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Fiber-optic probe for electro-optic sampling Chandani, Sameer M. 2002

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Fiber-Optic Probe For Electro-Optic Sampling by S ameer M . Chandani B.Sc .E. , Queen's University, 1998 A THESIS S U B M I T T E D I N P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F Master of A p p l i e d Science in T H E F A C U L T Y O F G R A D U A T E S T U D I E S (Department of Electrical and Computer Engineering) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June 2002 © Sameer M . Chandani, 2002 In p resent ing this thesis in partial fu l f i lment of t h e requ i rements fo r an advanced degree at the Universi ty o f British C o l u m b i a , I agree that t h e Library shall make it f reely available fo r re ference and study. 1 fu r ther agree that permiss ion f o r extensive c o p y i n g o f this thesis f o r scholar ly pu rposes may be g ran ted by the head o f m y d e p a r t m e n t or by his o r her representat ives. It is u n d e r s t o o d that c o p y i n g o r pub l i ca t i on of this thesis fo r f inancial gain shall n o t be a l l owed w i t h o u t m y w r i t t e n permiss ion . D e p a r t m e n t The Univers i ty o f Brit ish C o l u m b i a Vancouver , Canada DE-6 (2/88) A b s t r a c t In-circuit probing of high-speed circuits is becoming a common need as circuit complexity and operating frequencies increase. Electrical methods are not generally capable of probing internal points that are not matched to 50 £1. Electro-optic sampling is a proven technique for non-invasive in-circuit probing of high-speed circuits, but remains a laboratory tool used by a few experts. This work is aimed at designing and developing a fiber optic based electro-optic sampling system that can be used by test engineers to measure the voltage waveform at internal points. The use of a fiber based pulsed laser and confinement of the optical sampling pulses to fiber optic cables and components results in a compact probe station style system that is easy to use. A novel fiber optic based sampling tip has been designed, built, tested and incorporated into a custom designed microwave probe station. The sampling tip has been made by attaching A l G a A s , an electro-optic material to the end of a fiber optic cable and thinned to a thickness of 1.6 |-im using selective wet etching. A theoretical model has been developed to describe the characteristics of the tip when exposed to an external electric field. Measurements of the electric field over a coplanar waveguide structure with 60 \im center and 30 u,m gaps have been successfully made. The measurements are consistent with results obtained from an electrostatic simulation of the coplanar waveguide. The electro-optic sampling tip has a V„ of 2200 k V when used as a sensor over the coplanar waveguide at a height of 6 \xm above the surface of the conductor. The tip can also be accurately placed over a test point by monitoring the power reflected from the surface of the circuit. A phase locked loop (PLL) has been implemented to synchronize the optical sampling pulses to the signal driving the circuit. The P L L successfully locks the optical pulses and signal driving the circuit to a reference oscillator without degrading the phase noise of the optical sampling pulses. i i C o n t e n t s Abstract ii Contents iii List of Figures vi List of Tables ix Acknowledgments x 1 Introduction 1 1.1 Overview 1 1.2 Motivation 1 1.2.1 In-Circuit Probing 1 1.2.2 Sampling of High Frequency Signals 2 1.2.3 Ease of Use 3 1.3 Electro-Optic Sampling 5 1.3.1 Electro-optic Effect and Modulator 5 1.3.2 E x i sting and Pre vi ous E O S S ys terns 8 1.4 Overview of Thesis 9 1.4.1 Summary 9 1.4.2 Outline 14 2 Fiber-Optic Based EOS System Design 15 2.1 Introduction to Chapter 15 2.2 Description of System Components 15 2.2.1 Fiber Based Pulsed Laser 15 2.2.1.1 Description and Mode of Operation 15 i i i 2.2.1.2 Phase Noise Performance 18 2.2.2 Synchronization Scheme 21 2.2.2.1 P L L Description and Purpose 21 2.2.2.2 Performance and Measurement of P L L 24 2.2.3 Optical Path Design 26 2.2.3.1 Polarization State Considerations 26 2.2.3.2 Overall Design and Components 27 2.2.4 Sampling Tip Design and Height Control 30 2.2.4.1 Electro-optic Tip Design 30 2.2.4.2 Tip Height Control 31 2.2.5 Summary and Conclusions 32 3 Fiber-Based Electro-Optic Sampl ing T i p 33 3.1 Introduction to Chapter 33 3.2 Description of Fiber-Based E O Tip 33 3.2.1 Design and Description of T ip 33 3.2.2 Theoretical Description 36 3.2.2.1 Single Fabry-Perot Treatment of Fiber Tip 36 3.2.2.2 Double Fabry-Perot Treatment of Fiber T ip 40 3.2.2.3 Electro-Optic Effect in the Fiber Tip 45 3.2.2.4 Reflectance of Fiber Tip 49 3.3 Fiber Tip Characterization 54 3.3.1 D C Characterization 54 3.3.2 A C Characterization 57 3.4 Summary and Conclusions 70 iv 4 Future Work and Conclusions 72 4.1 Future Work 72 4.2 Conclusions 81 Appendix A 83 Appendix B 85 Appendix C 88 Bibliography 92 v List of Figures 1.1 Sampling of a periodic high frequency signal 4 1.2 Transmission of an electro-optic modulator with dual beam outputs. The x-axis shows the phase shift, 8 as a fraction of n and the y-axis is the transmission of the light through the electro-optic modulator 7 1.3 Block diagram of E O S system with P L L 10 1.4 Illustration of fiber sampling tip over circuit under test 11 1.5 Simulated and measured electric field amplitude over a C P W at a height of 6p.m using a novel fiber optic based electro-optic sampling tip. The solid rectangles represent the physical geometry of the C P W 13 2.1 Equipment schematic for operation of the fiber based pulsed laser 17 2.2 Phase noise spectrum of optical sampling pulses at 1 GFIz locked to two different microwave generators 20 2.3 Block diagram of phase locked loop configuration used in E O S system 23 2.4 Phase noise spectrum of optical sampling pulses operating at 1 G H z . Measurement taken for the case of synchronized and not synchronized to reference signal 25 2.5 Block diagram of E O S system optical path design. The solid lines with arrows depict fiber optic cables with F C / A P C connectors 28 3.1 Sketch of the GaAs wafer used for manufacture of fiber tips 35 3.2 Digital image of manufactured fiber tip showing A l G a A s 1.6 |xm piece attached with glue forming a fillet around the fiber end 37 3.3 Fabry-Perot structure with a left-incident optical wave 39 vi 3.4 Fabry-Perot structure with a right-incident optical wave 39 3.5 Reflectance of fiber tip Fabry-Perot cavity of F iber |AlGaAs |Ai r as a function of Alo.3Gao.7As thickness for A. = 1550nm 41 3.6 Transmittance of fiber tip Fabry-Perot cavity of F iber |AlGaAs |Ai r as a function of Alo.3Gao.7As thickness for A, = 1550nm 41 3.7 Illustrative contributions to reflected light in fiber tip 42 3.8 Conceptual diagram of double Fabry-Perot cavity created when fiber tip is placed above a conductor or metal line with an air gap of thickness d 44 3.9 Max imum case field intensity distribution for fiber tip with I = 1.6 mm, A, = 1550 nm, p e = 1. Fie ld is a maximum in Alo.3Gao.7As and minimum in air when the air gap thickness, d = 9 \im 46 3.10 M i n i m u m case field intensity distribution for fiber tip with I = 1.6 p.m, A. = 1550 nm, p e = 1. Fie ld is a minimum in Alo.3Gao.7As and maximum in air when the air gap thickness, d - l p.m 47 3.11 Calculated E„for fiber-based sampling tip for the case of pe = 0.9 and t = 1.6 |J,m 50 3.12 Plot of Transmission coefficient between two fibers of equal mode field diameter, OJQ = 8 (im, separated by a distance in air and operating at A = 1550 nm 52 3.13 Reflectance of fiber tip for the case of pe = 0.9 and A = 1550 nm 53 3.14 Simulated and measured reflectance of fiber tip over a metal line with pe = 0.83 56 3.15 Reflectivity measurement of fiber tip as it approaches conductor surface. When the fiber tip is in contact with the conductor surface, the Fabry-Perot fringes expand 58 vu 3.16 Plot of the vertical electric field amplitude, Ez above the C P W for different heights above the metal lines for a 5 VPk voltage applied. The solid rectangles represent the physical geometry of the C P W 59 3.17 Plot of the vertical electric field amplitude, Ez above the C P W when a fiber tip is present at the heights indicated for a 5 VPk voltage applied. The solid rectangles represent the physical geometry of the C P W 61 3.18 Measured and simulated normalized electric field amplitude above the C P W as a function of position. The solid rectangles represent the physical geometry of the C P W 63 3.19 Normalized optical reflected power from fiber tip as a function of distance along the C P W . The solid rectangles represent the physical geometry of the C P W 65 3.20 Simulated and measured normalized electric field amplitude at different heights above the C P W 66 3.21 Schematic plot of photoreceiver chain for reflected optical signal 68 4.1 Horizontal electric field, Ey above the C P W with 5 VPk sinusoidal signal applied to center conductor. The field is shown for different heights above the C P W when no fiber tip is present. The solid rectangles represent the physical geometry of the C P W 74 4.2 Horizontal electric field, Ey above the C P W with 5 VPk sinusoidal signal applied to center conductor. The fiber tip is at a height of 6 j im and the field is shown at different points above the C P W . The solid rectangles represent the physical geometry of the C P W 75 4.3 Reflectance for the LiTa03 based fiber tip. The two curves are for the O and E axes. The reflectivity of the circuit under test is pe = 0.6 77 4.4 Calculated En for the L i T a 0 3 based fiber tip with pe = 0.6 and 20 um thick L i T a 0 3 79 V l l l List o f Tables 2.1 Calculated rms jitter values for laser operating at 1 G H z and driven by Agilent 8648D R F Generator 21 3.1 Transmittance and reflectance measurements for fiber tips with 0 dBm optical power launched into tips. The highlighted rows indicate good tips as R+T = 1 55 3.2 Physical and Simulated values for quantitative characterization of fiber tip 70 ix Acknowledgments M y deepest gratitude goes to my father for supporting me throughout my education. I would like to thank my supervisor, Dr . Jackson, for giving me the opportunity to work in his lab, his knowledgeable guidance and patience made the completion of this work possible. Sincere and special thanks go to Roberto Rosales for the endless discussions on problems I had encountered during the course of this work. Without his willingness to listen and bounce ideas off of, his assurance that everything would be fine when things went wrong, and his technical support with all the electronics, I would not have made it as far as I did. I would also like to thank Jiaming Zhang and Daniel Langevin for all the technical support and ideas they provided. A special thank you to Luca Carraresi for the collaborative work done on this project, in particular the manufacturing of an early batch of fiber tips. The support of David Chu Chong and Don Dawson and the rest of the technical staff at the department of electrical engineering made the task of building the E O S system easier. Finally I would like to thank my family and close friends for their love, support, understanding and encouragement throughout the duration of this degree. x Chapter 1 Introduction 1.1 Overview The development of high-speed circuits, which include radio frequency (RF) and mm-wave integrated circuits (MMIC's), has been much more rapid than the techniques and tools used to test and debug them. Current tools such as network analyzers and sampling oscilloscopes are still limited to practical bandwidths of 110 GHz. These tools are also restricted to either S-parameter or voltage waveform measurements at designated input and output ports that are matched to 50£2. The increasing complexity of high-speed circuits has necessitated a method for high-speed in-circuit probing to allow debugging and characterization by circuit designers. Electro-optic sampling (EOS) techniques have proven to be an effective method to achieve this [1]. This chapter begins with an introduction to the advantages of EOS, its capability for high-speed in-circuit probing, and the motivation behind developing a fiber-optic based EOS system. A description of how electro-optic sampling works, previous and existing systems, and main features of the fiber-optic based system developed in this work is given. The chapter concludes with a summary and outline of the thesis. 1.2 Motivation 1.2.1 In-Circuit Probing High-speed characterization and measurements are difficult due to the requirement of impedance matching between the circuit under test, the transmission line and the measurement tool. The - 1 -transmission lines and the instrumentation tools are all designed with characteristic impedances of 50Q, thus requiring the input and output ports of high-speed circuits to be matched to 50 Q sources and loads. In order to probe an internal circuit node, the node must be connected to a buffer amplifier capable of driving a test instrument that is off chip. This buffer amplifier is required because the low impedance requires high currents to achieve realistic signals, for example a 0 . 5 V p k signal in 50£2 means signal swings of 10mA. The use of output buffers has several disadvantages. The buffer may distort the signal, load and degrade the circuit, and add a significant area overhead to the design. The availability of an in-circuit probing technique that is contactless and non-invasive overcomes all the above restrictions for testing internal nodes. Electro-optic sampling is a non-contact, non-destructive and non-invasive technique that does not load or introduce parasitic impedances i f suitably applied [2]. Other contactless techniques are also available such as electron beam testing [3] and electrostatic force microscopy ( E F M ) [4]. The former technique has been implemented in commercial testers available from Schlumberger. The above techniques allow design and test engineers to debug prototype circuits after fabrication so that production testing can run smoothly. A s circuits and the technology models used in their design get more complex, there is a need to close the gap between simulations and measurements. Effective testing tools capable of in-circuit probing can achieve this. 1.2.2 Sampling of H i g h Frequency Signals Electro-optic sampling is a time domain measurement technique capable of measuring signals up to 1000 G H z [1,2,5]. High-speed data acquisition electronics are not needed to measure these high frequency signals, as the signals are sampled at regular intervals. This well-known method to characterize high frequency periodic signals through the analysis of lower frequency signals is illustrated in Figure 1.1. Short pulses are used to sample the high frequency signal to produce a - 2 -replica of it at a lower frequency, which is equal to the difference between the sampled and sampling frequencies. The sampling pulses are offset from the signal frequency by A f to satisfy the following relationship: f5=Nfp+Af (1.1) where A f is the down converted signal frequency, fs is the signal frequency, fp is the sampling pulse frequency and N is an integer. B y fixing the detection frequency Af based on the data acquisition electronics, either fs or fp can be tuned to satisfy Equation (1.1). In most sampling systems, the detection frequency Af, is in the kHz or M H z range when signals greater than 1 G H z are being sampled. The advantage of this sampling technique is the ease of design and lower cost of data acquisition electronics. For current heterojunction bipolar transistors, which have figures of merit, f T > 295 G H z and fmax > 1 T H z [6] and are used in circuit designs approaching 185 G H z , such sampling techniques are needed to test these circuits at speed and verify the models used to simulate them. E O S has the capability to perform these time domain high frequency measurements. 1.2.3 Ease of Use To date, electro-optic sampling systems have achieved good results in research laboratories and several research groups have successfully characterized high-speed devices and circuits [7,8]. However it has remained a tool used by a few experts because of the difficulty in placing and moving the electro-optic sampling tip close to the nodes of interest. Past E O S systems have used cumbersome free space optics and electro-optic sampling tips. This results in bulky and complicated optics right near the circuit under test (CUT). Mov ing the optics is inconvenient, as it typically requires realignment every time the sampling location is changed. Alternatively, moving the circuit is not convenient either due to the use of electrical probes that - 3 -Signal Waveform, W +kf Repetition Rate > TIME > TIME Sampling Pulses, f Repetition Rate Sampled Waveform, Af Repetition Rate Figure 1.1: Sampling of a periodic high frequency signal are in contact with the circuit to provide input signals. These problems lead to a large setup time and require an optical engineer or expert to use the tool. To address these problems, this work aims to develop a fiber-based system where all the optical sampling pulses are contained in fiber-optic cables and components. With such a setup, all the optics are fixed and the light can be delivered to the test point using a fiber optic cable, which is flexible and can be moved with the sampling location. The recent availability of fiber-based picosecond pulsed lasers and cost effective fiber-optic components, combined with the design of a novel fiber-based electro-optic sampling tip developed in this work has enabled this move into the fiber-optic domain. This allows for miniaturization and ease of use; the objective of this thesis is to advance the development of such systems into a practical and convenient tool that can be used by the general test engineer. 1.3 Electro-Optic Sampling 1.3.1 Electro-optic Effect and Modulator Electro-optic sampling is based on the electro-optic effect or Pockels effect, which introduces birefringence in a crystal when exposed to an electric field [9]. A birefringent crystal is one that presents different indices of refraction depending on which of the crystal's orthogonal axes the light travels along. If the light passing through the crystal travels along both axes, a phase shift is introduced between the two orthogonal polarizations of light. The electro-optic effect occurs when the electric field, which modulates the indices of refraction of a crystal, modulates the polarization of the light traveling along both crystal axes. B y measuring this modulation of the polarization of the exiting light, the amplitude of the electric field applied to the crystal can be determined. Typical electro-optic materials used are GaAs , LiTa03, and ZnTe, characterized by their electro-optic coefficients and a figure of merit called the half-wave voltage, V„. The details of the electro-optic effect are well known, and their application to E O S is well documented. The - 5 -key results and equations that describe an electro-optic modulator are shown here and the reader is referred to references [9] and [10] for more details. The electro-optic effect is measured by placing the electro-optic crystal between two crossed polarizers to form an intensity modulator. Such an electro-optic modulator is optically biased at its quadrature point and the transmission coefficient of each of the two polarizations, Tx and Ty, after passing through the modulator is given as: ^ = | = sin 2 ( f ) = s i n 2 f e ) < L 2> r ^ | = cos 2 ( | ) = c o s 2 f e ) < L 3> where and 1% are the transmitted intensities of the two orthogonal components; Ij is the input beam intensity of the light; 8 is the phase difference between the two orthogonal components; and V is the external voltage causing the electric field in the crystal. Equations (1.2) and (1.3) are plotted in Figure 1.2, which shows the quadrature point at the center of the x-axis. The figure shows that i f the modulator is optically biased at its quadrature point, S = \ or V = \ , the transmitted beam changes linearly with the applied voltage and the two transmission coefficients change equally and oppositely with changes in the phase shift. In addition, the sensitivity of the modulator is the largest at this bias point. Differential detection is used for the two orthogonal polarization states of the laser light to cancel the common mode noise such as the amplitude noise of the optical pulses. As mentioned earlier, V„ is used as a figure of merit for describing an electro-optic modulator and the lower it is, the more sensitive the modulator is. It is the voltage at which the phase difference, 8, between the two orthogonal polarization components is equal to 7t, which results in circularly polarized light when the orthogonal components are combined. - 6 -Figure 1.2: Transmission of an electro-optic modulator with dual beam outputs. The x-axis shows the phase shift, 5 as a fraction of n and the y-axis is the transmission of the light through the electro-optic modulator. 1.3.2 Exis t ing and Previous E O S Systems Electro-optic sampling systems have been used to characterize high-speed solid-state devices since the 1980s. However, they have been confined to the laboratory because of their difficulty of use. Previous systems have used free space optics and electro-optic sampling tips, which are available commercially. Typical applications have included gate delay measurements on an inverter chain measured at 15 ps [2], characterization of non-linear transmission lines up to 700 G H z [1,11], transfer functions of a traveling wave amplifier up to 20 G H z [5], voltage signals on a 2:1 regenerative frequency divider [12], switching time for modulation-doped field-effect transistors of 4.2 ps [13]. Systems that have appeared in the literature use either a N d : Y A G 1.06 \im, Ti:Sapphire 830 nm, or InGaAs Fabry-Perot laser pulses and free space optics and sampling tips [1,2,5,7,9,14]. Because of these bulky lasers, large optical tables are used and cumbersome free space optics are needed to align the laser beam into and out of the electro-optic sampling tips. The kinds of tips used are called total internal reflection (TIR) probes and have a footprint of 200 (im by 200 (xm. There have been attempts at developing automated systems, most notably by" Shinagawa and Nagatsuma [15]. They incorporate their sampling tip and optics into an automated R F probe station. In order to achieve this, some of their components were fiber-based so they used an InGaAs Fabry-Perot laser for efficient transmission of the light in a fiber. Such lasers are unable to provide the necessary picosecond pulses necessary for good detection sensitivity and temporal resolution required in E O S , and thus prevented it from becoming a commonly used test tool. Recently, Yang et al [16] have demonstrated a fiber-based electro-optic probe used for electric field mapping. In all cases, the laser pulses have to be synchronized to the microwave signal provided to the circuit under test using a phase locked loop. Lock-in and differential detection is used in the above-mentioned works. 1.4 Overview of Thesis 1.4.1 Summary This thesis describes the work done to develop and implement a fiber-based electro-optic sampling system that uses a fiber-based picosecond pulsed laser, fiber optic components and a novel fiber-based electro-optic sampling tip that was designed, built and tested in this work. Figure 1.3 shows the block diagram of the fiber-based E O S system. The optical pulses are delivered to the sampling tip over the C U T via polarizing optics and the reflected signal is detected and displayed. A microwave source is used to provide an input electrical signal to the C U T . A l l the polarizing and detection optics have been implemented using miniature fiber optic components and cables that all fit compactly into an optical enclosure approximately 30 x 20 x 15 cm. The thesis addresses three main issues of such a fiber-based system. The first issue is the design of a suitable and non-invasive probe tip for in-circuit probing. The second issue is the stable positioning of the probe tip at the test point and the third is the required synchronization of the optical sampling pulses to the input electrical signal provided to the circuit under test. The first issue was addressed by replacing the conventional sampling tip with a novel fiber-based sampling tip. A n electro-optic material, A l G a A s , has been attached to the cleaved end of a fiber to form the sampling tip. Fabry-Perot like reflections between the f iber-AlGaAs-air interfaces result in enhanced modulation of the light in the A l G a A s by the electric field on the circuit. The interaction of the electric field around the transmission lines with the sampling tip is illustrated in Figure 1.4. The sampling tip is disposable and can easily be replaced by connecting a new one to the optical enclosure via a standard fiber connector. Fiber Based Picosecond Laser] A Polarizing Optics PLL Circui t ry A Microwave Source Circuit Under Test Reference Oscillator i i \M Detection Optics Figure 1.3: Block diagram of EOS system with P L L 10-Optical Beam AlGaAs — Fiber Sampling Tip Electric Field Lines V + V -Circuit Wafer Figure 1.4: Illustration of fiber sampling tip over circuit under test - 11 -The stable positioning of the tip over the test point is required to place the A l G a A s into the electric field around the test point, as shown in Figure 1.4. This arrangement requires a distance of 5-20 [im between the surface of the conductor on the C U T and the sampling tip. B y monitoring the total D C power reflected back into the fiber core, the tip can be servoed in a feedback loop to keep the tip height constant. A s mentioned earlier, the sampling pulses need to be synchronized with the input electrical signal supplied by an R F generator to the C U T , just as is the case for conventional sampling oscilloscopes. A phase locked loop (PLL) has been designed and implemented to achieve this without any degradation to the timing jitter of the optical sampling pulses. The optical pulse train was mixed with the electrical signal to provide an intermediate frequency signal, which was phase locked to the data acquisition trigger signal by configuring the laser as a V C O . The P L L is highlighted by the dashed rectangle in Figure 1.3. Simulated and measured results show that it is possible to measure the electro-optic effect using the novel fiber-based sampling tip designed in this work. Using tips that were successfully built by the author, the electrostatic field of a coplanar waveguide structure (CPW) was measured as illustrated in Figure 1.5. These results are explained in detail in Section 3.3.2. Measurements also show that the tip can be positioned over the circuit under test by measuring the total power reflected from the surface of the circuit under test. The tip is integrated into a custom designed vibration isolated R F probe station, capable of providing signals up to 20 G H z to a C U T . The system has been automated using computer-controlled nanopositioners and an imaging system to locate the internal node on a C U T and automatically move the tip to that position. - 12-• Measured — Simulated -100 -50 0 50 Distance along CPW (u.m) Figure 1.5: Simulated and measured electric field amplitude over a C P W at a height of 6iam using a novel fiber optic based electro-optic sampling tip. The solid rectangles represent the physical geometry of the C P W . - 13 -1.4.2 Outl ine The remainder of this thesis is divided into three chapters. Chapter 2 describes the overall system and its components, their design and performance. The components are: the fiber-based pulsed laser; synchronization scheme and the phase-locked loop; the optical path design and its components; and the tip design and height control. Chapter 3 describes the design, manufacture, a theoretical model, and the characterization of the fiber-based sampling tip. Measured and simulated results of the electro-optic behaviour of the tips are also presented. Chapter 4 concludes the thesis with a discussion of future work required to improve the tips, in particular their sensitivity. Circuit schematics of the P L L and detection circuitry are provided in Appendix A . A list of all the equipment used in the system can be found in Appendix B . Other automated aspects of the system such as data acquisition techniques and imaging system have been documented in Appendix C. - 14-Chapter 2 Fiber-Optic Based EOS System Design 2.1 Introduction to Chapter In this chapter the key components necessary for a fiber-optic based electro-optic sampling system are described. Section 2.2.1 describes the pulsed laser source. Section 2.2.2 describes the design and performance of the synchronization scheme used to phase lock the optical sampling pulses to the applied R F signal to the circuit under test. Section 2.2.3 describes the optical path design for the polarization and detection optics necessary to measure the electro-optic signal generated in the sampling tip. The chapter concludes with Section 2.2.4, which discusses the design requirements of an effective sampling tip and its ability to be positioned reliably and accurately at a test point. 2.2 Description of System Components 2.2.1 Fiber Based Pulsed Laser 2.2.1.1 Description and Mode of Operation Recent developments in optical communications and fiber optics have led to the development of high-repetition mode-locked lasers for use as optical clocks. A mode-locked laser is a laser that produces a train of pulses separated by the cavity round-trip time. Mode locking is generally achieved by modulating the gain or loss of the laser cavity in a periodic way so that the laser - 15 -oscillates at more than one frequency. Harmonically mode-locked Erbium-doped fiber lasers are stable sources of picosecond pulse trains at gigahertz repetition rates that can be used in electro-optic sampling. The laser utilizes intracavity soliton pulse compression to achieve pulse widths of 1-2 ps [17]. A Mach-Zehnder amplitude modulator in the laser cavity is driven by an external microwave generator to set the repetition rate of the optical pulses. Details on the theory of operation of the laser can be found in reference [18]. Mode-locking of the laser requires an external microwave source operating at the desired repetition rate. B y adjusting the D C bias on the Mach-Zehnder modulator and tuning the fiber cavity length, the laser can be mode locked to the driving microwave signal. The laser used in the E O S system is capable of repetition rates from 1 to 5 G H z in steps of 3.8 M H z and a pulse width of 2 ps. The average output power is -1.2 m W and can be amplified using a commercially available erbium doped fiber amplifier ( E D F A ) to an output of 30 mW, which is sufficient for the entire system. As is the case with any mode-locked laser, various properties of the optical pulses need to be monitored to achieve the mode locking and maintain it over the duration of the experiment. Figure 2.1 shows the set up required to run the laser in its mode locked state. Each of the laser's properties requires a different instrument which include; an electrical spectrum analyzer to monitor the repetition rate in the frequency domain and suppression of other adjacent modes (the laser has an internal photodiode to convert the optical pulse train to an electrical signal); a sampling oscilloscope to monitor the optical pulse train in the time domain; an optical spectrum analyzer (OSA) to set the operating wavelength to 1550 nm; and an autocorrelator to measure the pulse width. In most cases, the O S A and autocorrelator are only needed once or when there is doubt that the wavelength or pulse width has changed. For day-to-day operation and mode locking of the laser, the spectrum analyzer and sampling scope are always needed. - 16-Driving Signal RF Synthesizer Clock In Sampling Oscilloscope Optical Pulse Train Fiber-Based Pulsed Laser Autocorrelator Pulsewidth Sideband Suppression RF Spectrum Analyzer Optical Spectrum Analyzer Wavelength Figure 2.1: Equipment schematic for operation of the fiber based pulsed laser - 1 7 -For high-speed sampling purposes, the R F signal provided to the circuit under test can be locked to the optical pulses with a frequency offset as described in Section 1.2.2. In the case where the R F signal is out of the range of the laser repetition rate, the R F signal can be locked to a harmonic of the laser repetition rate as described in Equation (1.1). Thus the laser can be restricted to operate in the range of 1 - 2 G H z and the need for a higher frequency microwave source is eliminated. As wi l l be seen in the next section, it is the noise of the microwave source that is critical to the operation of the laser. 2.2.1.2 Phase Noise Performance One of the key requirements of the optical sampling pulses is their timing jitter. The pulse width determines the resolution of the measurement, and their timing jitter determines the accuracy of the measurement, that is, how accurately it samples a particular point in time. A timing jitter of less than 100 fs has been reported for this type of laser at a 10 G H z repetition rate [19]. The timing jitter is limited by the jitter of the driving microwave signal, making it essential to use a low noise microwave generator. A timing jitter of less than 5 ps is reasonable to sample signals in the G H z range. There are numerous methods available to measure the timing jitter of a periodic signal. The most popular methods involve measurements of the phase noise using an R F spectrum analyzer and then converting to the time domain to get the timing jitter. Time domain methods of measuring jitter require sophisticated tools such as high-speed sampling oscilloscopes. To verify the jitter specification of less than 300 fs of the laser used in the system, both phase noise and time domain techniques were used. The time domain technique is relatively simple and involves the measurement of the period of the signal using a high-speed sampling oscilloscope. These oscilloscopes are capable of measuring the period of a signal and providing statistical data on the measurement. Using a - 18-Tektronix T D S 8000 Digital Sampling Oscilloscope and a 30 G H z optical head, the measured period of a 1 G H z optical pulse train was 0.9948 nanoseconds with a standard deviation of 263.3 fs. The standard deviation of the period gives a measure of the total rms jitter between the sampling pulses. However, the intrinsic rms jitter of the oscilloscope is rated at 1.13 ps for the measurement made above. Thus the measured rms jitter of the optical pulses is an overestimate. The phase noise measurement technique is more indirect. Using an R F spectrum analyzer the frequency spectrum of the sampling pulses can be measured. Phase noise is quoted as dBc/Hz at a particular offset frequency from the center frequency; this is a relative measure with respect to the power of the carrier, that is, the power at the repetition frequency. Figure 2.2 shows the phase noise spectrum of the laser operating at 1 G H z and being driven by two different microwave generators. The phase noise spectrum of the optical pulse train when driven by the Marconi generator is worse between 1 k H z and 20 kHz than when driven by the Agilent microwave generator. The measurement illustrates that the phase noise is dependent on the driving signal making it desirable to use a low noise microwave generator. The rms timing jitter, Gj can be calculated from the phase noise spectrum and for a certain frequency bandwidth is given as [20], [21], where L(f) is the phase noise spectrum, /L is the repetition rate and// o v v and fhigh are the limits of the frequency bandwidth over which the calculation is done. The lower limit, fiow is chosen so that it is smaller than the inverse of the measurement time and fhigh is the detection bandwidth [22]. Equation (2.1) shows that the rms timing jitter is dependent on the area under the phase noise spectrum over the frequency bandwidth. The calculated rms timing jitter for the laser (2.1) - 19--20 -30 -40 -50 -60 -70 -80 -90 -100 r -110 10 10 10 Frequency Offset (Hz) M a r c o n i 2 0 3 1 Ag i len t 8 6 4 8 D 10" Figure 2.2: Phase noise spectrum of optical sampling pulses at 1 G H z locked to two different microwave generators. - 2 0 -operating at 1 G H z and driven by the Agilent 8648D R F generator for different frequency bandwidths is given in Table 2.1. flow (Hz) hgh (Hz) °~J (ps) 100 10000 84.88 500 10000 15.94 1000 10000 0.91 Table 2.1: Calculated rms jitter values for laser operating at 1 G H z and driven by Agilent 8648D R F Generator The values for the rms jitter are higher when the bandwidth is larger. However, when lower frequencies are used for fiow, the jitter is overestimated due to the large area under the phase noise spectrum, which is inaccurate. The minimum resolution bandwidth of the spectrum analyzer is 300 H z and at lower frequencies, the spectrum analyzer maps out its own filter response rather than the spectrum of the signal. Consequently this method of jitter measurement, as implemented in this work, is not accurate due to the limitations of the electrical spectrum analyzer. However, the phase noise measurement demonstrates the effect of the driving signal's noise performance on the phase noise of the optical pulse train. 2.2.2 Synchronization Scheme 2.2.2.1 PLL Description and Purpose A s mentioned earlier, in order to sample the signal on the circuit, the sampling pulses and the R F signal provided to the circuit under test need to be synchronized. This can be achieved by using the two signals in a phase locked loop (PLL) configuration. In most P L L applications, the two signals are at the same frequency but have random phases and one is locked to the other by way of frequency modulation of either one of the signals. However, in this case the sampling pulses are not at the same frequency as the signal, as mentioned in Section 1.2.2. In this case, the two -21 -signals are phase locked to a reference signal instead that is at the same frequency as the frequency offset between the two signals to be synchronized. This same reference signal is also used as the trigger for the data acquisition and in the current setup a 20 kHz square wave provided by a data acquisition card is used. As in all P L L applications, one of the signals to be synchronized is set up as a voltage controlled oscillator (VCO) whose control voltage is set by the phase difference between the two signals to be synchronized. In this case, the laser is used as the V C O , which implies that the microwave generator that drives the laser needs to be frequency modulated. This was achieved by D C coupled F M modulation of the Agilent 8648D R F generator that drives the laser. Figure 2.3 shows a block diagram of the P L L configuration used in the setup. A high-speed photodiode is used to convert the optical pulses to electrical pulses, which are then electrically mixed with the R F signal provided to the circuit under test. The output of the mixer is at the difference frequency and can be considered as the down converted version of the optical pulse train, where the signal provided to the circuit acts as a low noise local oscillator. The phase of the down converted signal is compared to that of a reference signal and the output is filtered to give an error voltage indicative of the phase difference between the two signals. The error signal is fed into the Agilent 8648D as a control voltage. This results in the frequency of the laser changing dynamically until the error signal is zero, at which point the phases are locked. For the system described above, synchronization can be achieved for a peak F M deviation of 0.05 k H z and the signals stay locked indefinitely. The photodiode and high frequency mixer used in the P L L are off the shelf standard microwave components, with specifications given in Appendix C . The phase detector and loop filter operate at low frequency and were designed and built as part of this work. Detailed schematics of the circuits are shown in Appendix A . - 2 2 -Agilent 8648D Fiber Based Picosecond Laser Phase Detector A Reference Oscillator LPF\ Circuit Under Test Vbias A A Microwave Source Figure 2.3: Block diagram of phase locked loop configuration used in E O S system -23 -2.2.2.2 Performance and Measurement of PLL The down converted signal obtained from mixing the optical pulse train with the signal driving the circuit under test is viewed on an oscilloscope along with the reference signal, which are both at 20 kHz . The ability to view both signals simultaneously on the oscilloscope, using either one of the signals as the trigger, is an indication that the two signals are phase locked and confirms the synchronization. The performance of the P L L can be measured by viewing the effect of the P L L on the phase noise spectrum of the optical sampling pulses. Figure 2.4 shows the phase noise spectrum of the laser operating at 1 G H z for two cases; 1) mode-locked to the external driving signal; 2) mode-locked to the same external driving signal and synchronized via the P L L to a reference signal. The two peaks at 40 and 80 k H z are harmonics of the laser relaxation oscillation frequency [19]. Since the laser is being F M modulated, via its driving signal, the phase spectrum of the laser when synchronized would look like an F M modulated signal for a large F M peak deviation. However, in this case, the peak frequency deviation is 0.05 kHz , meaning that the instantaneous frequency of the optical pulses changes at most by 0.05 k H z from the center frequency. The R F spectrum analyzer is unable to track this change in frequency due to its bandwidth resolution limitations. For low F M modulation depths, the phase noise spectrum of a F M modulated signal is unchanged and is validated by the negligible difference in the two spectra in Figure 2.4. Phase locked loops are used to track out low frequency noise, up to the bandwidth of the P L L , of a signal when it is locked to a cleaner source than itself. In this case, however, there is a negligible change, indicating that the phase noise and hence the timing jitter of the optical sampling pulses is limited by the jitter of the driving signal. This result is consistent with reference [19], where phase noise measurements on a harmonically mode-locked Erbium-doped fiber laser at 10 G H z were made. - 2 4 -Figure 2.4: Phase noise spectrum of optical sampling pulses operating at 1 G H z . Measurement taken for the case of synchronized and not synchronized to reference signal - 2 5 -2.2.3 Opt ica l Path Design 2.2.3.1 Polarization State Considerations The electro-optic effect is a change in polarization of an optical signal passing through a medium due to an electric field in the medium. It is important that any changes to the polarization of the light other than those due to the electro-optic effect either be minimized or controlled. Light undergoes polarization changes while propagating through a fiber due to the inherent birefringence in optical fibers due to microscopic manufacturing imperfections. The birefringence is relatively small for meter length fibers, i f the fiber is relatively straight. However, for fiber that is bent or twisted, the birefringence is significantly increased. Polarization maintaining (PM) fiber is available, however, this kind of fiber is intended for use with light linearly polarized exactly along one of the orthogonal axes of the P M fiber. This is not applicable in the case of electro-optic sampling as the electro-optic signal is elliptically polarized. Consequently, single mode fiber (SMF) has to be used, which is non-polarization maintaining. When using fiber optic components, it is unavoidable to have approximately 1-meter long cables connected to each of the ports of the component and thus they need to be wound and routed around the experimental setup. This introduces bends and twists in the fiber, increasing the birefringence in the fiber, which causes the light to change from linear to elliptical polarization. When designing the optics involved in a fiber based E O S system, it is imperative to consider the polarization state of the light at all times and how this can affect the measurement being made. Wi th this in mind, the next section describes the design of the optical path, which includes the polarization optics to deliver the light to the electro-optic sampling tip and the detection optics to detect the reflected signal to measure the electric field. - 2 6 -2.2.3.2 Overall Design and Components Figure 2.5 shows the block diagram of the optical path from the laser to the detection circuitry. The polarization optics and detection optics are highlighted by their respective dotted boundaries. The single line between the components indicates a fiber optic S M F cable, the solid triangles indicate a fiber angle polished connector ( F C / A P C ) and the light propagation direction, and the double lines indicate propagation in free space. The next few paragraphs describe the purpose of each component. The polarization optics are used to deliver the light to the fiber based sampling tip with the correct power and polarization state. The variable attenuator ( V A T T ) is used to set the average power delivered to the fiber. The polarizer and half wave plate (FTWP1) are used together to provide linearly polarized light with an extinction ratio of >30 dB at a controllable angle. This is based on the fact that the polarization direction of linearly polarized light passing through a half wave plate centered at the operating wavelength is rotated by 2(|> i f the plane of polarization is at an angle of <|> with the axis of the half wave plate. Thus by rotating H W P l , the linearly polarized light can be rotated so that it arrives at the sampling tip with the correct orientation. The intermediate optical fiber w i l l also rotate the plane of polarization as the light propagates to the tip and the H W P l acts to reverse this effect. In addition to rotating the plane of polarization, the birefringence of the fiber can also change the polarization of the light to an elliptical state. Thus the polarization controller (PC) is needed to change the polarization so that it arrives as linearly polarized light at the sampling tip. The polarization of the light exiting the sampling tip can be set to linear after all the fiber optic cables are securely fixed in place. The circulator is used to deliver the light to the sampling tip and to direct the reflected light to the detection optics. The isolation from ports 1 to 3 and from ports 2 to 1 is specified as greater than 50 dB. The insertion loss due to the Polarizer, H W P l and passing from port 1 to 2 of the - 2 7 -Fiber Based Pulsed Laser VATT Polar iz ing O p t i c s Polarizer 1 O O P HWP 1 PC Photoreceiver Circuit {X-JHVbias COMP Fiber HWP 2 Port Circulator 'F iber Sampling Tip PBSC [Circuit Under Test] Detect ion Opt i cs I Figure 2.5: Block diagram of E O S system optical path design. The solid lines with arrows depict fiber optic cables with F C / A P C connectors. - 2 8 -circulator is 2.2 dB. The detection optics are composed of free space optical components. A fiber port, which is a stable, miniature micropositioner, enabling active alignment of an aspheric lens for collimating a fiber beam to a free space beam, is used to couple the light from the circulator to a collimated beam of 2.4 mm diameter propagating in air. The optical loss of the circulator from port 2 to 3 and the fiber port is 1.1 dB. The light reflected from the sampling tip is elliptically polarized due to the birefringence of the optical fiber with the two orthogonal polarization components being modulated by the electric field in the sampling tip so that they have a time dependent magnitude. The total magnitude of each component however can be considered as an ac component added onto a dc component. The dc value of each component w i l l depend on the amount of birefringence experienced by the light while propagating through the fiber from the sampling tip to the fiber port. A second half wave plate (HWP2) is used to rotate the direction of the major and minor axes of the elliptically polarized light so that they are aligned with the axes of the polarizing beam splitter cube (PBSC). A t this point one of the outputs of the P B S C is a maximum while the other is a minimum. The above step is done with the component labeled C O M P , which is a quarter wave plate centered at the operating wavelength and referred to as a compensator, removed from the optical path. The rotation of the minor and major axes of the elliptically polarized light is based on the same principle as the rotation of linearly polarized light by a half wave plate. The purpose of C O M P is to introduce a known amount of birefringence between the components of the elliptically polarized light so that the major and minor axes are equal, thus achieving circularly polarized light. This is done to bias the electro-optic modulator as its quadrature point as shown in Figure 1.2. Linearly polarized light incident normally and polarized at 45° to the axis of a quarter wave plate results in circularly polarized light as the wave plate introduces a phase shift of a quarter wavelength or 7t/2. Since the detected light is not - 2 9 -linearly polarized, a phase shift of less than or greater than Tt/2 is needed to get circularly polarized light. To achieve this, the C O M P is tilted about its fast or slow axis as indicated in Figure 2.5. This tilting changes the effective thickness of the wave plate along the propagation direction of the light. Thus the light experiences a path length that is different from a quarter wavelength. The C O M P is tilted until the two polarization components of the light exiting the P B S C are equal. The photodiodes are connected to a photo receiver circuit to amplify and filter the signal. Detailed schematics of the circuit are shown in Appendix A . Details of the specifications and model numbers of all the optical components can be found in Appendix B . 2.2.4 Sampl ing T i p Design and Height Con t ro l 2.2.4.1 Electro-optic Tip Design The design of the electro-optic sampling tip is an important consideration in the system level design. The sampling tip contains the electro-optic crystal responsible for the modulation of the light passing through it when it experiences an external electric field. For a tip to be an effective sensor and be incorporated into a system, it must have a high sensitivity to electric fields, have the ability to direct a high percentage of the modulated light back to the detector, have a mechanism that allows accurate placement of the electro-optic crystal into the electric field in question, and finally it should be easy to manufacture. Taking these requirements into consideration, the fiber based sampling tip designed in this work was made by attaching a thin electro-optic piece of material to the end face of a cleaved fiber optic cable. The electro-optic material used in the tip and its geometry dictate the sensitivity of the tip. Once the light passes through the electro-optic crystal and experiences the electro-optic effect, it needs to be directed to the detection optics with minimum optical loss. For - 3 0 -a fiber-based tip, this can be achieved by coupling the light exiting the tip back into the fiber by reflecting the light off the circuit under test that provides the electric field. To get a high reflectivity, the tip should be placed over a metal line instead of the substrate. The electric field over a metal line is stronger in the vertical direction, so a material geometry that is sensitive to vertical fields should be used to exploit this fact. This idea of reflected light can be used to achieve the third requirement, which is to accurately place the tip above the conductor on the C U T . This is possible by monitoring the total reflected light as w i l l be shown later in Section 3.2.2. The final requirement is to make it easy to manufacture. Details of the tip designed in this work are presented in Section 3.2.1. 2.2.4.2 Tip Height Control The control of the tip height is just as crucial a requirement as is the sensitivity of the tip. The electric field over high-speed transmission lines is strongly dependent on the geometry and to accurately measure it, the sensor has to be placed reliably and stably in the field. The size of the transmission lines in question are usually less than 20 |-im and the electric fields are strongest close to the transmission line. A reasonable tip height over a metal line is expected to be 5-20 jxm. High resolution and precision nanopositioners that use piezoelectric materials to control motion are commercially available to allow sub micron movements of the fiber tip around the test point in any direction. A s wi l l be shown later, the total reflected power from the fiber-based sampling tip is sensitive to the tip height and can be used in a feedback system to servo the tip over the circuit under test. The tip height can be controlled in an open loop or closed-loop mode. In the former mode, the reflected power is not used to dynamically servo the tip height once an operating height is selected. Therefore, to avoid changes in the reflected power, the operating height should be chosen to minimize the sensitivity to fluctuations in the tip height due to any -31 -vibrations. In the closed-loop mode, a reference reflected power level is used to compare to the instantaneous reflected power level to generate an error voltage that can be used to control the piezo nanopositioners in a feedback control loop. The goal in either mode is to stabilize the height of the tip so that any fluctuations in the power reflected from the surface of the circuit under test are minimized. 2.2.5 Summary and Conclusions The work presented in this chapter describes the work done towards developing a fiber based electro-optic sampling system. The key achievements were the successful characterization and of a suitable laser that meets the requirements of E O S , design and implementation of a synchronization scheme that works well and does not affect the phase noise of the optical sampling pulses and a suitable optical path design that is capable of making a polarization sensitive measurement in a non-polarization maintaining environment. With all the pieces in place, the development and characterization of the fiber-based sampling tip was possible and is described in the next chapter. - 3 2 -Chapter 3 Fiber-Based Electro-Optic Sampling Tip 3.1 Introduction to Chapter In this chapter, the design, fabrication and characterization of a novel fiber-based electro-optic sampling tip is described. Section 3.2.1 gives a physical description of the tip and the manufacturing process. A theoretical treatment of the tip is presented in Section 3.2.2. The method and experimental setup used to characterize the tips is explained in Section 3.3, with a discussion of the results. 3.2 Description of Fiber-Based EO Tip 3.2.1 Design and Description of Tip The major advantage of a fiber based electro-optic sampling tip is to avoid having to collimate light out of the fiber and into a conventional electro-optic sampling tip and then couple the light back into the fiber for detection purposes. A fiber-based electro-optic sampling tip was designed using S M F and A l G a A s as the electro-optic material. A l G a A s was chosen because it can be easily grown on a GaAs wafer using molecular beam epitaxy ( M B E ) . The basic design is a piece of A l G a A s attached to the cleaved end of a fiber. The A l G a A s acts as the E O material and the fiber as the delivery mechanism for the light into and out of the E O material. If a 1-5 u.m thick piece is used, multiple reflections of the light between the fiber-AlGaAs-air interfaces leads to a longer interaction time between the light and the electric field on the circuit under test, resulting in enhanced modulation - 3 3 -of the optical pulses. Through careful selection of the E O material properties and thickness, a tip with optimum sensitivity and reflectivity can be realized. A simple way of creating a 1-5 | i m thick semiconductor layer is to use selective etching. Figure 3.1 shows a GaAs wafer with Alo.3Gao.7As grown on it. A straightforward method of selective etching in G a A s - A l G a A s systems is described in reference [23]. The paper describes a simple way to etch GaAs using citric acid and hydrogen peroxide. The present design uses a GaAs substrate with Alo.3Gao.7As as the E O material because of the high selectivity of the etchant between GaAs and Alo.3Gao.7As. Such a thin A l G a A s layer can be easily grown using M B E and the thickness can be tightly controlled. B y mechanically thinning the GaAs wafer to manageable thickness of 80 nm, and cleaving it into square pieces of 200 - 500 \im, the pieces can be attached and glued to the cleaved end of a fiber. Upon etching the GaAs substrate away, the A l G a A s layer remains at the end of the fiber. The GaAs wafer used was manufactured before the start of this work with an A l G a A s layer of 1.6 U-m. Industry standard fiber-optic glue from Epoxy Technology (353ND) was used to attach the square pieces of the GaAs wafer to the fiber end. The cleaved end of the fiber is glued onto an aluminum support so that it is vertically supported; the support is mounted onto a 5-axis translation stage. Before attaching the GaAs wafer piece, the fiber end is planarized so that it is parallel to the surface of the wafer. The planarization is achieved by monitoring the optical power reflected from the wafer surface and adjusting the pitch and yaw knobs so as to maximize the power reflected. A stereomicroscope is used to view this process. The fiber end is then dipped into a small drop of the glue and then placed over the wafer piece and lowered down. Upon contact, the capillary force of the glue attracts the piece, which gets pressed against the fiber end face. The glue is cured by positioning a soldering iron, mounted on a 3-axis translation stage, as close as possible to the fiber end, without touching the attached wafer piece - 3 4 -AlGaAs EO Material 1.6 \xm GaAs Wafer -100 |um Figure 3.1: Sketch of the GaAs wafer used for manufacture of fiber tips - 3 5 -or the fiber. The glue takes 5-10 minutes to cure, indicated by its color changing from amber to dark red. The fiber is removed from the support before placing it in a beaker of the etchant for 4-5 hours to remove the GaAs and leave the A l G a A s layer exposed. The epoxy is not affected by the etchant and remains between and around the fiber and wafer piece. A digital image of the fiber with a wafer piece attached to it is shown in Figure 3.2. It illustrates how the epoxy forms a fillet around the circumference of the fiber. 3.2.2 Theoretical Descript ion The theoretical analysis of the optical behavior of the fiber tips is similar to the analysis of a Fabry-Perot cavity due to the multiple reflections of the light within the A l G a A s . There are two cases in which the tip is analyzed; the first is to consider the tip as a single Fabry-Perot cavity created by the fiber, A l G a A s and air; the second is to consider the application in this work where the tip is placed over a conductor/metal line on a circuit under test, which results in a double Fabry-Perot cavity. The next two subsections present the equations needed to describe the tip in these two cases, respectively. Sections 3.2.2.3 and 3.2.2.4 describe the behaviour of the fiber tips in terms of their electro-optic efficiency and reflectance. The justification for neglecting diffractive losses when the light is propagating out of the fiber is presented in Section 3.2.2.4. 3.2.2.1 Single Fabry-Perot Treatment of Fiber Tip The analysis begins by first considering a single Fabry-Perot cavity made up of three materials with different wave propagation factors, ko, kj, and fo as defined in Figure 3.3. The figure shows the case for an incident optical wave from the left with interfaces of the three regions along the z-axis at zo and zi. Regions 0 and 2 are of infinite extent towards the left and right, respectively. The direction dependent reflection and transmission coefficients for the different interfaces are given as /?, and T;. - 3 6 -Figure 3.2: Digital image of manufactured fiber tip showing A l G a A s 1.6 p,m piece attached with glue forming a fillet around the fiber end. - 3 7 -Neglecting time as a variable, the incident optical waveform can be represented by its electrical field as: Et(z)=Epe-^ (3.1) The equations for Fabry-Perot reflections and transmissions are standard results and the reader is referred to reference [24] for detailed derivations. The reflected wave is given as Er(z) = Epe-ik°z°e -ik0(z0-z) -2iS Pa+Pc* (3.2) where 8 = kxd (3.3) The total optical field in region 0 is the linear superposition of the incident and reflected waves: Eo(z)=E,(z)+Er(z) (3.4) The fields in the other two regions are: E1{z)=EM = Epe-^ra -2iS E2{z)=Et{z)^Epe-ik^e 'Mo „-'*2(z-Zi) T T e a c -iS -lid (3.5) (3.6) } + PaPce~ Figure 3.4 shows the case for a right-incident optical wave. The equations for this case are similar and are: E0(z) = E,(z) = E / ^ - ' * ° ( z ° -- i s l + PaPce -2iS El{z)=Ejz)=Epe'K^TD e'ik,{zt'z) + pbe-iSe~ikAz'Zo> l + PaPce •2iS E2{z)=Ep g'k2Z + g'*2Zlg-'*2(z-Zl) PA + Pbe 1 + PaPce -US -2iS (3.7) (3.8) (3.9) - 3 8 -Er 2flh0 Zo . 2701, k, -Zi p a T a Ei A P" Xc lint d _ 2m2 /Co Xrf A Figure 3.3: Fabry-Perot structure with a left-incident optical wave _2m0 Zo A 2701, k, -Zi Ta A _ 27m2 Xb p c Xc '.Int P" Ei A Er Figure 3.4: Fabry-Perot structure with a right-incident optical wave - 3 9 -Equations (3.7) to (3.9) w i l l be needed later in section 3.2.2.2 when a double Fabry-Perot structure is analyzed. Equations (3.4) to (3.6) are enough to analyze the sampling tip as a single Fabry-Perot cavity. The reflectance and transmittance of the fiber tip are defined as the ratio of the optical power of the reflected beam to the power of the incident beam, and the ratio of the power of the transmitted beam to the power of the incident beam, respectively. Figures 3.5 and 3.6 show the reflectance and transmittance as a function of the A l G a A s thickness for an operating laser wavelength of k = 1550 nm. In this analysis, there is no loss of light and therefore, the transmittance and reflectance add up to unity for any thickness of the A l G a A s . 3.2.2.2 Double Fabry-Perot Treatment of Fiber Tip When the tip is placed over a particular conductor/metal line on the circuit under test, there are three interfaces from which the light can be reflected back into the fiber tip. These are the fiber-A l G a A s interface, the AlGaAs-a i r interface and the air-conductor interface as illustrated in Figure 3.7 where the three interfaces contribute to the overall reflected light. The constructive and destructive interference of these three contributions determines the overall reflectivity of the fiber tip. In this case, Equations (3.4) to (3.9) can be used to derive expressions for the reflected beam. The conductor acts as a reflective surface that redirects the optical beam back towards the Fabry-Perot in the opposite direction to the incoming beam from the fiber side. The air gap introduces a phase shift that is proportional to twice its length and the reflection of the light at the conductor introduces a phase shift of n. The length of the air gap determines how much the light diffracts as it is no longer guided in the fiber core. Diffractive losses are ignored in the current analysis and wi l l be addressed in section 3.2.2.4. Figure 3.8 shows a conceptual diagram of the fiber based sampling tip placed in front of a conductor, indicated by the hatched region - 4 0 -0.6 0 i , ' ' ' » 1.5 1.6 1.7 1.8 1.9 2 Thickness of A l G a A s (jim) Figure 3.5: Reflectance of fiber tip Fabry-Perot cavity of F iber |AlGaAs |Ai r as a function of Alo.3Gao.7As thickness for A. = 1550nm 1 0.4" 1 1 1 1 1 1.5 1.6 1.7 1.8 1.9 2 Thickness of A l G a A s (|im) Figure 3.6: Transmittance of fiber tip Fabry-Perot cavity of F iber |AlGaAs |Ai r as a function of Alo.3Gao.7As thickness for A, = 1550nm -41 -Input Beam AlGaAs Conductor — Reflected Beams — Fiber Sampling Tip V+ V-Figure 3 .7 : Illustrative contributions to reflected light in fiber tip - 4 2 -on the right. The figure shows the multiple reflections that occur at the three interfaces. The incoming beam is from the left side in the fiber. The thickness of the A l G a A s is shown as / and the air gap between the tip end and the conductor as d. In most cases the conductors on high-speed circuits are usually gold or aluminum and their reflectivity is not 100% due to surface roughness. The parameter p e is introduced as the effective reflectivity of the conductor and takes into account the effect of diffraction and of the reflectivity of the conductor. The total optical field in each region is an infinite sum of all the multiple reflections caused by the interfaces. Using Equations (3.4) to (3.9), expressions for the Ej(z) terms in Figure 3.8 can be derived and are shown below. The total field in the fiber, in the A l G a A s , and in the air, denoted as ETOT,O(Z)> ETOT,J(Z), ETOT,2(Z) respectively, are given as: ETOT0(z) = Epe~ik°z + Rie-ik°{z°-z) + e - t t o k > - ' ) 1 — Q2Q4 (3.10) r (z)- L + Q ^ 1 — V ^ 2 ^ 4 (3.11) 'TOT,2 (z) = Txe -<*2U-Zi) G , G : 5 g-'Mz2-z) 1 Q 1 Q 2 Q 4 c-ik2{z-z{ where the terms in Equations (3.10) to (3.12) are given below. (3.12) Rx=Ee - i t . 0^0 -US Pa+Pc* »  T l =  E p e -ik. T T e a c -id l + PaPce -2iS L, =Ene-ik°z°Tn 1 p a 1 + -US ' L2 - Td e'ik^'z) + pbe'iSe~ikAz~ZoY l + PaPce -2x5 1+PaPc* -H5 .e 3 1 + PaPc* -2x5 -U5 Pd + Pbe l + PaPce~2iS Q2=pee-m>d,Q5=pee -ik7d 8 = kxl -43 Zo Zi Eo(2) E.fe) E«(z) E,7(z) -I A A A A A T - - * 4 vAAAA/u A/VWU • A/WV\j P. Pc Xc E,(zJ E,(z) www www E»(z) A/WW >UGaAs i d Bfzj Eft A/WW E,(zj AWW www E.fzJ www A'rgap Figure 3.8: Conceptual diagram of double Fabry-Perot cavity created when fiber tip is placed above a conductor or metal line with an air gap of thickness d. -AA-The equations show that the optical field in all three regions depends on the thickness of the air gap, d, among other parameters. However, once the fiber tip is manufactured and a fixed laser wavelength is used, the only degree of freedom left is the air gap. B y changing the air gap, the amount of reflected light and the sensitivity of the electro-optic sampling tip can be controlled. Equations (3.10) to (3.12) can be used to determine the strength of the optical field in electro-optic material and hence simulate the electro-optic effect, and calculate the reflectance of the tip. The next two subsections describe the simulation of the electro-optic effect and the calculation of the overall reflectance of the fiber tip. 3.2.2.3 Electro-Optic Effect in the Fiber Tip Due to the constructive and destructive interference of the multiple reflections of the optical waves in the three regions, the intensity of the field w i l l depend strongly on the dimensions of the tip. For a fixed Alo.3Gao.7As thickness and laser wavelength, the air gap can be varied so that the field intensity in the Alo.3Gao.7As is a maximum. Conversely, the field intensity in the Alo.3Gao.7As can also be a minimum. These two cases are shown in Figures 3.9 and 3.10 for an Alo.3Gao.7As thickness of 1.6 pm, and an effective conductor reflectivity, pe = 1. The choice of 1.6 (im is representative of the A l G a A s thickness on the GaAs wafer manufactured previous to the start of this work. The field is a maximum in the Alo.3Gao.7As when the air gap thickness, d = 9 pan and a minimum when d - l | im. The plots show that it is possible to trap more of the optical field in the Alo.3Gao.7As than in the air which wi l l result in a stronger interaction between the optical and electric field. To calculate the phase difference between the two orthogonal polarizations of light due to the electro-optic effect, the index of refraction of the A l G a A s in the simulations was varied continuously from its equilibrium value to a value typically induced by electric fields in high--45 -Position (\im) Figure 3.9: Maximum case field intensity distribution for fiber tip with 1 = 1.6 mm, A, = 1550 nm, p e = 1. Field is a maximum in Alo.3Gao.7As and minimum in air when the air gap thickness, d = 9 | im - 4 6 -Position (\im) Figure 3.10: Min imum case field intensity distribution for fiber tip with 1 = 1.6 | im, A, = 1550 nm, p e = 1. Field is a minimum in Alo.3Gao.7As and maximum in air when the air gap thickness, d = 7 | im. - 4 7 -speed circuits. The change in index of refraction along the two crystal axes, nx and ny , for the two polarizations is given as: n x = n 0 + ^ r 4 l E z (3.13) n Y = n 0 - ^ E z (3.14) where no is the equilibrium index of refraction, r4I is the electro-optic coefficient for the material and Ez is the applied electric field in the direction normal to the conductor surface and fiber tip end face. Typical electric field strengths between two conductors on a high-speed circuit depends strongly on the separation t between the conductors, the height h above the conductors, and the voltage difference V, between the conductors and can be approximated to first order as: V E = — (3.15) t For a voltage difference of 1 V and a typical separation of 10 \xm, the change in nx and ny is on the order of ±10" 6 . Using this as a starting point, the phase difference between the incident optical wave and reflected optical wave for each of the two polarization directions can be calculated for the respective change in no. The phase difference is a function of the electric field in the tip and can be written as * = * ^ (3-16) where a figure of merit, En is introduced. The phase difference is a linear relationship with respect to Ez as seen in Equations (3.13) and (3.14). The slope of this linear relationship can be calculated and Equation (3.16) can be differentiated with respect to Etip to give: E„ -n\ ( dS V ' (3.17) 48 allowing the calculation of the figure of merit En for a given air gap thickness. E„ is a function of the air gap between the sampling tip and circuit under test and is illustrated in Figure 3.11 for a typical fiber-based sampling tip. The value of En changes as the air gap changes and for good detection sensitivity, the lowest value of En should be used. 3.2.2.4 Reflectance of Fiber Tip The metal line above which the tip is placed reflects light back into the fiber tip. Factors that affect the coupling efficiency of the light back into the fiber core are the reflectivity of the metal line, how parallel the fiber end face is to the metal line and the length of the air gap itself. The reflectivity of the metal line depends on the material used and its smoothness. In most technologies, gold, copper or aluminum is used, resulting in a reflectivity ranging from 0.9 to 1. Assuming that the fiber end face is parallel to the surface of the conductor, the only degree of freedom left is the air gap thickness. Light is guided in the fiber core and once it leaves the core, the light diffracts and follows Gaussian optics propagation laws. The total distance traveled by the light before it gets back to the fiber end face is twice the air gap thickness plus the Alo.3Gao.7As thickness. The optical wave front of the light diffracts during this propagation and not all of it w i l l be coupled back into the fiber core due to the mode mismatch between the fiber's propagation mode and that of the optical field. Using an overlap integral between the dominant propagation mode of the fiber core and the optical wave front [25], [26], it can be shown that the transmission coefficient between light exiting one fiber and entering another fiber of the same mode field diameter is T = 1 (3.18) 1 + Z 2 where Z = Ad 2nw20 (3.19) - 4 9 -- 5 0 -and A is the wavelength, d is the distance traveled by the light in air and Wo is the mode field diameter of the fiber. Equation (3.18) is plotted in Figure 3.12 for the case of A = 1550 nm and (Oo - 8 |0,m. The plot shows that for a typical air gap of 5-20 |^m, the corresponding d in Equation (3.19) is 10-40 |om and the transmission coefficient is close to unity. Consequently, diffraction loss can be can be neglected in this case. Thus i f the fiber end face is parallel to the metal line, the governing factor for the amount of optical power reflected back into the tip is the reflectivity of the metal. The effective reflectivity, pe of the conductor introduced in Section 3.2.2.2 can be replaced by the reflectivity of the conductor surface. The reflectance of the fiber based sampling tip can be calculated using Equation (3.10) by taking the ratio of the two terms to give: -ik0{z0-z) QlQlQi -ik0{z0-z)\ R = I-Q2Q4 E e~ikaZ (3.20) The modulus squared has been included here to give the power reflectance, R. Equation (3.20) is plotted in Figure 3.13 for the case of pe = 0.9 and A = 1550 nm. The plot is similar to the reflectivity of a simple Fabry-Perot cavity and confirms the constructive and destructive interference occurring between the three contributions to the reflected light shown in Figure 3.7. The result is promising as it indicates that it is possible to control the height of the fiber tip over the conductor surface by monitoring the total power reflected from the fiber tip. -51 -0.96r 0 95L 1 ' 1 1 1 ' 0 10 20 30 40 50 Gap Between Fiber End Faces (Jim) Figure 3.12: Plot of Transmission coefficient between two fibers of equal mode field diameter, (Oo - 8 pm, separated by a distance in air and operating at A = 1550 nm - 5 2 -3.3 Fiber Tip Characterization Once the tips are manufactured, the characterization can be grouped as D C characterization and A C characterization. The former is the characterization of the reflectance of the tips to determine i f the electro-optic material has been attached correctly to the fiber end face. The latter refers to the measurements made to determine the effectiveness of the tips in measuring an electric field above a circuit. The next two subsections describe in detail the experimental set up and results of the measurements. 3.3.1 D C Characterization The transmission and reflectance of the fiber tips depend on the thickness of the A l G a A s after the selective etching of the GaAs substrate. The most critical manufacturing step is making sure that the GaAs wafer is attached parallel to the fiber end face. The transmittance and reflectance were measured for each fiber tip after etching. A n optical circulator was used to direct the light into the tip and to measure the reflected light. In all cases 0 d B m of optical power was launched into the tip and the transmittance measured in free space using a power meter on a translation stage. This allows precise movement of the power meter close to the fiber tip end face. The reflected light is fiber coupled so it can be measured directly using the power meter. Table 3.1 shows reflectance and transmittance measurements made for fiber tips manufactured in this work. The highlighted rows show tips considered good as the transmittance and reflectance add to unity, indicating the GaAs wafer was attached parallel as possible to the fiber end face. The next test performed on the good fiber tips is the reflectance of the tip when placed over a metal line on a test circuit. As the tip gets closer to the metal, light is coupled back into the fiber core and the reflectance increases from the values quoted in Table 3.1. The fiber tip is - 5 4 -Fiber # T (dBm) R (dBm) R+T 1 -4.40 -2.90 n s T , •> -5.80 -1.85 0.916 3 -3.30 -3.00 0.969 1 -3.15 -3.35 0.947 5 -6.90 -2.20 0.807 6 -5.55 -2.85 n - o -1 7 *.""() -2.75 0.957 8 -4.15 -3.00 0.886 9 -2.70 -3.40 0.994 10 1 10 -2.05 0.987 Table 3.1: Transmittance and reflectance measurements for fiber tips with 0 d B m optical power launched into tips. The highlighted rows indicate good tips as R+T = 1. mounted on a nanopositioner capable of less than 0.1 | i m steps over a range of 20 | i m and with pitch and yaw adjustment controls. Before the measurement is made, the fiber is planarized with the metal line using the pitch and yaw adjustment by maximizing the peak reflected power. A high-resolution camera above the circuit under test is used to monitor the position of the fiber tip over the circuit under test. The tip height is decreased until it is in the same focal plane as the circuit under test, indicating that it is 5-20 um above the conductor surface. Figure 3.14 shows the results of the measurement on one of the good fibers. Since the reflectivity pe of the metal line is not known, the value is changed in the simulation to fit the data measured. The value attained for this fiber is pe = 0.83. The figure shows a good agreement between measured and simulated values, indicating that the fiber tip is working well . The figure shows the reflectivity versus relative height, meaning that the zero of the x-axis is not the point at 0 j im above the metal and is in fact less than 1 | im. When the fiber tip bumps into the metal, the distance between the previous minimum and the next increases from a - 5 5 -Simulated " • " Measured 0.3 1 J • ' • • 1 0 1 2 3 4 5 Airgap Thickness (um) Figure 3.14: Simulated and measured reflectance of fiber tip over a metal line with pe = 0.83 - 5 6 -standard 0.8 pm to 1 - 1.2 | i m as illustrated in Figure 3.15. It is believed that the tip is being compressed against the metal and this effectively changes the lengths of Fabry-Perot cavities. 3.3.2 A C Characterization The A C measurement set up of the fiber tip is similar to that of the D C measurement. However, a known electric field is needed to verify the electro-optic behavior of the fiber tip. To simplify the measurement, a low frequency field is used so that it can be easily simulated and measured. The fields were simulated using a freeware tool named Poisson Superfish available from the Los Alamos National Laboratory website [27]. The tool is capable of calculating the components of an electrostatic field. The test circuit is a coplanar waveguide structure (CPW) similar to those found on high-speed circuits. The C P W is gold on an alumina substrate and has a center conductor of 60 p.m with 30 u;m gaps between the conductor and ground planes; it has a characteristic impedance of 50 Q. A l G a A s is considered a longitudinal type electro-optic material. This means that the electro-optic effect is sensitive to electric fields that are parallel to the propagation direction of the light passing through the crystal. Thus it is only the vertical electric field around the C P W that can be detected electro-optically i f the fiber tip is normal to the C P W substrate. Figure 3.16 is a plot of the vertical field, ZsZ; above the C P W when a 5 V p k sinusoidal voltage is applied. The plot shows the field amplitude at different heights above the C P W conductor. The field is relatively constant with height above the center conductor, over the range shown, and the field decays everywhere else as height increases. In particular, the sharpness of the maximum and minimum decreases as height increases. - 5 7 -1 Ql l I I I I I 0 1 2 3 4 5 6 Relative Ai r Gap Thickness (pirn) Figure 3.15: Reflectivity measurement of fiber tip as it approaches conductor surface. When the fiber tip is in contact with the conductor surface, the Fabry-Perot fringes expand - 5 8 -2000 Distance Across C P W (pirn) Figure 3.16: P lo t o f the vert ical electric f i e ld ampli tude, Ez above the C P W for different heights above the metal l ines for a 5 V p k voltage appl ied. T h e so l id rectangles represent the physical geometry o f the C P W . - 5 9 -When the fiber tip is placed above the C P W , the shape of the field w i l l remain relatively same but the field values wi l l change inside the electro-optic material. This too has been simulated with the results plotted in Figure 3.17. The plot shows the electric field inside the A l G a A s at the same corresponding heights as in Figure 3.16 so that a direct comparison can be made. Immediately, one can notice some differences from the case where no tip is present above the C P W . Firstly, the electric field magnitude is lower by about a factor of five. This is due to the introduction of a high dielectric constant material above the C P W . The simulation results from this case also show that the field between the conductor and the A l G a A s , which is the air gap, is larger than the field inside the tip by a factor of C A R T A S higher, which is equal to 12. This result is not surprising since the vertical electric fields are not continuous across a boundary and are changed by the ratio of the dielectric constants on either side of the boundary. The second observation is that the field is no longer insensitive to the tip height above the center conductor. This can be attributed to the minimal capacitive loading that the tip introduces. A s mentioned earlier, the data acquisition electronics are set up for a frequency offset of 20 kHz between the optical sampling pulses and the R F signal applied to the circuit under test. To keep with this, a 20 kHz , 5 V P k sinusoidal voltage is applied to the C P W to set up a quasi-static field. Once the field shape and magnitudes are known, a measurement can be made to verify that the fiber based sampling tip works as an electro-optic sensor. The reflected optical signal is fed into the photoreceiver circuit, which has two D C and two A C outputs. The D C outputs are a measure of the reflected optical power for both orthogonal polarization components. The A C outputs are the amplified and filtered versions of the A C optical signal. The two A C outputs are fed to a lock-in amplifier (LIA) and differentially coupled. The reference signal to the L I A is the same signal provided to the C P W , forcing the L I A to lock to a signal at the same frequency. The magnitude of the A C signals depends on the total power reflected, so the measured A C voltage - 6 0 -300 > t W s 0 -lOOh -40 -20 0 20 40 Distance Across C P W (|im) Figure 3.17: Plot of the vertical electric field amplitude, Ez above the C P W when a fiber tip is present at the heights indicated for a 5 V p k voltage applied. The solid rectangles represent the physical geometry of the C P W -61 -is divided by the total D C voltage to give a standardized output reading. To validate the electro-optic behavior of the tip the electric field shape above the C P W was measured. The tip is planarized and placed above the C P W so that the height is less than 10 | im. It is desirable to adjust the height of the tip so as to maximize the reflected optical power to get a good signal-to-noise ratio. A s can be seen from Figure 3.13, the peak reflectance occurs periodically with height and is relatively insensitive to any height changes at this local maximum. Working at this operating point also avoids noise from vibrations that may be occurring around the experiment. Thus the height of the tip is always adjusted so that the operating point is at the maximum reflectance point. Setting the height to an operating point close to 5 - 10 [im and about 150 p:m in the x-y plane from the center conductor, the fiber tip was moved in increments of 3 p.m up to the opposite end of the C P W . Each time the fiber tip was moved in the x-y plane, the tip height was readjusted to maximize the reflected optical power. The results of the measurement are shown in Figure 3.18 as the normalized field amplitude. Plotted along side is the simulated vertical electric field in the A l G a A s at a height of 6 | i m above the C P W . There is a good agreement between the measured and simulated field above the center conductor. A s the tip moves away laterally from the center conductor, the measured and simulated values start to deviate. This is attributed to the fact that the simulations were carried out for a fiber tip centered above the center conductor of the C P W . So for a 125 U-m wide S M F , the A l G a A s extends 62.5 [im on either side of the center conductor of the C P W , leading to a symmetrical configuration. But in the case of the measurement, the fiber tip actually moves laterally across the C P W and is not centered over the center conductor, except when at a position of 0 p.m along the axis shown in Figure 3.17, thus loading the C P W asymmetrically unlike in the simulations. For a true simulation to be conducted, the fiber tip has to be moved every 3 u,m in the simulation and the vertical - 6 2 --0.6 • • -150 -100 -50 0 50 100 150 Distance along CPW (ujn) Figure 3.18: Measured and simulated normalized electric field amplitude above the C P W as a function of position. The solid rectangles represent the physical geometry of the C P W . -63 -electric field at the center of the fiber tip has to be plotted. This is impractical as the simulations take an hour for each configuration and gives asymmetrical results due to the uneven loading of the C P W . In a true measurement setting, it is desirable to keep the fiber tip centered over the C P W to avoid uneven loading of a test circuit. The shape of the measured electric field is still consistent with simulations as it decays to zero as the tip moves further away from the center conductor. Another slight discrepancy is also introduced due to the size of the mode field diameter of the fiber. The light is guided in the fiber core, which has a mode field diameter of 8 | jm, and it is the electric field in this region that interacts with the optical beam. Thus the beam interacts with the electric field over a lateral span of 8 (J,m. The electric field amplitude plotted at a particular position is for a single point above the C P W and not representative of the electric field in the A l G a A s that the optical beam interacts with when the fiber tip is at that position. Figure 3.19 also shows the normalized reflected optical power as the tip is moved. It clearly illustrates the decreased reflectivity when the fiber is between the conductor and above the alumina substrate. The change is not exactly at the boundaries once again due to the finite size of the fiber mode diameter. The above measurement clearly indicates that the fiber based sampling tip is capable of measuring the electric field above a C P W . To further validate operation of the fiber tip, the electric field dependence on the height above the C P W can also be verified. As seen in Figure 3.17, the electric field magnitude decays as the height increases. In order to measure this, the fiber tip was centered above the center conductor and lowered down from one local maximum in reflectance to the next so that the measurement is again taken at the maximum reflectance operating point. The results are plotted in Figure 3.20 along with those from simulations. There is a good agreement between measured and simulated values. - 6 4 -nO .9 o IJO.8 10.7 • i-H <3 O 0.6 •••• • •• • •••• 50 -100 -50 0 50 Distance along C P W (um) 100 150 Figure 3.19: Normalized optical reflected power from fiber tip as a function of distance along C P W . The solid rectangles represent the physical geometry of the C P W . - 6 5 -Height Above CPW (pirn) Figure 3.20: Simulated and measured normalized electric field amplitude at different heights above the C P W . - 6 6 -Having established that the tip works as an electro-optic sensor in a qualitative manner, attention must be paid to the signal strength and its quantitative behavior. Calculation of the expected A C signal is based on details of the photoreceiver circuit and the reflected optical power. Figure 3.21 shows a schematic plot of the photoreceiver chain that the optical signal goes through and is used to derive the next few equations. The optical signal at the photodiodes goes through a transimpedance amplifier and then into an A C and D C chain to give SDC and S A C as the outputs. The electro-optic modulator is always biased at its quadrature point for optimum sensitivity. This is the point where 8 = 7t/2 in Figure 1.2. Equation (1.2) is expanded in a Taylor expansion around the quadrature point. The transmission though the optics is given as: r(V) = s in : (3.21) and expanded in a Taylor series at the quadrature point where V=\V2 gives: T(V) = T( (V > dT + dV 1 „ • = —+2sin 2 Y*. 2 cos f 7lV A 2V. (3.22) 1 n ••-+ va 2 2V Where vac is the peak voltage on the circuit under test. The A C signal out of the photoreceiver chain can be written as, noting that the D C component of T(V) is filtered out in the A C chain: sAC = p:p,nv)SizGAC •AC 2V„ (3.23) - 6 7 -Figure 3.21: Schematic plot of photoreceiver chain for reflected optical signal - 6 8 -where P i n o p t is the optical power at the photodiodes, 91 is the responsivity of the photodiodes, Z is the transimpedance of the input transimpedance amplifier and G A c is the gain of the A C amplifiers. The voltage at the output of the D C chain is: c _ poptrp KZGDC V 2 J (3.24) 'DC 2 Combining Equations (3.23) and (3.24) gives: v V, S DC AAc n V  ADC J (3.25) The two quantities that depend on the fiber tip and the circuit under test are V„ and vac. Referring to Figure 3.17, the field in the tip can be approximated to 125 V / c m for a height of 6 [im above the C P W . To relate the electric field magnitude, Equation (3.15) can be used to calculate an effective distance between the conductors, teff, on which the voltage vac is applied to. This allows one to calculate Vn for the particular configuration in which the electro-optic sampling tip is being used. For the C P W used in simulations and measurements, an equivalent teff can be found: v 5 V , — — = 0.04cm (3.26) Etip 125VI cm Using this value as teg, Vniox the fiber tip can be calculated for the particular configuration used here using E„ = 5 . 5 x l 0 7 V / c m (taken as the average value from Figure 3.11). S A c can be calculated using the values shown in Table 3.2, which are the values used in the experiment. - 6 9 -Vac 5Vpk V7t=E„teff 2200 kV AAC 872 V/V ADC 1 V/V P. °P< in 2mW SI 0.95 A/W z 470 V/A Table 3.2: Physical and Simulated values for quantitative characterization of fiber tip SAC = 7 T S1 A ° DC"-AC = 71-5V 2200&V (2mW)(0.95A/W)(47Qy / A)(872V IV) IVIV = 5.60mV (3.27) The voltages measured using the L I A over the course of the measurements were 3-4 m V p k , confirming that the estimated expected signal level is close to the actual measured signal. The signal is small due to the small electric field in the fiber tip. This is directly due to the fact that a longitudinal type electro-optic material was used, resulting in the electric field being smaller by a factor of £AiGaAs-Due to the signal strength and poor signal to noise ratio at m V levels, a time resolved measurement could not be made by amplifying the signal to detectable levels. The measurement had to be restricted to a L I A , which is able to measure low-level voltages. Subsequently, the tip was not used to make a time resolved measurement on a high-speed signal. 3.4 Summary and Conclusions A fiber optic based electro-optic sampling tip was designed, built and characterized. D C measurements confirmed that it is possible to accurately place the tip above a circuit and use a feedback method to keep its height stable with respect to the circuit substrate. A C measurements showed that the tip is able to measure electric fields and shapes above a coplanar waveguide structure, similar to those on high-speed circuits. However, the signal levels were too low to - 7 0 -perform any time resolved measurements on high-speed circuits. In addition, any effort with the existing tip would make it difficult to detect an electro-optic signal due to low voltage levels used on high speed circuits, which are lower than the 5 Vpk used in the measurement set up. -71 -Chapter 4 Future Work and Conclusions 4.1 Future Work To improve upon the existing fiber based E O S system, the fiber sampling tip needs to be redesigned so that a time resolved measurement can be made. As shown in the previous chapter, the electric field strength in the electro-optic material is decreased significantly due to the dielectric constant of the material and the fact that the vertical electric field at the air-AlGaAs interface is not continuous. One way of improving the sampling tip is to use a more sensitive electro-optic material. A popular material used in most E O S systems is lithium tantalate (LiTaOj). The design of the tip would remain the same and the attached LiTa03 piece could be polished down to a typical thickness of 20 \xm, as is the case in free space electro-optic sampling tips. In addition to LiTa03 being a more sensitive electro-optic material, it has the advantage of being sensitive to horizontal electric fields, meaning to fields perpendicular to the propagation direction of the light. This is desirable as the tangential fields across the air-LiTa03 are continuous and not degraded due to the dielectric constant of the electro-optic material. There are two significant drawbacks of using LiTa03; the material has a high dielectric constant and may load the circuit more than A l G a A s ; and the thickness of the tip cannot be tightly controlled as is the case with selective etching of the A l G a A s based tip. The LiTa03 -72-would have to be polished down to the desired thickness once it has been attached to the fiber tip. Nevertheless, using L i T a 0 3 is a viable option for the redesign of the fiber-based sampling tip required for the further development of the E O S system. The next few paragraphs present results of simulations on the electric field, reflectivity and sensitivity of a L iTa03 based sampling tip. A LiTa03 based tip is sensitive to the horizontal electric field above a circuit under test when used in the transverse configuration. The horizontal field is strongest between the conductors as opposed to right above the conductors, which was the case for the vertical field. Figure 4.1 shows the horizontal electric field, Ey above the C P W used in Chapter 3. The electrostatic simulation is the same as that conducted in Section 3.3.2 so that a direct comparison can be made. The figure shows that the horizontal field is strongest between the conductors. When a LiTa03 based tip is placed above the C P W , the field changes its magnitude and this is shown in Figure 4.2 where the horizontal field has been plotted for a fixed tip height of 6 |J,m. The field is shown at four different points above the C P W : 1) just below the a i r - L i T a 0 3 interface; 2) just above the air-LiTa03 interface; 3) in the middle of the L iTa03; and 4) just below the LiTa03-fiber interface. Inside the LiTa03 , the field shape is similar at all three points and decays in magnitude as one goes deeper into the tip. The field is continuous across the boundary and any differences shown in the figure are due to the finite mesh size used in the simulation tool. A smaller mesh decreases the difference but substantially increases the simulation time. Nevertheless, this drop is not as large as was the case with the vertical field, which drops by a factor of er of the material. For L iTa03 , E r is 43 and would represent a large drop in the field, so by choosing to use an electro-optic material that is sensitive to the horizontal -73 -2000 1500 1000 500 ? o > O h — \\ = 2 Lim h — 6 Lim h = 10 Lim • h = 14 Lim h = 18 Lim h = 22 Lim -40 -20 0 20 40 Distance Across CPW (Lim) 80 Figure 4.1: Horizontal electric field, Ey above the C P W with 5 V p k sinusoidal signal applied to center conductor. The field is shown for different heights above the C P W when no fiber tip is present. The solid rectangles represent the physical geometry of the C P W . - 7 4 -300 -300r -40Q1 1 1 • • • ' ' 1 -80 -60 -40 -20 0 20 40 60 80 Distance A c r o s s C P W (Lim) Figure 4.2: Horizontal electric field, Ey above the CPW with 5 V p k sinusoidal signal applied to center conductor. The fiber tip is at a height of 6 \xm and the field is shown at different points above the CPW. The solid rectangles represent the physical geometry of the CPW. -75 -field, this large dielectric constant does not affect the magnitude of the horizontal field. LiTaC>3 is a naturally birefringent material, meaning that even in the absence of an electric field, light polarized at different angles to the two crystal axes, experiences a different index of refraction. The two axes are called the ordinary (O-axis) and the extraordinary (E-axis) axes. A s was the case in A l G a A s , the light should be polarized at 45° with respect to the crystal axes so that the axes are equally excited for efficient modulation. When a horizontal electric field (Enor) is applied perpendicular to the light propagation direction, the change in index of refraction is given as n 0 = n o - ^ - r u E h o r (4.1) n e = n e - ^ r 3 3 E h o r (4.2) where rxy are the electro-optic coefficients specific to LiTaC»3 and n0 and ne are the two indices of refraction. Because of its natural birefringence, each of the two orthogonal components of the light w i l l experience a different reflectivity from the tip and when both are excited, the resulting reflectance wi l l be a combination of the two depending on the phase difference between the two components. The reflectance curves for each polarization are shown in Figure 4.3 for the case of pe = 0.6. The periodicity of the reflectance is similar to what was seen with the A l G a A s tip and the reason a lower value was chosen for pe is because the fiber tip w i l l be placed in between the conductors to maximize the horizontal electric field resulting in a lower reflectivity off the circuit substrate, which can be alumina, silicon or GaAs. To compensate for the lower reflectance the input optical power can be increased without any negative effect on the circuit's performance. - 7 6 -1 2 3 Airgap Thickness ((im) Figure 4.3: Reflectance for the LiTa03 based fiber tip. The two curves are for the O and E The reflectivity of the circuit under test is pe = 0.6. - 7 7 -Electro-optic measurements are usually done at wavelengths below 1 u,m and material properties for L iTa03 are not available at 1550 nm. Using published values for n0, ne, rI3, and r33 at a wavelength of 550 nm and 633 nm [24,28], the electro-optic simulation can be carried out as it was for the A l G a A s with the only difference being taken into account in Equations (4.1) and (4.2). The results of the calculation of En for the L i T a 0 3 based tip using the C P W introduced in Section 3.3.2 is shown in Figure 4.4 and exhibits the same periodicity as the reflectance with the air gap thickness. There is a significant improvement in En over the A l G a A s design (see Figure 3.11). Simulations show that for different thicknesses of LiTaC>3, the reflectance and En can be optimized for maximum reflectance and minimum E^ This can be achieved with a thickness of 18-20 um. Carrying out a similar calculation as presented in Equation (3.27), the expected output voltage for the system using an average value 1.8xl0 6 V / c m for i s land a % o f 0.025 cm is: ^ DC A AC AC -"-j-'-Vn V "-DC J , / ( 2mW)(0 .95A/W)(470V/A) (872V/V) \ (IV / V )(l .8 x 10 6 VI cmfpjQlScm) = 272mV (4.3) and represents an increase of a factor of 50 over the A l G a A s based tip. The results presented so far are promising and warrant the design of a LiTaC>3 based tip. The only hurdle is the manufacturing process. Commercially available LiTaC>3 wafers have typical thickness of 300 - 500 | im and a diamond cutter capable of cutting the wafer into square pieces of 200 - 500 u.m is available in house. The remaining issue is the polishing of the tip to achieve a final thickness of -20 um. There are two options to achieve this. One option is to purchase a L iTa03 wafer that is polished down to a manageable thickness of~100 urn. This wafer can then be cut into 200 urn -78 -- 7 9 -squares and attached to the end of a fiber optic cable that is already placed in a ferrule. The advantage of this is that the ferrule is polished flat and LiTa03 can be attached to it easily. With this arrangement, the ferrule-LiTa03 can be polished down using common techniques available for polishing of ferrules. The only concern is that the ferrule is 2.5 mm wide, which is not a desirable size for a sampling tip. It may be possible to grind the edges of the ferrule so that it has a tapered shape with a size comparable to the diameter of the fiber. The second option is to start with a nominal thickness (300 - 500 |Jm) LiTaC>3 wafer and attach it on to another substrate, such as alumina or some other kind of support, using a soluble adhesive that can be chemically removed. Loctite Corporation has a line of cyanoacrylate adhesives accompanied by solvents to quickly and safely remove the adhesive. Another good adhesive is photoresist used in semiconductor processing, which can be easily dissolved with acetone. The second substrate acts as a strong support for the LiTaC>3 wafer. This new substrate combination can then be polished on the LiTaC>3 side to the desired thickness of 18 - 20 |im. The substrate can then be cut into the 200 p,m squares, which can be attached to the fiber tip. The second substrate can then be removed using the adhesive solvent to dissolve it, leaving the 18-20 |im thick LiTa03 at the end of the fiber. It is important to make sure that the solvent does not dissolve the fiber-optic epoxy used to attach the LiTaC>3 to the end of the fiber. It is also possible to continue using AlGaAs as the electro-optic material by growing it in a different orientation so that it is sensitive to horizontal fields. AlGaAs can be grown in three different directions and growing it in the (110) direction makes it sensitive to electric fields that are perpendicular to the propagation direction of the light [28]. However, the change in the indices of refraction by the electro-optic effect is still governed by Equations (3.13) and (3.14) with the only change being the electric field amplitude. Calculations similar to the ones above -80-show that the stronger horizontal field only results in a factor of 8 increase in the electro-optic signal. 4.2 Conclusions In the course of this work, significant success was made in the development of a fiber-optic based electro-optic sampling system. The three main issues involving the development of the system were dealt with: a fiber based electro-optic sampling tip was designed, built and characterized; it was shown that it is possible to place the tip above the circuit under test and control its height accurately; and a synchronization scheme for the optical pulses and signal driving the circuit under test was designed, built and tested. A l l the other necessary components such as the optics, detection circuitry and data acquisition electronics were designed and implemented. The fiber based sampling tip was successfully characterized and shown to be working as predicted by theory. However, its sensitivity was too low to allow for a time resolved measurement on a high-speed circuit. This was primarily due to the reduction of the electric field in the sampling tip material, due to its high dielectric constant, so as to reduce the electro-optic effect. The reflectivity of the tip was shown to be a function of the air gap thickness between the tip and the surface of the circuit under test. This allowed for a technique to determine the height of the sampling tip above the circuit under test and to stabilize the height using a feedback system. The optical pulses and the signal supplied to the circuit under test were successfully phase locked to a reference signal, which is used as the data acquisition trigger. It was shown -81 -that the locking scheme did not affect the timing jitter or phase noise of the optical pulses, thus retaining the temporal accuracy of the sampling technique. The conclusion of this work is that it is possible to design, build and use a fiber optic based electro-optic sampling tip based on attaching an electro-optic material to the end of an optical fiber. In particular, the fiber based sampling tip was used to measure static electric fields around transmission lines. The material used as the electro-optic material proved to be inefficient to provide a large signal to noise ratio. Consequently, future work must be done to redesign the tip so that a more efficient electro-optic material, such as LiTaC>3 can be used. Calculations show that the redesign wi l l provide the necessary electro-optic signal needed to make a time resolved measurement on a high-speed circuit. - 8 2 -Appendix A - Circuit Schematics Appendix A Ci rcu i t Schematics id Figure A - l : Circuit schematic for phase locked loop. Shown are the input amplifier, low pass filter, and differential amplifier, followed by the phase detector and loop filter - 8 3 -Appendix A - Circuit Schematics Figure A-2: Photoreceiver chains for both polarization components of optical input. Shown is an input transimpedance amplifier followed by buffers for the D C outputs and A C amplifier chains for the A C outputs. - 8 4 -Appendix B - Components Used in E O S System Appendix B Optical, Electrical and Mechanical Components Used in EOS System 1. Polarizer & Half Wave Plate OZ Optics, FPR-12-ll-1550-9/125-S-S-l&2-60-3A3A-3-l-ER=30 This is a fiber coupled ( F C / A P C connectors) polarization rotator, which has a plate polarizer and half wave plate on rotation stages centered at 1550 nm. The insertion loss is < 1.3 dB and the extinction ratio is > 30 dB. 2. Circulator Optics for Research (OFR), OC-3-1550-FC/APC The circulator is fiber coupled with F C / A P C connectors centered at 1550 nm. The P D L (Port 2 to Port 3) is 0.08 dB. The loss data table (dB) is: O U T P U T I Ports 1 2 3 N 1 58dB 0.9dB 51dB P u 2 34dB 58dB 1.3dB T 3 52dB 36dB 58dB 3. Fiber Port Optics for Research (OFR), PAFE-X-11-1550 The fiberport allows coupling of a beam from a fiber to a collimated free space beam with x,y,z,0 and p adjustments. Only F C / A P C connectors are to be used. The collimated beam is 2.4 mm in diameter. 4. Half Wave Plate Newport, 10RP02-40 The waveplate is a zero-order quartz half waveplate centered at 1550 nm. 1" Dia . 5. Polarizing Beam Splitter Cube (PBSC) Newport, 10BC16PC.il The P B S C is a laser line polarizing beam splitter cube centered at 1550 nm and an extinction ratio of >1000:1. 1" cube. 6. Compensator Melles Griot, 02WRQ011/1550 The compensator is a first order quartz quarter waveplate centered at 1550 nm. The plate is made from two quartz plates, each 1mm thick and 30 mm dia. 7. Polarization Controller BT&D, MPC1000 The controller is a manual polarization controller with three paddle wheels and F C / A P C - 8 5 -Appendix B - Components Used in E O S System connectors on each end. 8. Optical Attenuator EXFO, FVA-3100 The variable attenuator is a front panel and GPIB instrument. The input and output are D C connectors. The wavelength range is 1200 -1650 nm and an attenuation > 80dB depending on wavelength. 9. Optical Amplifier Thomas&Betts, Photon, LT4000A-30 The amplifier is an Erbium Doped Fiber Amplifier with S C / A P C connectors for single mode fiber, optimized for 1550 nm. The maximum output is 30 m W with input power of - 4 to 8 dBm. It has an RS-232 interface. 10. Pulsed Laser PtiTel, UOC-3E The laser is an Erbium doped fiber laser with tunable wavelength from 1545 to 1565 nm. The repetition rate can be set from 1 G H z to 5 G H z . Average output power is 1.27 m W with 2 ps pulses. Output fibers are F C / A P C connectors. 11. Photodiodes EG&G Canada, Perkin Elmer Optoelectronics, C30723G These are large diameter (5 mm) InGaAs photodiodes with high responsivity from 1300 nm to 1700 nm. The bandwidth is below 5 M H z . 12. Nanopositioners Melles Griot, 17MAX301, 17NST101 The nanopositioners are x,y,z stages with piezo feedback controllers. The range is 4 mm using the stepper motor controllers and 20 (im with the piezo controllers with a resolution of 50 nm. 13. Rotation Stages New Focus Inc. Model 8401, Model 8732 Controller The stages are motorized or manual and can be controlled using the controller and GPIB interface. They come with standard adapters for Vi" and 1" optics. 14. Camera Navitar, 12XZoom 1-50487D The camera has 8 set zoom levels with 3 mm fine focus & coaxial illumination. The zoom is continuous over the whole range and can be set to any of the 8 levels as well . It has a 2 X standard adapter and capable of zooming into 2 (J,m features. The working distance is 37 mm. 15. Data Acquisition a. National Instruments, PC-1409 Monochrome Image acquisition card. Up to four cameras can be connected to the card. - 8 6 -Appendix B - Components Used in E O S System b. National Instruments, PCI-6110E High speed data acquisition card able to sample 4 channels simultaneously at 5 MSamples/s. 16. W i d e Bandwid th P I N Photodiode Discovery Semiconductors, Inc, DSC30S-59-FC/APC-K 22 G H z High Power, L o w Distortion P I N diode with internal 50 Q load 17. Frequency M i x e r Miteq Inc, DB0130LA2 Double balanced mixer, 1-30 G H z R F and L O ranges and DC-0.5 G H z IF range. L O power maximum is 13 d B m - 8 7 -Appendix C - Description of Imaging and Data Acquisition System Appendix C Description of Imaging and Data Acquisition System A student, Daniel Langevin, working as a research assistant over a period of 8 months, developed the automated aspects of the system. The student has written the following descriptions. Imaging System This system has been designed to be able to precisely position the E O S probe over a sample using a digital image of the sample. This system deals in two separate reference frames: The reference frame of the E O S probe's nanopositioners, and the reference frame of the digital images. In order to use a location in the image frame to position the probe in its own frame, a calibration is needed to convert between the two frames. First, a reference point is established on the sample chuck using a pinhole. This pinhole is an optical fiber, which is positioned perpendicular to the surface of the sample chuck. The probe tip can be precisely positioned above the pinhole by coupling light from the probe into the pinhole. When maximum coupling is achieved, it can be assumed that the probe is positioned at the pinhole. So the pinhole position is then known in the reference frame of the probe. In order to use this information in the system, this pinhole must be located in the reference frame of the digital image as well , in order to correlate between positions in the image, and positions in the probes reference frame. To accomplish this, an image is taken containing the pinhole. Software is then used to locate the pixel coordinates of the pinhole. Thus the pinhole has been located in the reference frame of the image. - 8 8 -Appendix C - Description of Imaging and Data Acquisition System In order to complete the mapping between the two frames, a conversion is needed to convert distances from one frame to the other. To do this, an object is needed whose dimensions can be measured in both frames. Some characteristics of the pinhole are known. The pinhole is simply an optical fiber, which is comprised of a core and a cladding. The diameter of the cladding is known to be 250 pm. This is the distance as would be measured in the probes reference frame. When imaging the pinhole, the cladding wi l l be visible in the image as well . Using software in Labview, it is possible to measure the diameter of the cladding in pixels. It is then possible to calculate a calibration constant for converting distances between the two frames of reference. This constant is only valid for the magnification in which it is calculated. If the magnification of the imaging system is changed, then this constant must be re-calculated. The software handles this by having the user calibrate the system for all magnifications before beginning the experiment. Once this is done, the camera cannot be moved. When a sample is placed on the chuck, the pinhole is no longer visible. The pixel location of the pinhole during the calibration is then used as the reference point. This means the reference point has been translated from the probe's frame to the image's frame. This translation is only valid i f the image position remains fixed in the probes frame. In other words, once the calibration has been completed, the camera cannot be moved. Also , as the calibration constant must be calculated for each magnification, it is imperative that the pinhole is not moved until all the calibrations are complete. - 8 9 -Appendix C - Description of Imaging and Data Acquisition System D A Q System and Interface This system has been designed to acquire two separate signals at a rate of 2 Msamples per second. It saves the average value of the voltage, and the average value of the square of the voltage, to disk. When the first trigger is received, the card begins to acquire data and store it in the buffer. It continues to acquire data until the program is ended. A loop structure reads the data from the buffer in chunks of 1000 samples per read sequence. It reads in the data from the buffer, and outputs it as a 2D array of scaled voltage data. These blocks of data are then analyzed in real time. The analysis sequence takes the array of data, and calculates two values. It calculates the sum of the voltage, and it calculates the sum of the square of the voltage. After this analysis, two structures occur simultaneously. The first structure plots the data to the screen. Since this slows the processing speed of the P C drastically, the frequency at which this occurs is reduced. A comparison of the number of iterations of the inner loop is used to set the frequency to about 6-10 screen updates a second. This is sufficient for the display. The second structure that occurs is the final part of the analysis. Because the average value of the data is required, this section is configured to execute when 1000 blocks of data have been collected and summed. This section divides both voltage values, the sum and the sum of the square, by the number of blocks summed, and then saves these values to disk in two files: mean.txt and sumsquared.txt. After this, it re-initializes the sums to zero, and sets the counter to zero as well , so the process can repeat. It also keeps track, using a counter, how many sets of 1000 data points have been stored in the files. The inner loop wi l l continue to execute and read data until the stop button is pressed, or an error occurs. When the inner loop ends, the memory allocated to the buffer is de-allocated, and the D A Q board is re-initialized. If an error occurred, the program wi l l check to see what the - 9 0 -Appendix C - Description of Imaging and Data Acquisition System error is. If it is a buffer overrun error, the board waits for the next trigger pulse, and restarts the acquisition process. It continues to save the data to the same files. If the quit button is pressed, the program stops acquiring data, closes the data files, and ends. The data being acquired is a voltage produced by the E O S Photo receiver Board. This board takes the output from two diodes into transimpedance amplifiers, couples out the D C component, and sends the amplified A C component to the D A Q board. These are 20 k H z frequency signals. -91 -Bibliography [I] T. Pfeifer et al, "Optoelectronic On-Chip Characterization of Ultrafast Electric Devices: Measurement Techniques and Applications," IEEE J. Selected Topics in Quantum Electronics, vol . 2, pp. 586-604, 1996. [2] K . J. Weingarten, M . J. Rodwell , and D . M . Bloom, "Picosecond Optical Sampling of GaAs Integrated Circuits," IEEEJ. Quantum Electronics, vol . 24, pp. 198-220, 1988. [3] E . Menzel , E . Kubalek, "Fundamentals of electron beam testing of integrated circuits," Scanning Electron Microscopy, V o l . 5, pp. 305-322, 1983. [4] Z . Weng, C.J . Falkingham, G . E . Bridges and D . J . Thomson, "Quantitative voltage measurement of high-frequency internal integrated circuit signals by scanning probe microscopy," Journal of Vacuum Science & Technology A , V o l . 20, No. 3, M a y 2002. [5] F . Taenzler, T. Novak, E . 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