Measurement of Spatio-Temporal Terahertz Field Distribution by Using Chirped Pulse Technology

Transcription

1 1214 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 36, NO. 10, OCTOBER 2000 Measurement of Spatio-Temporal Terahertz Field Distribution by Using Chirped Pulse Technology Zhiping Jiang and Xi-Cheng Zhang, Senior Member, IEEE Abstract The authors report the use of an optoelectronic system for the measurement of terahertz (THz) pulses by using chirped pulse technology. This system measures the spatio-temporal distribution of free-space pulsed radiation with an unprecedented data acquisition rate. Using a linearly chirped optical probe pulse with an electro-optic crystal, a temporal waveform of a copropagating THz field is linearly encoded onto the frequency spectrum of the optical probe pulse and then decoded by dispersing the probe beam from a grating to a detector array. Acquisition of picosecond THz field pulses without using mechanical time-delay devices have been achieved. A single-shot electro-optic measurement of the temporal waveform of a THz pulse has been demonstrated. Unparalleled by other THz sampling techniques, this single-shot method provides what is believed to be the highest possible data-acquisition rate. Temporal resolution, sensitivity, optimal optical bias point of electro-optic modulation, potential applications, and possible improvements are also discussed. In principle, this technique can also be used in magneto-optic measurements. Index Terms Chirped-pulse technology, electro-optic, magneto-optic, THz, THz imaging. I. INTRODUCTION ELECTRO-OPTIC sampling is a powerful technique for the characterization of an electrical waveform such as an electrical signal in an integrated circuit [1], [2] or a terahertz (THz) beam in a free-space environment [3] [5]. Conventional time-domain electro-optic sampling is based on the repetitive property of the signal to be tested. A sequential plot of the signal versus the time delay reassembles the temporal waveform. If the signal to be measured is from a single-event experiment, such as an explosion or breakdown, this technique is clearly not suitable. However, the modulation of the optical probe pulse in the electro-optic (EO) sampling technique may provide the means to overcome this shortfall. The temporal modulation can be converted to the wavelength domain by use of free-space wavelength-division multiplexing and demultiplexing. With the introduction of a linearly chirped optical probe beam in the electro-optic sampling experiment [6], [7], it is finally possible to measure a THz pulse with an unprecedented data-acquisition rate, even with single-shot temporal measurement capability [8] [10]. Conventional time-domain optical measurements, such as THz time-domain spectroscopy in pump/probe geometry, use a Manuscript received March 8, 2000; revised June 28, This work was supported by the U.S. Army Research Office and the U.S. National Science Foundation. The authors are with the Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, Troy, NY USA. Publisher Item Identifier S (00) mechanical translation stage to vary the optical path between the pump and the probe pulses [11] [14]. The intensity or polarization of the optical probe beam, which carries information generated by the pump beam, is repetitively recorded for each sequential time delay. In general, the data acquisition for the temporal scanning measurement is a serial acquisition; the signal is recorded during the probe pulse sampling through a very small part of the THz waveform (roughly the pulse duration of the optical probe beam). Therefore, the data acquisition rate in this single channel detection is limited to less than 100 Hz for a temporal scan on the order of tens of picoseconds. Clearly, this relatively slow acquisition rate cannot meet the requirement for real-time measurements, such as time-domain THz spectroscopy of fast-moving objects or flame analysis. In order to increase the acquisition rate, parallel data acquisition or multichannel detection is required. One possible method is to extend the novel design from real time picosecond optical oscilloscopes for the local-field characterization, to freely propagating THz field applications [6]. This paper is arranged as follows: in Section II the measurement principle is described and proved mathematically. The experimental setup is detailed in Section III. Section IV gives the experimental results, including single point, single-shot measurements, spatio-temporal imaging, and dynamic subtraction. Section V is the analysis of the temporal resolution, theoretical simulation, experimental design, etc. This technique is also applicable to magnetic optical measurement, which is discussed in Section VI. Section VII proposes possible applications and improvement, and concludes the paper. II. PRINCIPLE The measurement principle can be understood according to Fig. 1. A femtosecond laser beam is split into pump and probe beams. The geometry is similar to the conventional free-space electro-optic sampling setup, except for the use of a grating pair for chirping and stretching the optical probe beam and a grating-lens combination with a detector array for the measurement of the spectral distribution. Due to the negative chirp of the grating (instantaneous frequency in the pulse decreases with time), the blue component of the pulse leads the red component. The fixed delay-line is only used for the positioning of the THz pulse, within the duration of the synchronized probe pulse (acquisition window) and for temporal calibration. The pump beam is used to generate a THz beam from an emitter then focused onto the electro-optic sensor via a polyethylene lens. The probe beam is frequency chirped and temporarily stretched by a grating pair. When the chirped probe /00$ IEEE

2 JIANG AND ZHANG: MEASUREMENT OF SPATIO-TEMPORAL TERAHERTZ FIELD 1215 function of the spectrometer and the square of the Fourier transform of the chirped pulse (4) where is the spectral function of the spectrometer. By using (3), (4) can be written as Fig. 1. Schematic of experimental setup of electro-optic measurement with a chirped optical probe beam. beam and a THz pulse co-propagate in the electro-optic crystal, different portions of the THz pulse modulate different wavelength components of the chirped pulse through the Pockels effect. Therefore, the THz waveform is encoded onto the wavelength spectrum of the probe beam. A spectrometer and a detector array (LDA or CCD) are used to measure the spectral distribution. The temporal THz signal can be extracted by measuring the difference between the spectral distributions of the probe pulse with and without THz pulse modulation. We can also prove mathematically that the measured signal is proportional to THz field under some conditions. Assuming that the unchirped probe beam is a diffraction-limited Gaussian pulse with a central frequency where is the time variable, and is the pulse duration, which is related to the laser spectral bandwidth through. After diffraction by the grating pair, the electric field component of the chirped probe beam can be written in the form where is the chirp rate, and is the pulse duration of the chirped pulse. When the chirped probe pulse copropagates through the EO crystal with a THz field of electric field, the transmitted probe pulse is given by where is the time delay between THz and the probe pulse, and is a constant. The value of, which is related to the modulation depth, depends on many factors, such as the electro-optic coefficient, optical bias, scattering, thickness of the crystal, and the group velocity mismatch. In general, is also dependent on THz frequency, and we neglect this frequency dependence because the frequency range in this measurement is far away from the phonon resonance (5.3 THz for ZnTe). Since a spectrometer is used to disperse the probe beam, the spectral modulation is spatially separated on the CCD array. In that case, the measured signal on a CCD pixel with optical frequency is proportional to the convolution of the spectral (1) (2) (3) The integral in (5) can be evaluated by using the method of stationary phase if is sufficiently large [15]. Since and the THz pulse duration are much longer than the oscillation period of the optical beam, the factor is a slowly varying function of time. The phase factor in (5) gives a self-canceling oscillation, so as to allow the contribution of the integrand to be neglected everywhere except in the vicinity of certain critical points. At the critical point the derivative of the phase term of (5) with respect to is zero. In this case it gives Defining a normalized differential intensity it can be proved that is proportional to the input THz field under certain approximations. Since is true for typical electro-optic measurements, by keeping only the zero and first order terms (with respect to ), and applying (6), we have When the spectral resolution is so high that the spectral function of the spectrometer can be expressed as a function, we have This equation shows that the measured spectral profile is indeed proportional to the temporal profile with respect to the input of the THz waveform when the chirp rate is sufficiently large and the resolution of the spectrometer is sufficiently high. The validity and the influence of these conditions will be discussed in the following sections. (5) (6) (7) (8) (9)

3 1216 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 36, NO. 10, OCTOBER 2000 III. EXPERIMENTAL SETUP In this experiment, the laser is an amplified Ti:sapphire laser (Coherent RegA 9000) with an average power of 0.9 W and a pulse duration of 200 fs at 250 khz. The center wavelength of the Ti:sapphire laser is about 820 nm with a spectral bandwidth of 7 nm. The THz emitter is an 8-mm wide GaAs photoconductor with the bias voltage ranging from 2 to 5 kv. The focal lens for THz beam is a polyethylene lens with a 5-cm focal length. A 4-mm thick ZnTe crystal is used as EO sensor. The optical probe pulse is frequency chirped and time stretched by a grating pair, and the time window can be easily adjusted by changing the grating distance. This distance is several centimeters corresponding to a time window of tens of picoseconds. For electro-optic modulation, two polarizers are used with perpendicular polarization in order to get the highest modulation depth induced by the THz field. The detailed analysis will be given in Section V. The dispersion element is a spectrometer (Instrument SA, SPEX 500M) with spectral resolution of 0.05 nm and dispersion of 1.6 mm/nm. The detector array is a CCD camera (Princeton Instruments, Inc., CCD-1242E). This CCD camera has pixels and a full well capacity greater than electrons, dynamic range 18 bits, and minimum exposure time 5 ms. The data are transferred to a PC computer. Fig. 3. Normalized differential spectral distribution (1I =I) by adjusting the fixed delay line at a step of 1.3 ps. IV. EXPERIMENTAL RESULTS The experimental results will be presented for three cases: single-point measurement, spatio-temporal imaging, and dynamic subtraction. A. Single-Point Measurement In this case, the chirped probe beam is focused onto the EO crystal, and hence the THz waveform of a single point is measured. Fig. 2 shows the spectral distributions of the chirped probe pulse with and without THz modulation and the differential spectrum distribution. This differential distribution reconstructs both the amplitude and phase of the temporal waveform of the THz pulse. The differential spectrum in Fig. 2 shifts horizontally by adjusting the fixed delay line. Moving the fixed delay line is equivalent to placing the THz field in a different portion of the probe beam spectrum and it can be used as a marker to calibrate the time scale. Fig. 3 shows the normalized differential spectrum distribution when adjusting the fixed time delay line at a step of 1.3 ps. The offset of the spectrum is shifted for better display. The noise at the edge pixels comes from the spectrum normalization with a small background. The waveforms shift linearly with the fixed time delay step. The total spectral window (1024 pixels) is equivalent to 44 ps, corresponding to 43 fs/pixel. The results shown in Figs. 2 and 3 are obtained with a single CCD exposure, but with thousands of laser pulses. However, unlike the conventional sampling techniques, where only a small portion of the entire THz waveform is measured at each time, for this chirped pulse measurement technique each pulse contains all the information of the entire THz pulse, therefore a single-shot measurement is possible. Fig. 4 gives the first single-shot measurement of a THz pulse; the signal-to-noise ratio (SNR) is better than 60:1. In this experiment, a single laser Fig. 4. A single-shot spectral waveform of a THz pulse measured by a chirped optical probe pulse. It reconstructs the temporal waveform of the THz pulse. Fig. 2. Spectral distribution of the chirped probe pulse with and without a copropagating THz field pulse. pulse was selected [8]. We took a single-shot spectrum without the THz field first and saved it as the background, then we took a single-shot spectrum with the THz field and performed a subtraction of the background. Although this is not a real single shot in the sense that we need to take the reference spectrum, the real single-shot experiment can be done with dynamic subtraction, which will be given in the Part C of this section. B. Spatio-Temporal Imaging With a slight modification of Fig. 1, it is possible to get onedimensional (1-D) spatial information of THz field. As shown in Fig. 5, the probe beam is focused to a line onto the EO crystal by a cylindrical lens. The image of this line is formed at the entrance plane of the spectrometer, and therefore 1-D spatial and 1-D temporal information of the THz field are measured simultaneously. Depending on specific requirement, either vertical or horizontal spatial distribution can be readily measured.

4 JIANG AND ZHANG: MEASUREMENT OF SPATIO-TEMPORAL TERAHERTZ FIELD 1217 Fig D THz imaging of a quadrupole. Fig. 5. Schematic of experimental setup for spatio-temporal THz imaging. Unlike in Fig. 1, cylindrical lenses (CL) are used to focus the probe beam to a line on ZnTe crystal and then image it to the entrance plane of the spectrometer. Fig. 8. Single-shot 1-D THz imaging of a dipole field without any signal average. The y-axis corresponds to the spatial position across the dipole emitter. Fig D THz imaging of a dipole. The experimental procedure is the same as for the singlepoint measurement, that is the background spectrum is taken and saved as the reference with THz off, and then another spectrum is measured with THz on; the difference gives the signal. Figs. 6 and 7 show the measured distribution images of THz fields as a function of spatial position and time delay emitted from dipole and quadrupole emitters [16], respectively. The measured spatial resolution in the imaging system is better that 1 mm, which is close to diffraction limited resolution in other unchirped THz techniques. The data was measured with one camera exposure, representing an average over 1250 laser pulses in 5 ms exposure time. Spatial filtering was used to improve the spatial uniformity. Fig. 8 is a plot of a single-shot image from a GaAs photoconductive dipole antenna. This plot shows the original data without signal average or smoothing. The total time for wavelength division multiplexing and demultiplexing is a few picoseconds. The dipole length is 7 mm, and the bias voltage is 5 kv. One-dimensional spatial distribution across the dipole and its temporal THz waveform are obtained simultaneously in a single laser pulse. The size of the spatio-temporal image is 10 mm by 25 ps. In this single-shot measurement the background light per pixel on the CCD camera is 200 counts, whereas that of the modulated probe pulse is 50. Typical oscillation features and the sym- Fig D THz imaging of a quadruple field. The y-axis corresponds to the spatial position across the quadrupole emitter. metric spatial distribution of the far-field pattern from a dipole photoconductive emitter are obtained. Fig. 9 shows a spatio-temporal image of the THz field from a quadrupole antenna. The size of the spatio-temporal image is 10 mm by 40 ps. The quadrupole has three parallel electrodes separated by 3 mm. The center electrode was biased and the two adjacent electrodes were grounded. The field pattern from two back-to-back dipoles shows opposite polarity depending on the spatial position ( axis). Temporal oscillation from each dipole can be resolved individually. The layered structure in the -axis direction is due to the optical inhomogeneity of the sensor crystal. Point defects in the ZnTe crystal cause offsets in the field strength of the temporal waveform ( axis in the figure). A high-quality ZnTe crystal with good spatial homogeneity will provide better spatial resolution.

5 1218 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 36, NO. 10, OCTOBER 2000 a given input THz waveform. Assuming a bipolar THz waveform which has the form (10) here we define a characteristic time which is the interval between the maximum and minimum. The spectral function of the spectrometer can be approximated by a Gaussian function (11) Fig. 10. Dynamic subtraction. The signal beam (S) and the reference beam (R) are sent to the spectrometer simultaneously. Because the reference beam is picked up before the second polarizer, the THz modulation is negligible and can be used as a good reference. C. Real Single-Shot Measurement (Dynamic Subtraction) As mentioned before, to get the THz signal, we need two CCD exposures, one without THz modulation and one with THz modulation; therefore, they are not real single-shot measurement. However, since a two-dimensional (2-D) CCD camera is used, it is very easy to measure the spectra with and without THz modulation at the same time using different CCD location. Fig. 10 shows the setup. Before the second polarizer, a beam splitter is used to split part of the beam, this beam is used as a real-time reference and sent to the spectrometer with the signal beam simultaneously. This dynamic subtraction, on one hand, realizes real single-shot measurement, and improves the SNR on the other hand because the signal spectrum and the reference spectrum are from the same laser pulse; therefore the laser fluctuations are mostly canceled. Fig. 11 gives some single-shot experimental results. The left panels show the images of the CCD spectral traces of the signal and reference beams; the corresponding spectra are in the right panels. When there is no THz, the signal and the reference spectra are in good agreement, indicating that the reference is good. When THz is on, its modulation on the signal spectrum is quite visible even in the CCD image picture. The dynamic subtraction is demonstrated only for the measurements of a single spatial point, but it is also possible for the spatio-temporal imaging, because only part of the CCD is used in the above imaging. However, it is more difficult to align the optics and requires more data processing, including pattern match and the correction of the inhomogeneity of the EO crystal. V. ANALYSIS A. Temporal Resolution We showed in Section II that when the chirp rate is sufficiently large and the spectral resolution of the spectrometer is sufficiently high, the measured signal is proportional to the THz field. However, the chirp rate is limited by the laser pulse bandwidth or the pulse duration. This finite chirp rate limits the temporal resolution. In order to find the chirp rate and the dependence of the temporal resolution on the spectral resolution of the spectrometer, we studied the output waveform distortion for where is the spectral resolution of the spectrometer. By substituting (10) and (11) into (7), it can be shown that the normalized differential intensity function can be written as: where the dimensionless time is defined by and (12) (13a) (13b) So the measured normalized differential intensity function in (12) is similar to the bipolar THz field in (10), except that the characteristic time increases by a factor of.as increases, and decrease, and the distortion decreases. Therefore, the larger the chirp rate, the better the temporal resolution. For a linear system, the transfer function is the ratio of the output signal over the input signal in frequency domain. From (10) and (12), the transfer function can be readily obtained as (14) with the dimensionless circular frequency. For a given chirp rate, the temporal resolution is defined at the point where the input pulse is so narrow that the broadening factor is equal to. In the experiment, the measurement window should be much larger than the THz time scale, (i.e., ). Therefore we have (15) If the spectral resolution of the spectrometer is about nm, or equivalently THz and THz, then. Therefore, is a very good approximation for (15). With the time-domain and frequencydomain expressions of the chirped probe beam it is easy to prove that Combining and,wehave (16) (17)

6 JIANG AND ZHANG: MEASUREMENT OF SPATIO-TEMPORAL TERAHERTZ FIELD 1219 Fig. 11. Results of the dynamic subtraction. The left panel is the images of the CCD spectral traces without THz signal (a) and with THz signal (c). The right panel is the spectral plots without THz signal (b) and with THz signal (d). The difference spectra are also plotted. Notions: R: reference, S: signal, and D: difference. Therefore, if the laser pulse is diffraction-limited with a simple Gaussian profile, the temporal resolution is equal to the square root of the product of the original probe beam duration and the chirped pulse duration. The physics can be understood in following way: since the THz pulse within the duration of the synchronized probe pulse window (acquisition window) modulates only a portion of the probe pulse spectrum, the limited frequency bandwidth in the modulated spectrum cannot support the required temporal resolution. If the pulse duration of the chirped probe beam is comparable to the duration of the THz waveform, then the temporal resolution will be. Compared with the sampling method by varying the optical path, the temporal resolution decreases by a factor of. For example, assuming an original probe beam duration of 0.05 ps and a chirped pulse duration of 20 ps, the estimated limit of the temporal resolution is 1 ps. The simulated distortion of the THz waveform with several different chirp rates is shown in Fig. 12. In this simulation we assume that and focus on the chirp rate dependence of the temporal resolution. The axis is dimensionless time as defined in (13), and the axis is the relative signal. The solid curve ( for ) is the original waveform without distortion. As increases, decreases, and the distortion will become smaller. It is seen that the distortion is determined by the quantity which is a combination of the chirp rate and the pulse duration. In order to improve the temporal resolution, or must be reduced. The smallest is determined by the measurable time window, which should be larger than the THz duration. Therefore, a shorter original probe pulse (or equivalently a broader spectrum) is more desirable. A white-continuum probe pulse with a higher chirp rate should provide better temporal resolution. Fig. 12. Simulated output results for a bipolar input THz waveform. The legend represents the dimensionless quantity. B. Working Point for Electro-Optic Modulation As mentioned before, the THz signal is extracted by subtracting the probe spectra with and without THz modulation. In order to get good signal, a large modulation depth is essential. For this reason, two crossed polarizers (zero optical bias) are used instead of the balance detection geometry (linear optical bias) as in most experiments. Ideally, if the EO crystal is perfect, i.e., there is no scattering and no birefringence, then the system works at real zero optical bias, and the extinction ratio should only be limited by that of the polarizers. Then the system response is not linear but quadratic, and the modulation depth is always close to one. However, it has been found that the insertion of the EO crystal reduces the extinction ratio dramatically, and the system response is nearly linear in most cases. Most importantly this phenomenon limits the achievable modulation depth.

7 1220 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 36, NO. 10, OCTOBER 2000 Experimentally we can use a birefringence compensator to increase the extinction ratio, indicating that residual birefringence is one reason. However, the compensator cannot eliminate the background light completely; this suggests possible scattered light within ZnTe crystal which has a random phase. By including the contribution from both the strain-induced birefringence and the scattering effects, the transmitted light in the Fig. 1 geometry can be described by a modified equation (18) where is the input light intensity, the contribution by the scattering, the optical bias induced by the residue birefringence of the ZnTe crystal plus the intrinsic birefringence of the compensator, and the electric field induced birefringence contribution. Note that (18) is slightly different from the common notation [17]. For simplicity, we add to include the scattering contribution, and the optical phase terms are twice their value of their counterparts in [16]. We define the modulation depth as Because is much smaller than one, we have (19) (20) We experimentally measured the modulation depth versus optical bias, and the result is shown in Fig. 13; the dots are the experimental data while the solid curve is calculated by (20). The excellent agreement between the experiment and the theoretical calculation proves the model as given by (18). It is seen that there exists a maximum modulation depth when is given by the root of the equation and (21) (22) Substituting (21) into (18), the transmitted light at the maximum modulation depth point is (22) Experimentally, it is easy to find the maximum modulation depth point. When THz is off, we can adjust the compensator to minimize the transmitted light, which equals according to (18), and then double the transmitted light by rotating the compensator. In this manner, we can come close to the optimum operating point. C. Sensitivity In this part, we estimate the minimum measurable electric field. 4 mm thick ZnTe is used as an example. Let be the THz electric field, then the THz induced birefringence is (23) Fig. 13. Measured (dots) and calculated (curve) modulation depth versus optical bias 0. where is the crystal thickness, is the electro-optic coefficient, and is the wavelength of the probe beam. In Eq. (23), the group velocity mismatch (GVM) is not considered, since for ZnTe crystal, the influence of GVM is not significant. For ZnTe, m/v, and we use mm, nm, therefore (24) the unit of is in V/cm. Substituting Eq. (24) into (22), and using the measured scattering parameter, the maximum modulation depth is (25) The modulation depth should be larger than the laser fluctuation which is on the order of 1%. In (25), when V/cm, then %, this is roughly the minimum modulation depth and therefore the minimum measurable electric field. One should also note that the above modulation depth is in the time-domain, the frequency domain modulation depth is smaller due to the limited temporal resolution, hence the practically measurable electric field is higher. VI. MAGNETO-OPTICAL MEASUREMENT For THz measurements, we mainly measure the electric field component of the radiation. However, it has been demonstrated that the magnetic field component of the freely propagating THz radiation can also be measured through the so-called Magneto-Optical (MO) sampling [18], [19]. This technique uses the Faraday effect instead of the Pockels effect as in EO measurement. Inside a MO material, if a time dependent magnetic field is applied along the direction of the probe beam, then the polarization of the probe beam is rotated by an angle (26) where is the Verdet constant of the MO material, and is the thickness in the direction of the probe beam. Strictly speaking, (26) holds only for DC magnetic field. For fast changing magnetic fields, the velocity mismatch should be considered, for a detailed discussion, please see [18]. In principle, the chirped pulse technique discussed above should be applicable to MO measurements. However, because

8 JIANG AND ZHANG: MEASUREMENT OF SPATIO-TEMPORAL TERAHERTZ FIELD 1221 Fig. 14. The coordinate definition for Magneto-Optical measurement. the MO signal is much smaller (more than two orders of magnitude in our system) than EO signal, it seems unlikely to obtain the signal with the chirped pulse techniques at first glance. But analyzing the MO measurement carefully, we found it is still possible. The following analysis is similar to its EO counterpart. In Fig. 14, is the polarization of the input probe beam (before the MO material), is the polarization of the output beam (after the MO material). represents the rotation angle of the polarization of the probe beam. If the intensity of the input beam is, then we have, (27a) (27b) In the balanced detection, a Wollaston prism is used, with two polarization axes in and directions, respectively and. In this case, the signal is given by the difference, therefore (28) The rotation angle can be easily obtained by (28). As in the EO measurement, we have to use the crossed polarizers in order to increase the modulation depth. In this case, is very close to the axis,. The transmission axis of the analyzer is in the direction. Only is used. Again, as in the EO case, a term denoting the contribution of the scattered light should be added, the transmitted light is written as (29) there represents the ratio of the scattered light to the input light. Follow the definition of (19) of the modulation depth for EO, we have (30) When is fixed, the smaller is, the larger the modulation depth. Figure 15 plots the relation with several values. radian in Fig. 15, which is a typical experimental value calculated by Eq. (28). It is seen that there exists a maximum modulation depth too. The maximum position is determined by setting, this gives. Therefore (31) Fig. 15. Modulation depth versus angle at three. The values are shown in the figure by the corresponding curves. =10 radian. Because is on the order of, and even for the best polarizer,, the relation holds. Hence Inserting (32) to (30), the maximum modulation depth is (32) (33) It can be seen that the maximum modulation depth is mainly determined by the scattered light once the THz magnetic field is given. Fortunately, the scattering of MO materials (such as TGG, SF-59) is so small that it is negligible, and the extinction ratio of the polarizers is the dominant contribution to. Let (corresponding to the extinction ratio of ), the modulation depth %. This modulation depth is detectable by a CCD camera. Inserting (32) into (29), the transmitted light at the maximum modulation point is (34) This relation is similar to (22). It is also useful in finding the optimal modulation point for MO measurement. VII. CONCLUSIONS AND OUTLOOKS We have demonstrated THz measurement by using a chirped pulse technique. This novel technique allows us to acquire a THz signal at extremely high data rate. Single-shot spatio-temporal imaging has been realized. We proved the measurement principle mathematically. The analysis of the temporal resolution, the optimal modulation condition, and the sensitivity analysis are given. By taking advantages of these features, the chirped pulse measurement can be used in fields where conventional sampling techniques can not be used. Possible applications include emitter break down, unsynchronized microwave measurement, spatio-temporal imaging of non-thz signal, other unsynchronized fast phenomena, and nonlinear effects. The followings are some of the possible improvements of the technique: 1) Increase of the spectral bandwidth of the laser pulse to improve the temporal resolution.

9 1222 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 36, NO. 10, OCTOBER ) Combination with FROG (frequency resolved optical gating). In our experiments, only the information of the laser spectral amplitude is used, if the full information of the probe pulse is characterized, much higher temporal resolution can be expected. 3) Combination with streak camera [20]. (Far infrared streak camera) In this case, the EO crystal is uses as a converter, which turns the far infrared radiation into probe light modulation. This modulation can be detected by a streak camera. The temporal resolution is mainly determined by the streak camera. With the up-to-date streak camera, 200 fs temporal resolution can be obtained. 4) Better EO crystal to improve the sensitivity and signal-tonoise ratio. 5) Two-dimensional spatio-temporal imaging with dimension reduction system. Two-dimensional spatial and 1-D temporal imaging is possible provided that the 2-D to 1-D converter is available (e.g., using the fiber optics techniques). REFERENCES [1] B. H. Kolner and D. M. Bloom, IEEE J. Quantum Electron., vol. QE-22, p. 69, [2] J. A. Valdmanis and G. A. Mourou, IEEE J. Quantum Electron., vol. QE-22, p. 79, [3] Q. Wu and X.-C. Zhang, Appl. Phys. Lett., vol. 67, pp , [4] A. Nahata, D. H. Auston, T. F. Heinz, and C. J. Wu, Appl. Phys. Lett., vol. 68, pp , [5] P. U. Jepsen, C. Winnewisser, M. Schall, V. Schyja, S. R. Keiding, and H. Helm, Phys. Rev. E, vol. 53, p. R3052, [6] J. A. Valdmanis, Proceeding of Ultrafast Phenomena V. Springer-Verlag, presented at the Proc. Ultrafast Phenomena, vol. 82, Solid State Technology/Test Measurement World, Nov. S40, [7] Galvanauskas, J. A. Tellefsen Jr., A. Krotkus, M. Oberg, and B. Broberg, Appl. Phys. Lett., vol. 60, pp , [8] Z. Jiang and X.-C. Zhang, Appl. Phys. Lett., vol. 72, pp , [9] P. Y. Han, Z. Jiang, J. A. Riordan, L. Wang, and X.-C. Zhang, Proc. SPIE, vol. 3277, p. 198, [10] Z. Jiang and X.-C. Zhang, Opt. Lett., vol. 23, pp , [11] Ultrashort Laser Pulses and Applications, Topics in Applied Physics: Springer-Verlag, 1988, vol. 60. [12] P. R. Smith, D. H. Auston, and M. C. Nuss, IEEE J. Quant. Elec., vol. 24, p. 255, [13] Ch. Fattinger and D. Grischkowsky, Appl. Phys. Lett., vol. 54, p. 490, [14] Q. Wu and X.-C. Zhang, Appl. Phys. Lett., vol. 70, p. 1784, vol. 71, p. 1285, [15] M. Born and E. Wolf, Principles of Optics, 6th ed. New York, NY: Pergamon, 1980, p [16] Z. G. Lu, P. Campbell, and X.-C. Zhang, Appl. Phys. Lett., vol. 71, p. 593, [17] A. Yariv, Optical Electronics, 4th ed: Oxford Univ. Press, 1991, p [18] J. A. Riodan, F. G. Sun, Z. G. Lu, and X.-C. Zhang, Appl. Phys. Lett., vol. 71, pp , [19] J. A. Riodan, Ph.D. Thesis, Rensselaer Polytechnic Inst., [20] Z. Jiang, F. G. Sun, and X.-C. Zhang, Terahertz pulse measurement with an optical streak camera, Opt. Lett., vol. 24, pp , technology. Zhiping Jiang received the M.Sc. and Ph.D. degrees in physics from NUDT, China, in 1986 and He was a Visiting Scholar at Electrotechnical University of St. Petersburg, Russia, in He worked as postdoc at Institute of Solid State Research, Juelich, Germany, from 1996 to In 1997, he joined Rensselaer Polytechnic Institute as a Research Associate. Currently he is the Principal Investigator of ZOmega Technology Corp. and a Research Assistant Professor at Rensselaer Polytechnic Institute. His research interests include mainly THz Xi-Cheng Zhang (SM 95) received the M.Sc. and Ph.D. degrees in physics from Brown University, Providence, RI, in 1983 and He was a Visiting Scientist at MIT in From 1985 to 1987, he worked in the Physical Technology Division of Amoco Research Center. From 1987 to 1991, he was in the Electrical Engineering Department at Columbia University. Since 1992 he has been in the Physics Department at Rensselaer Polytechnic Institute. Currently he is a Professor of Physics and Professor of Electrical Engineering. His research interests include mainly THz technology.