griot XLL-785.0-12.5M 3nm bandwidth interference filter Thorlabs C280TME-B aspheric lens Thorlabs 30 mm cage mount components Piezoelectric transducer stack   Results The results of the knife-edge diffraction beam profiling can be seen in Figure 20. This test determined the size of the beam waist at the focal point of the lens.  17     Figure 20. Gaussian beam waist profile.  There are many methods for interpreting the size of the beam waist from this data.  The most accurate technique is to fit the power profile to the error function.  A few short-hand techniques just look at the distance between the 90% and 10%, or 70% and 30% power data points and use a scaling factor.  Since we were just interested in the order of the beam waist size, a rough estimate on the order of 10 μm from the data in Figure 20 is sufficient.  Using the knife-edge methods described previously, the results of the focal length tests are shown in Figure 21. From this graph it can be seen that the focal length decreases as the cavity length increases. This can be attributed to the divergence of the beam.   Figure 21. Focal length vs. cavity length.  18    Another interesting feature is the difference in focal length for the vertical and horizontal directions. This result represents the degree of astigmatism in the output of the laser beam.  The transmission test of the interference filters at various angles is shown in Figures 22 and 23. The data from these figures puts an upper limit on the range of angles for the interference filters to be set at. Using the angle sensitivity of the filters [20], the width of the filters can be inferred from Figures 22 and 23. The 3 nm filter has an angle sensitivity of 0.7 nm/deg. For a band pass of approximately 3.5 degrees, this corresponds to a filter width of 2.45 nm. The 0.3 nm filter has an angle sensitivity of 0.5 nm/deg. For a pass band of approximately 1 degree, this corresponds to a filter width of 0.5 nm. These values are close to the specifications of the filters.  Figure 22. Transmission vs. incident angle for the 3nm interference filter.   Figure 23. Transmission vs. incident angle for the 0.3 nm interference filter.  19    The results of the self-heterodyne linewidth measurement are shown in Figure 24. Spectra were taken for cavity lengths 150 mm and 310 mm at 30 mm increments. Additionally, spectra were taken for various distances between the mirror and the cat’s eye lens. Detailed results of these experiments can be found in Appendix D.  Figure 24. Self-heterodyne linewidth measurement for a 230 mm cavity with simulations.  The parameters for the fits in Figure 24 are given below. The Python code used for the fitting routine can be found in Appendix E. Parameter Value Fiber Length 5000 m Refractive index of fiber .682 V (Speed of Light in Fiber) Refractive index of fiber *c Cable Delay Fiber Length/V Alpha (ratio of beams) 1 k (1/f noise constant) 1488301280  Each spectrum was overlaid with a few simulated spectra to give upper and lower bounds on the linewidth. For a detailed analysis of the frequency noise spectrum, see Appendix A. The bounding simulations were determined from the depth of modulations in the wings of the spectra, which are indicative of the linewidth. From Figure 24 it can be seen that the linewidth is on the order of 4 kHz, although a more definitive method of measurement is required before this claim can be substantiated. 20    Qualitatively, a trend towards more narrow linewidths can be observed as the cavity length increases, and very little difference can be observed as the distance between the mirror and the cat’s eye lens is varied by approximately 1 - 2 mm about the nominal focal length. At variations larger than 1 – 2 mm, the laser becomes unstable. The two laser heterodyne linewidth measurement produced a beat note that quickly drifted back and forth on the spectrum analyzer. The drift range for a 310 mm cavity was approximately 100 MHz and for a 150 mm cavity it was 20 MHz. The drifting was too fast for a measurement of the linewidth to be made.  Discussion of Results Knife-Edge Diffraction Test The results of the knife-edge diffraction test showed that the astigmatism of the beam resulted in a difference of up to 0.5mm in the horizontal and vertical focal lengths.  Since the lens does not have a single focus, some averaging between the two is necessary.  Further tests were done to determine the sensitivity of the linewidth to variations about this average focal length.  The resulting spectra indicated that deviations from this average focal length by approximately 1-2 mm did not significantly affect the linewidth.  At farther deviations, the laser became unstable and would not go into single mode operation. As a result of these tests, it was decided that using a caliper to set the distance between the lens and the mirror would be sufficient. It also indicated that since different diodes would have different degrees of astigmatism, that the lens mount and the kinematic mount for the mirror would need some range over which the distance can be adjusted. The kinematic mount selected for the final design has an adjustment range of 3.56mm.  This range could be increased by introducing some variation in the set position of the lens mount. Additionally, the length of the metal slug that the mirror is mounted to could be custom cut for every build. It was decided that the simplest thing would be moving the lens mount because if the diode ever burns out and the new diode has a different degree of astigmatism, it would be undesirable to have another slug machined. Figure 25 shows the design of the lens mount with slotted holes, allowing the mount to be moved by up to 5mm along the beam path. 21     Figure 25. Final design for the cat’s eye lens mount.  Interference Filter Transmission Test From the transmission tests, it can be seen that the 3nm filter has a band pass that cuts off after 18 degrees.  This puts an upper limit on the angle tuning range of the interference filters. The length of the actuator needs to be long enough to realize this angle range.  Furthermore, the resolution of the actuator needs to be sufficient to select center frequencies at the desired resolution. From previous work done with the filters [20], we know that the angle sensitivity of 3 nm filter is 0.7 nm/deg and 0.5 nm/deg for the 0.3 nm filter. The frequency difference between two wavelengths is given by           (2) Where λ is the lower wavelength, Δλ is the difference in wavelengths, and c is the speed of light. The change in angle due to a change in actuator length is given by           (3) Where Δd is the change in actuator length and w is the length of the pivot arm at θ=0 degrees. Using the known angle sensitivity, the change in wavelength due to a change in angle is given by           (4) Where  is the angle sensitivity. Putting together (2), (3), and (4), we can solve for the required actuator resolution         (5) 22    Using a desired frequency resolution of 1 GHz at a nominal wavelength of 780 nm and the known angle sensitivity, a value of 2 μm for actuator resolution is required for a pivot arm of 30 mm. The final design for the interference filter mount assembly is shown in Figure 26. The micrometer shown is a Thorlabs DRV505 which provides 2 μm actuator resolution over a distance of 16.2 mm. The first filter holder pivots about a ball and cone contact to keep a tight pivot point without over constraining the design. An extension spring counters the action of the micrometer.  Figure 26. Final design for the interference filter mount assembly.  The second filter holder pivots on the first one on two balls, and is pulled together by extension springs. A 100 TPI fine adjustment screw is used to set the relative angle between the two plates with an extension spring countering the action of the set screw. The interference filters are held in place in the mounts with a standard 1” retaining ring. This method allows the filters to be held in place parallel to the mounting face much better than by using a set screw. Detailed schematics of the laser assembly design are in Appendices B and C.  Self-Heterodyne Linewidth Measurement The purpose of the self-heterodyne experiment is to produce two decoupled beams by passing one through an optical fiber and then combine them to produce a beat note. However, due to the long coherent length of the laser, complete decoherence is not possible with the available equipment and therefore the analysis of the measurement is made more difficult. The results of the self-heterodyne measurement failed to match the theoretical model and we could not precisely fit our data. The experimental results have much wider coherence peaks at 80 MHz and the 23    central lobe is not as high as predicted by the theoretical model. Therefore, we could not use this method to get definitive values for the 1/f noise and white noise. However, the depth of the lobe modulations in the sidebands are positivity correlated to the laser’s linewidth. Fortunately, for this region of the frequency spectrum the model and data were in agreement and we were able to fit an upper and lower bound to the linewidth. This can be seen in Figure 15. Using this technique we can confidently determine that our linewidth is less than 10 kHz and in the range of 5 kHz, although more definitive measurements must be made. Although we can qualitatively say that there is a trend towards more narrow linewidths for longer cavity lengths, the resolution of this measurement process limits a quantitative determination of this trend. Additionally, the decrease in linewidth from a 150 mm cavity to a 310 mm cavity can be estimated to be on the order of a few kHz. Taking this into account, we designed our laser cavity to be as small as practically possible.  Sources of Error in the Self Heterodyne measurement The most obvious error with this method is the premise that laser noise can be accurately modeled by a random white noise parameter and a 1/f noise factor. It assumes that the contribution of systematic noise sources can be neglected when compared to the effect of the previously mentioned terms. This may not be valid for lasers with narrow linewidths [19]. We also believe that temperature stability of the optical fiber could be an issue. Small temperature changes result in the expansion and contraction of material which are magnified when working with a 5 km long fiber. These changes in length can introduce phase artifacts between the beams which can distort the interference signal. Finally, from discussion with Daniel Steck, a researcher at the University of Oregon who is also working on similar laser designs, it may possible that our laser is in a multiple mode state with frequencies outside the bandwidth of the Fabry-Pérot. All of these factors could contribute to the accuracy of this measurement technique.  Two Laser Heterodyne Linewidth Measurement We investigated the cause of low frequency oscillations of the beat frequency. We hypothesized these fluctuations arose from mechanical instability of our design which caused the cavity length to change because of thermal fluctuation, vibrations, and air flow around the device. We tested the lasers at cavity lengths of 310 mm and 150 mm. We observed an oscillation range of 150 MHz and 20 MHz for the 310 mm and 150 mm cavity lengths, respectively. We also used custom made enclosures to protect our laser from air currents but observed no significant change in oscillation range. This indicates that cavity length is an important mechanical factor in the final laser design. However, precise quantitative measurements of prototype stability as a function cavity length and design are irrelevant for our design because the final product will be milled out of aluminum rather than mounted on optics rails.   24    Conclusions The focal length of the lens depends on cavity length and the degree of astigmatism in the diode, but measurements on the linewidth as the distance between the mirror and the lens was changed showed that the linewidth is not very sensitive to the exact positioning of the lens. As a result, the cat’s eye configuration was designed to allow for adjustment of the mirror to lens distance, with the expectation that a caliper would be sufficient to gauge this length.  Testing the sensitivity of the transmission of the interference filter with respect to the angle of the filter was important in designing the filter mount. Given that the desired resolution of the filter was 1 GHz at 780 nm, for a 30 mm pivot arm, 2 µm of resolution was necessary. Thus, the final design of the filter mount includes a Thorlabs DRV505 micrometer, which is capable of providing a resolution of 2 µm over a distance of 16.2 mm.  Experiments were conducted relating cavity length to the spectral linewidth of the beam using a self- heterodyne mixing technique. However, since the linewidth of the beam is too small for the length of the fiber delay in the self-heterodyne setup, we were unable to accurately fit our data. However, from a qualitative analysis we can conclude that our spectral linewidth was below 10 kHz, well below our objective. As expected, we were able to see that longer cavity lengths were more susceptible to mechanical vibrations. Since the linewidth gains for longer cavity lengths were not enough to justify building a longer laser, the laser housing was designed to be a more practical size.      25    Project Deliverables List of Deliverables The initial deliverable was a completely characterized interference filter stabilized diode laser. However, when beginning the design it was clear that many important design parameters which could affect laser performance were yet to be investigated. This issue was predicted as a possible set back in our project proposal. Therefore our first task was to first characterize the performance of the prototype laser to gain insight on our laser design.  Unfortunately, the techniques which we intended to use to characterize the device were found to be not accurate enough to provide necessary resolution for sensitive linewidth measurements. As a result, after consulting with our project sponsor, the scope of our project changed. It now focused on developing experimental methods for investigating narrow linewidth diode lasers and using the results to design a monolithic interference filter stabilized laser to be characterized in the future. The following table outlines the current state of all deliverables and what the project sponsor can expect to receive from our group now and in the future. Item Status Comment One working prototype interference filter stabilized laser. Completed Characterization of the linewidth, stability and beam profile of prototype lasers. Completed Optical setup for heterodyne interference linewidth measurements. Completed Successfully produce beat signal of the two prototype lasers. Design and Solidworks drawings of an interference filter stabilized external cavity diode laser with thermal control and electrical systems. Completed Submitted to machine shop for manufacturing on March 30, 2011. Lock in control system for stabilizing heterodyne interference linewidth measurement. Not Completed To be completed by April 22 Characterization of interference stabilized external cavity diode laser. Not Completed To be completed by June/July 2011   26    Financial Summary Part Quantity Material / Vendor Cost ($) Extended Cost ($) Machined Components Base 1 6061-T6 Aluminum - Laser Housing 1 6061-T6 Aluminum - Laser Top 1 6061-T6 Aluminum - Diode Holder 1 Copper - Generic Holder 1 6061-T6 Aluminum - IF Holder Base 1 6061-T6 Aluminum - IF Holder Front 1 6061-T6 Aluminum - IF Holder Back 1 6061-T6 Aluminum - Lens Holder 1 6061-T6 Aluminum - Slug 1 Copper - Total material cost   60 est 60.00 Total labour cost   800 est 800.00  Other Components U50-AL1 kinematic mount 1 Newport 114 114.00 DRV505 micrometer 1 Thorlabs 275 275.00 10mm beam splitter cube 1 Thorlabs 161 161.00 PM1 clamping arm 1 Thorlabs 10 10.00 MLD 780-100S5P 5.6 mm diode with 9 mm adapter 1 Meshtel 200 200.00 A230TM-B aspheric collimating lens f=4.51mm 1 Thorlabs 80 80.00 SM9RR 9mm retaining ring 1 Thorlabs 10 10.00 N100B2 1/16 threaded bushing 1 Thorlabs 6 6.00 UFS075 1/16 x 3/4 set screw 1 Thorlabs 13 13.00 AD1T 1” internal threaded optic holder 1 Thorlabs 18 18.00 LM1-A 1” optic holder, inner ring with angle markings 1 Thorlabs 20 20.00 SM1RR 1” retaining ring 3 Thorlabs 5 15.00 V1025-1 or V1021-1 vacuum valve 1 Cryocomp 400 est 400.00 CP1.0-63-08L TEC 1 Melcor 13 13.00 RL0503-5820-97-MS thermistor 1 GE 3 3.00 A34066-ND female DE-15 connector 1 Digi-Key 5 5.00 450-1522-ND toggle switch 1 Digi-Key 3 3.00 Microscope slide 1 - - 0.00 Torr seal 4.2 oz Thorlabs 85 85.00 Halfwave plate 1 Thorlabs 400 400.00 Lens 1 Thorlabs 70 70.00 Mirror 1 Thorlabs 15 15.00 Piezo stack 1 Thorlabs 100 100.00  Fasteners 27    3/8-24 x 1/2 socket cap screw 3 McMaster Carr 10.56/10 3.17 1/4-20 x 1/2 socket cap screw 4 McMaster Carr 6.76/50 0.54 1/4-20 x ½ swivel ball bearing set screw 1 McMaster Carr 3.22/1 3.22 10-32 x 1/2 socket cap screw 4 McMaster Carr 6.63/100 0.27 8-32 x 1 1/2 socket cap screw 4 McMaster Carr 7.33/50 0.59 8-32 x 3/4 nylon socket cap screw 4 McMaster Carr 5.85/100 0.23 8-32 x 1/2 vented socket cap screw 7 McMaster Carr 6.93/5 9.70 8-32 x 1/4 soft tipped set screw 4 McMaster Carr 6.13/10 2.45 4-40 x 1/4 socket cap screw 2 McMaster Carr 2.74/100 0.05 1/4 washer 4 McMaster Carr 1.09/100 0.04 #10 washer 4 McMaster Carr 4.64/435 0.04 #8 washer 13 McMaster Carr 4.64/435 0.14 3/32 x 1 1/4 dowel pin 1 McMaster Carr 2.46/5 0.49 3/32 x 3/4 dowel pin 2 McMaster Carr 8.78/100 0.18 3/32 x 5/16 dowel pin 3 McMaster Carr 8.63/100 0.26 0.180 dia. X 0.544 ultra precision extension spring 4 McMaster Carr 8.18/3 10.91 5/16 steel ball 3 McMaster Carr 5.42/250 0.07 5/32 steel ball 6 McMaster Carr 3.14/500 0.04 3/32 thick 10” inner dia.Viton o-ring 1 McMaster Carr 6.29/1 6.29 1/16 thick 3/8 inner dia. Viton o-ring 3 McMaster Carr 6.82/100 0.20 0.072 thick 0.495 outer dia. silicon o-ring 1 McMaster Carr 3.28/50 0.07  Total Unit Cost       2914.94  Ongoing Commitments We have not received an exact completion time for the laser from the UBC machine shop, however we estimate that it will take approximately four to six weeks.  During this time, all three group members will implement the control system needed to lock the two prototype lasers together to stabilize the beat note. William Bowden will contact the UBC electronics workshop to fabricate the required surface mount circuits for the diode control and electrical protection. It is likely the final laser will arrive after the beginning of summer semester. Jon-Paul Sun will be unable to work on the project directly because he is leaving Vancouver for Co-op. William Bowden and Damien Quentin will be available to work on assembling and characterizing the laser this summer. These tasks are outlined in the following table and scheduled with respect to when the machine shop finishes the laser. Group Remember(s) Task Duration All Set up laser locking system for heterodyne beat note April 4 to April 8 William Bowden Submit surface mount PCB designs for fabrication April 4 to April 8 William Bowden Test laser protection circuit  Upon Completion of PCB (1 day) 28    William Bowden/ Damien Quentin Assemble Laser including wiring for TEC, Peizo and diode 1 week after laser manufactured William Bowden/ Damien Quentin Characterize linewidth and stability 1-2 week after laser manufactured William Bowden/ Damien Quentin Characterize frequency tuning range and resolution of filters 2-3 week after laser manufactured William Bowden/ Damien Quentin Compare single custom .3 nm bandpass filter to two angle 3 nm bandpass filters 3 week after laser manufactured William Bowden Conduct hydrogen leak test to examine vacuum seal integrity 1 day (when measurement system is available)   29    Recommendations Based on our results from characterizing the prototype laser we recommend that the design for a monolithic interference stabilized diode laser proposed should be manufactured along with the necessary electronics for the diode protection circuit. While the device is being manufactured, a control system to lock the laser to stabilize the beat note must be implemented. This is required to characterize the final laser design. Once finished, the linewidth of the final design can be known precisely by producing a beat signal with the two prototype lasers individually and then beating the two prototypes to produce a final beat spectrum. This will produce 3 Lorentz spectrums which can used to simultaneously solve for the three linewidths. The device must also be characterized for stability—both when it is vacuumed sealed and kept at room temperature. This can be done by analyzing the output on a Fabry–Pérot Interferometer.  Furthermore, the robustness of the vacuum should be tested using a helium leak test.  If the laser meets the required specifications for its experimental applications of a stable output with a linewidth less than a 100 KHz, we recommended more units should be manufactured for general purpose lab use.    30    Appendices  Appendix A: Frequency Noise Model The optical field of a single mode diode laser can be modeled as a monochromatic field with random phase fluctuations as defined in the following equation:  ] (1)  The mean square phase fluctuations are related to the noise spectrum by:   (2)  where the noise spectrum is modeled by a power-dependent white noise factor and a power independent 1/f noise factor, given by:   (3)  The detected field for a delayed self-heterodyne linewidth measurement is the sum of the laser field and a time delayed, frequency shifted, copy of the original beam:   (4)  where  is the amplitude ratio between the fields, is the time delay and  is the mean frequency difference. The optical intensity correlation function at the detector is:   (5)  Substituting equation (4) into (5) and using (2) and (3), it can be shown that the autocorrelation function is:   (6)  Evaluating the integral results in the following expression:   (7)  31      where   (8)  and    (9) The spectrum observed on the RF spectrum analyzer is the Fourier transform of the autocorrelation function.  32     Appendix B: Laser Design  33     34     35     36     37     38     39     40     41     42     43     44     45     46     47     48     49     50     51     52     53     54     55     56     57     58     59     60     61     62     63     64     65     66     67     68     69     70      71    Appendix C: Diode Protection Circuit  Figure 27. Surface mount PCB design of diode protection circuit.   Figure 28. Circuit diagram of diode protection circuit.  72    Appendix D: Self-Heterodyne Linewidth Measurements Date: January 8, 2011 Purpose: To determine linewidth dependence on cavity length. Parameters: Cavity Length (mm) Current driver (mA) Temperature driver (kΩ) Piezo driver (V) Resolution bandwidth (kHz) Integrations (#) 280 98.6 10.117 52.0 3 10 260 103.6 10.117 52.0 3 10 240 103.0 10.117 54.0 3 10 220 102.1 10.116 54.0 3 10 200 100.7 10.115 45.0 3 10 180 102.1 10.115 45.0 3 10 160 101.1 10.115 45.0 3 10 140 99.4 10.115 45.0 3 10    140 mm     160 mm   180 mm     200 mm 73      220 mm     240 mm   260 mm     280 mm Figure 29. Spectra from first test of linewidth dependency on cavity length.  Results: The spectra observed in Figure 29 are very noisy and do not clearly show the characteristic lobes of a narrow linewidth self-heterodyne measurement. The trend for linewidth dependence on cavity length is not clear from these results and more investigation needs to be done. Future measurements should focus on producing less noisy spectra by increasing integration times and increasing the signal power at the photodiode.   74    Date: January 16, 2011 Purpose: To determine linewidth dependence on cavity length. Parameters: Cavity Length (mm) Current driver (mA) Temperature driver (kΩ) Piezo driver (V) Feedback (%) Resolution bandwidth (kHz) Integrations (#) 280 106.3 10.340 53.5 47 3 20 270 105.9 10.340 53.5 38 3 20 260 122.6 10.340 54.3 56 3 20 250 94.4 10.340 42.7 18 3 20 240 94.8 10.340 42.7 29 3 20 230 99.0 10.340 42.7 20 3 20 220 98.4 10.340 42.7 7 3 20 210 97.1 10.340 42.7 24 3 20 200 114.7 10.340 50.8 33 3 20 190 112.0 10.340 52.3 16 3 20 180 115.5 10.340 54.3 49 3 20 170 117.5 10.340 52.3 49 3 20 160 121.9 10.340 71.6 56 3 20 150 116.6 10.340 71.6 33 3 20 140 113.1 10.340 71.6 56 3 20 130 114.1 10.340 71.6 11 3 20    130 mm     140 mm 75      150 mm     160 mm   170 mm     180 mm   190 mm     200 mm 76      210 mm     220 mm   230 mm     240 mm   250 mm     260 mm 77      270 mm     280 mm Figure 30. Spectra from second test of linewidth dependency on cavity length.  Results: The spectra observed in Figure 30 are still very noisy. However, some of the spectra are starting to show the characteristic lobes of a narrow linewidth self-heterodyne measurement. The feedback ratio was also changed in these tests to optimize laser stability for each measurement. The trend for linewidth dependence on cavity length is still not clear from these results and more investigation needs to be done. Future measurements should focus on producing less noisy spectra by increasing integration times to 100 averages. The resolution bandwidth should also be reduced to 1 kHz since the laser linewidth is expected to be less than the 3 kHz bandwidth used for taking these spectra. It was also observed that the IntraAction ATM 801A2 oscillator used for the AOM is not very stable and drifts about the 80 MHz set frequency. A very stable digital oscillator is available in the lab and will be used for future measurements.  78    Date: January 20, 2011 Purpose: To determine linewidth dependence on feedback ratio. Parameters: Cavity Length (mm) Threshold current (mA) Current driver (mA) Temperature driver (kΩ) Piezo driver (V) Feedback (%) Resolution bandwidth (kHz) Integrations (#) 230 38 113.3 10.109 56.2 5 1 100 230 37 102.2 10.109 56.2 24 1 100 230 35 99.9 10.109 56.2 44 1 100 230 34 103.1 10.109 56.2 67 1 100 230 34 99.9 10.109 56.2 89 1 100    5% feedback     24% feedback   44% feedback     67% feedback 79      89% feedback Figure 31. Spectra from test of linewidth dependency on feedback ratio.   Figure 32. Linewidth and threshold current as the feedback ratio is varied. The linewidths attained for this graphs were done by a rough eyeball estimate of the lorentzian peaks of the spectra in Figure 31.  Results: Using the spectra in Figure 31, the linewidths were estimated from the widths of the lorentzian peaks. This method for estimating linewidths has been shown to have large uncertainties and this data will have to be retaken at a future date using a beat note-locked two laser heterodyne linewidth measurement. The resulting trend is shown in Figure 32. The threshold current as a function of feedback ratio is also shown on the same graph. This data trend is in agreement with the theory that more feedback to the laser diode would reduce the threshold current for lasing.  80    Date: February 7, 2011 Purpose: To investigate the effect of moving the mirror away from the ideal focal length. Parameters: Cavity Length (mm) Threshold current (mA) Current driver (mA) Temperature driver (kΩ) Piezo driver (V) Feedback (%) Mirror position away from nominal (mm) Resolution bandwidth (kHz) Integrations (#) 240 30.5 116.2 10.235 62.0 22 0 1 100 240 30.9 118.4 10.235 62.0 33 -1 1 100 240 32.1 129.7 10.235 62.0 33 +1 1 100 240 32.2 125.0 10.235 62.0 33 +2 1 100   Figure 33. Spectra of 240 mm cavity length as the distance between the mirror and cat’s eye lens is varied. The spectra have been overlaid and offset to make them overlap in the center.  Results: From Figure 33, it can be seen that the effect of changing the distance between the mirror and the cat’s eye lens does not have a large impact on the linewidth, as inferred by the depth of the modulations in the wings of the spectra. For distances greater than the ones tested, the laser became unstable and would not go into single mode operation. This test puts range on the allowable uncertainty in setting the distance between the mirror and the lens. From this we concluded that ultra fine precision in setting the lens position would not be required, and that a calliper would be sufficient.  81    Date: February 13, 2011 Purpose: To determine linewidth dependence on cavity length, and to test a custom current driver against the Thorlabs current driver to see the difference. Parameters: Cavity Length (mm) Threshold current (mA) Current driver (mA) Temperature driver (kΩ) Piezo driver (V) Feedback (%) Driver Resolution bandwidth (kHz) Integrations (#) 310 31.5 125.3 10.235 61.9 33 Thorlabs 1 100 310 31.5 138.1 10.235 61.9 33 Custom 1 100 270 36.5 121.7 10.235 59.7 33 Thorlabs 1 100 270 36.5 121.4 10.235 59.7 33 Custom 1 100 230 36.7 120.5 10.235 59.7 33 Thorlabs 1 100 230 36.3 123.5 10.235 59.7 33 Custom 1 100 190 37.7 116.1 10.235 59.1 33 Thorlabs 1 100 190 36.6 126.5 10.235 59.1 33 Custom 1 100 150 37.9 116.4 10.235 54.6 33 Thorlabs 1 100 150 37.2 116.8 10.235 54.6 33 Custom 1 100    Figure 34. Spectra taken using the Thorlabs LDC 500 current driver as the cavity length is changed. The spectra have been overlaid and offset for easier viewing.  82     Figure 35. Overlaid spectra of the Thorlabs LDC 500 current driver and the custom current driver. For each cavity length the Thorlabs driver is the darker line. The spectra have been given offsets for easier viewing.  Results: From Figure 34, there appears to be a clear trend towards deeper modulations in the wings of the spectra at longer cavity lengths. There is also a trend towards a broadening of the central spike, which indicates higher 1/f noise as the cavity length increases. These observations are in line with the theory. An interesting thing to note is that the linewidth does not drastically change as the cavity length increases. From the spectra plotted in Figure 35, it can be seen that the slope of the wings for the Thorlabs driver is consistently steeper than the custom driver. Using the frequency noise model as outlined in Appendix A, and modeled in Appendix E, this sloping cannot be attributed to any parameters. This indicates that the frequency noise model is most likely insufficient for our setup. There are noise components that the model is unable to account for.   83    Appendix E: Python Code for Fitting Self-Heterodyne Linewidths 84    85    86    87    88      89     References  [1] Wiemen, C. & Hollberg, L. (1991). Using diode lasers for atomic physics. Rev. Sci. Instrum. 62 (l). [2] Sands, D. (2005). Diode Lasers. Bristol, UK: IOP Publishing. [3] Levac, L. (2010). Interference filter stabilized cavity laser. Master Thesis at Univ. Madison Wisconsin. [4] Ye, C. (2004). Tunable External Cavity Diode Lasers. Singapore; World Scientific Publishing Co. [5] Baillard, X., Gauguet, A., Bize, S., Lemonde, P., Laurent, P., Clairon, A. et. al. (2006). Interference- filter-stabilized external-cavity diode lasers. Optics Communications, 266 (2). [6] Ricci, L., Weidemuller, M., Esslinger, T., Hemmerich, A., Zimmerman, C., Vuletic, V. et al. (1995).  A compact grating-stabilized diode lasers system for atomic physics. Optical Communications 117, p 541- 49. [7] Gavra, N. & Rosenbluh, M. (2010). Behavior of the relaxation oscillation frequency in vertical cavity surface-emitting laser with external feedback. J. Opt. Soc. Am. B 27 (12), pg 2482-87. *8+ Williams, J. (1977). Designer’s Guide to Temperature Control. EDN Magazine. [9] Zorabedian, P. & Trutna, W.R. (1988). Interference-filter-tuned, aligned-stabilized, semiconductor external-cavity laser. Optics Letters 13 (10), pg 826-28. [10] Meyrath, T. (2003). An analog current controller design for laser diodes. Atom Opics Laboratory Center for Nonlinear Dynamics, University of Texas at Austin. [11] Okoshi, T.,  Kikuchi, K.,  & Nakayama, A. (1980). Novel  method  for high  resolution  measurement of  laser  output  spectrum. Electron  Lett. 16, pg. 630-1. [12] Ludvigsen, H., Tossavainen, M. & Kaivola, M. (1998). Laser linewidth measurements using self- homodyne detection with short delay. Optical Com. 55, pg. 180–6. [13] Boshier, M.G.,  Berkeland, D., Hinds, E.A.  & Sandoghdar, V. (2003). External-cavity frequency- stabilization of visible and infrared semiconductor lasers for high resolution spectroscopy. Optical Communications 85, pg/ 355-9. [14] Flemming, M.  (1981). Spectral Characteristics of External-Cavity Controlled Semiconductor Lasers. Journal IEEE of Quantum Electronics 17 (1). [15] Hawthorn, C. J. et al. (2001). Littrow configuration tuneable external cavity diode laser with fixed direction output beam. Rev. Sci. Instrum. 72 (12). 90    [16] MacAdam, K.  & Wiemen, C. (1992). Narrow Band tunable diode laser system with grating filterbank absorbers. Am. J of Physics 60 (12). [17] Patrick, H. & Wieman, C. (1991). Frequency stabilization of a diode laser using simultaneous optical feedback from a diffraction grating and a narrowband Fabry-Perot cavity. Rev. Sci. Instrum. 62 (11). [18] Siegman, A. (1986). Lasers. Mill Valley, CA: University Science Books. [19] Horak, P. & Loh, W. H. (2006). On the delayed self-heterodyne interferometric technique for determining the linewidth of fiber lasers. Opt. Express 14 (9), 3923. [20] Wienands, J. (2011). Construction and Characterization of a Prototype External Cavity Diode Laser. Directed StudiesThesis at Univ. British Columbia.  

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