Frozen wave generation of bandwidth-tunable two-cycle THz radiation

Holzman et al. Vol. 17, No. 8/August 2000/J. Opt. Soc. Am. B 1457 Frozen wave generation of bandwidth-tunable two-cycle THz radiation Jonathan F. Holzman, Fred E. Vermeulen, and Abdul Y. Elezzabi Ultrafast Photonics Laboratory, Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta, T6G 2G7, Canada Received January 3, 2000 We report on the application of a photoconductive frozen wave generator (FWG) for the generation of 0.36-THz radiation. Through the excitation of a bipolar photoconductive array, a two-cycle THz electrical transient is created. The THz electrical transient occurs on a time scale much shorter than the carrier lifetime in the semiconductor. Furthermore, variations in the uniformity of the optical excitation intensity across the photoconductive array introduce a controlled THz temporal chirp, thus providing for fine bandwidth tunability of the device. Modeling of the FWG is successful in describing both the time variation and the amplitude spectrum of the photogenerated THz radiation. 2000 Optical Society of America [S0740-3224(00)00108-9] OCIS codes: 320.7080, 320.5390, 320.7160, 130.5990. 1. INTRODUCTION With recent advances in the application of ultrashort laser pulses to optoelectronics, a new ultrahigh-frequency electromagnetic frontier ranging from 0.1 to 10 THz is being explored. Ultrashort THz pulses are currently being investigated for applications including inter- and intrachip communication, 1 spectroscopy and chemical identification, 2 6 miniature impulse radar, 7,8 and imaging. 9,10 A wide variety of techniques have been proposed and demonstrated in the generation, propagation, and detection of this freely propagating THz radiation. Although certain generation techniques exploit nonlinear interactions, such as photomixing in semiconductors 11,12 and optical rectification in electro-optic materials, 13 the most common approach to generate ultrashort THz pulses employs the excitation of a Hertzian dipole source that has an ultrafast time dependence and a length smaller than the radiated THz wavelengths. In such a technique, an ultrashort laser pulse photoconductively shorts 14 17 a charged coplanar transmission line to produce an ultrashort THz pulse. Although it is possible to generate THz radiation with long lifetime substrates by edge illuminating 18,19 a coplanar transmission line and exploiting the depletion field at the metal semiconductor interface to accelerate the carriers, the amplitude of the generated THz radiation is relatively weak compared with that of the radiation generated by electrically biased Hertzian dipoles. In this paper we report on the application of an optoelectronic technique for the generation of tunable THz radiation. Our approach employs the concept of frozen wave generation 20 24 in the formation of ultrahighfrequency radiation. Operation of our device is independent of the semiconductor substrate carrier lifetime as long as the carrier lifetime, c, is longer than both the transit time of the waveform across the frozen wave generator (FWG) segments and the discharge time of the photoconductive switches. The concept of the photoconductively excited frozen wave generator (PC-FWG) as a potential dc-to-rf converter was first demonstrated by Proud and Norman 20 as an alternative to the existing electronically driven or spark-gap-switched FWG modules. 21,22 These authors activated three sequential silicon photoconductive switches (Auston switches) with a 10-ns excitation laser pulse to produce a two-cycle waveform with a bandwidth of 100 MHz. Lee, 23 by using a similar experimental arrangement and a shorter laser pulse duration of 1 ps, later demonstrated a two-and-onehalf-cycle waveform with a bandwidth of 200 MHz. Since optically activated FWG s offer low jitter and high switching efficiency, the potential exists for these devices to operate at even larger bandwidths. Thaxter and Bell 24 successfully demonstrated a two-and-one-half-cycle device that produced a 6-GHz pulse train. Interestingly, all the previously reported FWG devices have bandwidths in the MHz to GHz range, 20 25 are operated as singlefrequency generators, are cumbersome in size, and require a relatively high energy per pulse to close the photoconductive switches. In these devices, the maximum bandwidth is limited by two factors: the rise time of the switches and the inherent propagation delay between the sequential photoconductive switches that is due to cable interconnections. Thus to tune the waveform duration (or bandwidth), one must physically modify the length of the cable interconnecting the photoconductive switches. Although this approach might be simple for GHz devices, it proves to be a challenge at higher bandwidths (THz) at which the delay-line lengths require monolithic integration. Device tuning in this high-frequency regime is therefore extremely difficult, as the dimensions of the interconnections are only a few hundred micrometers in length. The principal objectives of our work are to demonstrate the operation of a THz FWG and to describe a temporalchirping mechanism for bandwidth tuning of the THz radiation. To our knowledge, the demonstration of an 0740-3224/2000/081457-07$15.00 2000 Optical Society of America

1458 J. Opt. Soc. Am. B/ Vol. 17, No. 8/ August 2000 Holzman et al. ultrahigh-bandwidth, temporally chirped FWG has not been reported in the literature. The free-space characteristics of the FWG THz radiation are demonstrated as well, through transmission and reception of these THz radiation pulses by resonantly coupled integrated planar dipole antennas. For a propagation distance within the near-field regime, it is found that the received signal accurately replicates the transmitted signal. 2. EXPERIMENTAL ARRANGEMENT The experimental arrangement for the generation and detection of the THz radiation is shown schematically in Fig. 1. The FWG microcircuit and the integrated dipoles are fabricated by use of standard photolithographic techniques on a 600- m-thick semi-insulating ( 10 7 cm) GaAs substrate. Onto the substrate Ti and Au metallization is performed, with respective thicknesses of 50 and 150 nm. The FWG microcircuit comprises four 20- mwide bias electrodes, each separated by 30 m. The four FWG electrode segments are biased to 10 V and 10 V, with their alternative polarities arranged in the manner depicted in Fig. 1. The coplanar transmission line, which is responsible for propagating the ultrafast electrical signal from the FWG to the integrated antenna pair, is fabricated by use of two 20- m-wide conductors separated by 20 m. Both the FWG coplanar transmission line and the receiver coplanar transmission line are terminated by identical dipole antennas, separated by 400 m. The planar dipole antennas are patterned with 20- m-wide conductors with an overall length of 160 m. Such an antenna length corresponds, approximately, to a halfwave resonance at 0.35 THz, taking into account the dielectric loading of the GaAs on the antenna. 26,27 The transmitting dipole is driven by the FWG waveform propagating on the coplanar transmission line, whereas the receiving dipole antenna is driven by the freely propagating THz electric field waveform that is polarized parallel to the receiving dipole antenna. A standard pump probe experimental arrangement is incorporated for the generation and detection of the THz radiation. The pump and probe pulses are delivered by Fig. 1. Pump probe experimental arrangement for the FWG, the dipole transmitter and dipole receiver, and the LiTaO 3 electro-optic transducer. an 8-fs, 80-MHz, 800-nm Ti:sapphire laser. The pump beam, with an average power of 100 mw, illuminates all the photoconductive gaps in the FWG. Through the creation of effective short circuits between the four bias electrodes, a bipolar two-cycle voltage transient is launched on the coplanar transmission line. The probe beam, with an average power of 20 mw, is delivered, by means of a 20 microscope objective and a total-internal-reflection mount, to a 20- m-thick LiTaO 3 electro-optic crystal transducer positioned over the coplanar transmission line 28 at a distance of 400 m from the nearest end of the FWG. By means of scanning through the temporal delay between the pump pulses and probe pulses and monitoring the polarization rotation of the probe beam, a time-domain representation of the electrical signal on the coplanar transmission line is constructed. To achieve noise reduction, high-frequency (3 MHz) electrical signal mixing 29 and differential lock-in detection techniques are incorporated into the biasing arrangement of the electrodes. Rather than biasing the electrodes of the FWG with dc voltages of alternating polarity, a 3-MHz signal is applied where a phase shift of 180 exists between adjacent FWG electrodes. 3. TERAHERTZ FROZEN WAVE GENERATION Electro-optic sampling at location A yields the temporal shape of the electrical waveform generated by the FWG. Excitation of the generator is carried out by the pump pulse, which is carefully focused to achieve a nearuniform intensity across all the FWG photoconductive gaps. The time-domain waveform measured is shown in Fig. 2(a). The figure shows four prominent voltage peaks of alternating polarity, spanning a time interval of 6.4 ps. The amplitude of these voltage peaks decreases steadily with time such that the second positive peak amplitude is 35% of the first positive peak amplitude. The decaying amplitude is due to multiple electrical reflections from the impedance mismatch between the transmission line segments and the photoexcited gaps as the pulse train propagates through the FWG segments. Portions of the voltage waveform that are generated furthest from the point of sampling will undergo the largest number of reflections and therefore suffer the greatest attenuation. 26 The detected signal of Fig. 2(a) shows two voltage cycles, both with a period of 3.2 ps. Since the 0.31-THz central frequency associated with this period is generated in a spatially periodic structure, of which a significant length (60%) consists of an optically generated plasma, the corresponding wavelength is expected to differ significantly from that of a standard dielectric-loaded transmission line. With an effective dielectric constant of 12.0 and a wavelength of 100 m (corresponding to one spatial period of bipolar electrode arrangement), standard dielectric-loaded transmission line analysis 24 would suggest that the full-wave period is approximately 1 ps, corresponding to a central frequency of 1 THz. The large difference between this predicted period and the measured period in Fig. 2(a) makes clear that this array of photoconductive switches acts very differently from a standard transmission line of similar dimensions. The

Holzman et al. Vol. 17, No. 8/August 2000/J. Opt. Soc. Am. B 1459 Fig. 2. (a) Time-domain waveform of the THz electrical signal measured at point A for the case of uniform excitation of the FWG gaps. (b) Spectral intensity of the electrical signal showing both the experimental curve (circles) and the calculated curve (solid curve) for T 0 s/m. Fig. 3. Equivalent circuit representation of a single photoconductive switch consisting of a time-dependent conductance, G(t), parallel with a gap capacitance, C. spectral intensity of the time-domain signal produced under uniform illumination of the FWG is shown in Fig. 2(b). The peak-frequency response of this two-cycle voltage waveform is f 0 0.31 THz, while the full width halfmaximum (FWHM) of the spectral intensity is 0.20 THz. The time-varying conduction current and displacement current within an individual photoconductive gap of the FWG can be modeled by the parallel combination of a conductor and a capacitor, since the dimensions of each switch are much smaller than the wavelengths in the generated current pulse. 30,31 This circuit model is shown in Fig. 3, where Z 0 is the characteristic line impedance of the device, G(t) is the time-varying conductance of the photoconductive switch, C is the capacitance of the photoconductive switch, and q(t) is the time-varying charge stored in the gap. After the illumination of the photoconductive switch, the time-varying voltage that exists on the transmission line can be analyzed in terms of three propagating voltage transients as shown in Fig. 3: v i (t) is the incident voltage waveform, v r (t) is the reflected voltage waveform, and v t (t) is the transmitted voltage waveform. 30,31 In treating each gap as an independent element, it is assumed that the rise time of each switch is less than the time required for reflected voltage transients to return from adjacent gaps. As is evident from Fig. 2(a), the 1-ps rise time inherent to each gap is, in fact, less than the 2 ps required for a reflected voltage transient to return from an adjacent electrode, and hence, the reflected waveforms do not interfere with the generation process. On optical excitation, the conductance across each gap increases rapidly. For an excitation pulse of duration much less than the response time of the circuit, as is the case in our experiment, one can model the conductance of each photoconductive switch as a step response in which 0; t 0 G t G; t 0. (1) At the same time, the parallel capacitors discharge, and a voltage waveform is created at the output of the FWG. The speed with which this process occurs is limited by the interaction of these internal circuit elements with the external transmission line. The transmitted voltage waveforms, v t (t), is related to the circuit elements by v t t V b 2Z 0 G 1 2 1 2Z 0 G exp, t (2) where the rise time of the voltage waveform is limited by the time constant 2Z 0C 1 2Z 0 G, (3) and V b is the initial bias voltage across the photoconductive gap. 31 An interesting relationship is seen to exist between the exponential time constant in Eq. (3) and the gap conductance G, where the conductance can be related to the incident intensity, I, through G w eff e d I. (4) lh Here w is the width of the gap, l is the length of the gap, eff is the effective mobility of GaAs, is the frequency of the optical pulse, d is the pulse duration, e is the electronic charge, and h is Planck s constant. For low levels of photoinjection, G is small, suggesting an electrical time constant of 2Z 0 C. As the level of excitation is increased, however, the conductance across the gap increases and the time constant of the transmitted signal decreases significantly. Owing to this relationship, the electrical response time of the photoconductive gap can be increased or decreased, simply by adjusting the level of photogenerated carrier density within the gap. 30,31

1460 J. Opt. Soc. Am. B/ Vol. 17, No. 8/ August 2000 Holzman et al. The dependence of the electrical response time of the photoconductive gaps in the FWG on the incident pump intensity can be exploited as a frequency control mechanism for the photogenerated THz signal. By illuminating the photoconductive gaps of the entire FWG with a pulse intensity that gradually increases or decreases along the length of the structure, a variation in the rise times of the voltage waveforms generated at each gap can be introduced. This effect broadens the spectral intensity of the generated electrical waveforms. This scenario is investigated by focusing the pump beam into an elliptical pattern of large eccentricity and positioning the FWG onto a side lobe of the Gaussian beam profile to approximate a linearly varying intensity along the length of the structure. The results obtained are shown in Fig. 4(a), in which the photoconductive gap furthest from the point of sampling receives the greatest level of excitation. The variation in the rise time across the electrical waveform is readily apparent from this time-domain signal, as the temporal period of each successive peak is seen to decrease in time. The spectral intensity curve of Fig. 4(b) illustrates this point in the frequency domain where, by introducing a variation in the periods of the waveforms in the time domain, we have in effect broadened the spectrum of the electrical waveform. For the present case of nonuniform linear illumination, the central frequency has increased to f 0 0.36 THz and the power spectral density FWHM has increased significantly to 0.36 THz. To gain further understanding of the relationship between the uniformity of illumination and the electrical response of the FWG, a model of the experimentally observed time-domain signals is developed. Taking the intensity that illuminates the FWG to be in fact linear, the intensity distribution is described by I x I 0 I x, (5) where the term I 0 is the intensity that is incident on the photoconductive gap closest to the point of sampling, I is the intensity linearization constant, and x describes the spatial dimension across the FWG, as shown in Fig. 1. Through Eq. (4), it is apparent that this linear intensity distribution across the FWG will manifest itself as a linear variation in conductance in which G x w eff e d I 0 I x. (6) lh The conductance distribution function of Eq. (6) can be linked to the rise time through Eq. (3). On expansion of the resulting equation, for I x I 0, it is found that the rise time across the device varies as where 0 T 0 T x, (7) 2Z 0 Clh lh 2Z 0 w eff e d I 0, (8) 4Z 0 2 Clh w eff e d I lh 2Z 0 w eff e d I 0 2. (9) Fig. 4. (a) Time-domain waveform of the THz electrical signal measured at point A for the case of nonuniform excitation of the FWG gaps. (b) Spectral intensity of the electrical signal showing both the experimental curve (circles) and the calculated curve (solid curve) for T 1.1 10 9 s/m. Indeed, the broadening of the spectral intensity curve in Fig. 4(b), relative to that of Fig. 2(b), is a result of this linear variation in the electrical rise time. The circuit response slows with decreasing x along the length of the FWG and a linear chirp in the temporal period is introduced. To illustrate this point further and to obtain a value of the chirp parameter, T, the experimental FWG pulse trains for both uniform and nonuniform excitations are fitted to two-cycle THz waveforms of exponentially decaying amplitude and, in the case of nonuniform illumination, a linear distribution of rise times across the device. The calculated Fourier transforms for uniform and nonuniform illumination are shown as solid curves in Figs. 2(b) and 4(b), respectively, and are found to fit the corresponding experimental data well. The bandwidth broadening that is due to nonuniform illumination, as shown in Fig. 4(b), is accurately obtained from the case of uniform illumination, depicted in Fig. 2(b), with the introduction of a linear variation in the electrical rise time, where 0 0.8 ps and T 1.1 10 9 s/m provide the best fit between the calculated and the experimental results. Indeed, the larger the amount of period chirping, the wider the bandwidth of the THz signal. This rise-time-induced chirping mechanism can be used to fine tune the bandwidth of the THz radiation.

Holzman et al. Vol. 17, No. 8/August 2000/J. Opt. Soc. Am. B 1461 4. FREE-SPACE THz PROPAGATION The FWG generates THz electrical transients on the transmission line, and a method is required to launch these transients to make them useful for applications. The free-space propagation characteristics of the THz electrical signal are investigated through the use of integrated planar dipole antennas for the transmitter and the receiver, as shown in Fig. 1. The electrical waveform generated by the FWG under nonuniform illumination, as shown in Fig. 4(a), is fed to the dipole transmitter, and electro-optic sampling is performed on the coplanar transmission line at position B. The time-domain waveform measured is shown in Fig. 5(a). The time scale for this figure is adjusted so that the zero time correlates with the time at which the electrical signal arrives at the transmitting dipole. Though several features are evident, the most prominent characteristic of the waveform is the twocycle bipolar THz oscillation commencing at 15 ps. This time interval corresponds to the time it takes the THz radiation pattern to reflect off the back side of the GaAs substrate and be picked up again by the receiver, an effect similar to that observed by McGowan and Grischkowsky. 1 For a 600- m-thick substrate and a transmitter receiver separation of 400 m, this propagation distance is in the near-field regime. The similarity between the transmitted signal of Fig. 4(a) and the close-up of the THz oscillation in Fig. 5(b) confirms this point, as the received signal is simply a scaled replica of the transmitted signal. An important point related to the fact that the integrated dipole pair is operated both in a near-field regime and in a dielectric half-space, is that near-field surface pulses can propagate directly from the transmitter to the receiver both in the air and through the GaAs substrate. This effect manifests itself as the superposition of two signals at the receiver, one corresponding to propagation through the air and the other through the substrate. These artifacts are clearly shown in Fig. 5(a). At a time of 1.3 ps the first pulse, corresponding to propagation through the air, arrives after traveling the 400 m from the transmitter to the receiver. The propagation time of 1.3 ps for this direct pattern is clearly evident in the timedomain signal of Fig. 5(a), where a waveform is seen to commence at this moment. At a later time (4.8 ps), this signal is superimposed with the direct-wave pattern corresponding to propagation through the GaAs substrate. The resonance response of the dipole transmitter and receiver can be illustrated through a half-wave resonance approach, incorporating the loading of the dielectric halfspace. The free-space half-wave resonance frequency of the dipole, f r 0.92 THz, is modified by the dielectric constant of the GaAs substrate, 12.8, to give an effective half-wave resonance frequency of f eff 0.35 THz for 0.36 THz. The power spectrum of the signal measured at the dipole receiver is shown in Fig. 5(c) and is found to peak at a frequency of f 0 0.30 THz. Though the frequency response of the received waveform is similar in form to the frequency response of the transmitted f eff f r / eff, (10) where the effective dielectric constant, eff is eff 1 /2. (11) The dipole length is therefore well suited for the transmitted signal of Fig. 4(b), which is centered at f 0 Fig. 5. (a) Time-domain waveform of the THz electrical signal measured at point B for the case of nonuniform excitation of the FWG gaps. (b) Expanded view of the near-field pattern measured at point B. (c) Spectral intensity of the electrical signal in (b).

1462 J. Opt. Soc. Am. B/ Vol. 17, No. 8/ August 2000 Holzman et al. waveform, the peak value is shifted downward by 50 GHz, indicating that the dipole resonance occurs at a value lower than predicted. This downward shift in the resonant frequency has been observed in other center-fed dipole investigations (as opposed to end-fed dipoles for which little resonant frequency shifting is observed). 11 5. CONCLUSION In conclusion, we have reported on a method for the generation of THz radiation. The high-frequency response of the photogenerated THz radiation is found to depend on both the device dimensions and the illumination uniformity. The FWG allows for the creation of two-cycle radiation in which the central frequency and the spectral bandwidth are tunable through variations in the laser pump-beam uniformity. The free-space propagation characteristics of the FWG THz radiation are demonstrated through the use of resonantly coupled planar dipole antennas. The generation method of the waveform can be described with a model that involves a linear risetime chirp of the waveform train. Indeed, by increasing the number of the photoconductive switches in the FWG, it is possible to achieve narrower bandwidth THz radiation. This task can be accomplished by the use of an injection-fwg that does not suffer from multiple electrical reflections from the impedance mismatch between the transmission line segments and the photoexcited gaps. This new FWG configuration is currently being investigated. ACKNOWLEDGMENTS This study is supported by the Natural Sciences and Engineering Research Council of Canada, province of Alberta Intellectual Infrastructure Partnership Program, and the Canadian Foundation for Innovations. The corresponding author, F. E. Vermeulen, can be reached at the address on the title page, by telephone at 780-492-3332, by fax at 780-492-1811, or by e-mail at vermeulen@ee.ualberta.ca. The other authors can be reached at the address on the title page or by telephone at 780-492-0756. REFERENCES 1. R. W. McGowan and D. Grischkowsky, Experimental timedomain study of THz signals from impulse excitation of a horizontal surface dipole, Appl. Phys. Lett. 74, 1764 1766 (1999). 2. L. Thrane, R. H. Jacobsen, P. Uhd Jepsen, and S. R. Keiding, THz reflection spectroscopy of liquid water, Chem. Phys. Lett. 240, 330 333 (1995). 3. B. B. Hu, E. A. De Souza, W. H. Knox, J. E. Cunningham, M. C. Nuss, A. V. Kuznetsov, and S. L. Chuang, Identifying the distinct phases of carrier transport in semiconductors with 10 fs resolution, Phys. Rev. Lett. 74, 1689 1692 (1995). 4. N. Katzenellenbogen and D. Grischkowsky, Electrical characterization to 4 THz of n- and p-type GaAs using THz time-domain spectroscopy, Appl. Phys. Lett. 61, 840 842 (1992). 5. D. Grischkowsky, S. R. Keiding, M. van Exter, and Ch. Fatinger, Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors, J. Opt. Soc. Am. B 7, 2006 2015 (1990). 6. M. van Exter and D. Grischkowsky, Optical and electronic properties of doped silicon from 0.1 to 2 THz, Appl. Phys. Lett. 56, 1694 1696 (1990). 7. R. A. Cheville and D. Grischkowsky, Time domain terahertz impulse ranging studies, Appl. Phys. Lett. 67, 1960 1962 (1995). 8. R. W. McGowan and D. Grischkowsky, Direct observation of Gouy phase shift in THz impulse ranging, Appl. Phys. Lett. 76, 670 672 (2000). 9. D. M. Mittleman, R. H. Jacobsen, and M. C. Nuss, T-ray imaging, IEEE J. Sel. Top. Quantum Electron. 2, 679 692 (1996). 10. B. B. Hu and M. C. Nuss, Imaging with terahertz waves, Opt. Lett. 20, 1716 1718 (1995). 11. K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczara, Terahertz measurements of resonant planar antennas coupled to lowtemperature-grown GaAs photomixers, Appl. Phys. Lett. 69, 3632 3634 (1996). 12. S. Matsuura, M. Tani, and K. Sakai, Generation of coherent radiation by photomixing in dipole photoconductive antennas, Appl. Phys. Lett. 70, 559 561 (1997). 13. A. Nahata and T. F. Heinz, Generation of subpicosecond electrical pulses by optical rectification, Opt. Lett. 23, 867 869 (1998). 14. P. Uhd Jepsen, R. H. Jacobsen, and S. R. Keiding, Generation and detection of terahertz pulses from biased semiconductor antennas, J. Opt. Soc. Am. B 13, 2424 2436 (1996). 15. R. K. Lai, J. Hwang, T. B. Norris, and J. F. Whitaker, A photoconductive, miniature terahertz source, Appl. Phys. Lett. 72, 3100 3102 (1998). 16. C. W. Siders, J. L. W. Siders, A. J. Taylor, S. G. Park, M. R. Melloch, and A. M. Weiner, Generation and characterization of terahertz pulse trains from biased, large-aperture photoconductors, Opt. Lett. 24, 241 243 (1999). 17. X.-C. Zhang and D. H. Auston, Optically induced THz electromagnetic radiation from planar photoconducting structures, J. Electromagn. Waves Appl. 6, 85 106 (1992). 18. F. G. Sun, G. A. Wagoner, and X.-C. Zhang, Measurement of free-space terahertz pulses via long-lifetime photoconductors, Appl. Phys. Lett. 67, 1656 1658 (1995). 19. C. Wang, M. Currie, R. Sobolewski, and T. Y. Hsiang, Subpicosecond electrical pulse generation by edge illumination of silicon and phosphide photoconductive switches, Appl. Phys. Lett. 67, 79 81 (1995). 20. J. M. Proud, Jr., and S. L. Norman, High-frequency generation using optoelectronic switching in silicon, IEEE Trans. Microwave Theory Tech. 26, 137 140 (1978). 21. E. S. Weibel, High power rf pulse generator, Rev. Sci. Instrum. 35, 173 175 (1964). 22. H. M. Cronson, Picosecond pulse sequential waveform generation, IEEE Trans. Microwave Theory Tech. 23, 1048 1049 (1975). 23. C. H. Lee, Picosecond optics and microwave technology, IEEE Trans. Microwave Theory Tech. 38, 596 607 (1990). 24. J. B. Thaxter and R. E. Bell, Experimental 6-GHz frozen wave generator with fiber-optic feed, IEEE Trans. Microwave Theory Tech. 43, 1798 1803 (1995). 25. M. L. Forcier, M. F. Rose, L. F. Rinehart, and R. J. Gripshover, Frozen-wave hertzian generators: theory and applications, IEEE International Pulsed Power Conference Digest of Technical Papers (Institute of Electrical and Electronics Engineers, New York, 1979), Vol. 2, p. 221. 26. Y. Pastol, G. Arjavalingam, J. M. Halbout, and G. V. Kopcsay, Characterization of an optoelectronically pulsed broadband microwave antenna, Electron. Lett. 24, 1318 1319 (1988). 27. P. R. Smith, D. H. Auston, and M. C. Nuss, Subpicosecond

Holzman et al. Vol. 17, No. 8/August 2000/J. Opt. Soc. Am. B 1463 photoconducting dipole antenna, IEEE J. Quantum Electron. 24, 255 260 (1988). 28. J. A. Valdmanis, G. Mourou, and C. W. Gabel, Picosecond electro-optic sampling system, Appl. Phys. Lett. 41, 211 212 (1982). 29. J. M. Chwalek and D. R. Dykaar, A mixer based electrooptic sampling system for submillivolt signal detection, Rev. Sci. Instrum. 61, 1273 1275 (1990). 30. J. F. Holzman, F. E. Vermeulen, and A. Y. Elezzabi, Ultrafast photoconductive self-switching of subpicosecond electrical pulses, IEEE J. Quantum Electron. 36, 130 136 (2000). 31. D. H. Auston, Impulse response of photoconductors in transmission lines, IEEE J. Quantum Electron. 19, 639 648 (1983).