The propagation and diffraction of few-cycle, even sub-cycle THz pulses have attracted much attention recently both theoretically and experimentally. Many interesting phenomena have been reported, including pulse shaping, spectral shift, Gouy phase shift, and superlumina [1
1. D. You and P.H. Bucksbaum, “Propagation of half-cycle far infrared pulses,” J. Opt. Soc. Am. B. 14, 1651–1655 (1997). [CrossRef]
8. J. Bromage, S. Radic, G.P. Agrawal, C.R. Stroud Jr., P.M. Fauchet, and R. Sobolewski, “Spatiotemporal shaping of half-cycle terahertz pulses by diffraction through conductive apertures of finite thickness,” J. Opt. Soc. Am. B 15, 1953–1959 (1998). [CrossRef]
]. THz pulse is a good candidate to study the propagation and diffraction effects. Because both the generation and detection of few-cycle, or even sub-cycle THz pulses are mature. Besides, the measurement of THz pulses are coherent, i.e. both the amplitude and phase are measured simultaneously.
Nevertheless, although the detection techniques of the THz electric field are mature, most available techniques are based on single point measurement, i.e. spatially only one point is measured at one time. If an image of 2D distribution is needed, it is necessary to scan the detecting system. This scanning involves mechanic movement, and therefore is very time consuming and not in real-time. Besides, it is difficult to keep the exact timing between the pump and probe beam. The lack of adequate experimental measurement prevents one from getting deep insight into the complicated propagation of few-cycle pulses.
In this paper, we use the recently improved electro-optic and CCD based THz imaging system to study the propagation of the few-cycle THz pulses. We are able to measure 2D electric field distribution of the THz pulses with unprecedent speed and signal-to-noise ratio (SNR) without mechanic movement except for the time delay. The experiments show striking spatio-temporal shaping effect in the 2f-2f imaging system, leading to time dependent beam diameter and wave front. Theoretical explanation is given.
2. Experimental Setup
The experiment setup is given in Fig. 1
. This setup is similar to a typical THz measurement setup with electro-optic sampling. A femtosecond laser pulse is spit into a probe and a pump pulse by a polarizer beam splitter. The pump pulse, the timing of which can be controlled by a mechanic delay line, illuminates a THz emitter to generate few-cycle THz pulse. The THz pulse is then focused onto an electro-optic (EO) crystal by either parabolic mirrors or a polyethylene lens. To realize 2D imaging, the probe pulse is expanded and collimated to be bigger than the THz spot size at the EO crystal plane. After passing a polarizer P, the probe pulse is reflected by a pellicle mirror to propagate collinearly through the EO crystal with the THz pulse. The phase of the probe pulse is modulated by the THz electrical field inside the EO crystal via Pockels effect, and this phase change is converted into intensity modulation by an analyzer A. A CCD camera is used to catch the spatial distribution of the probe beam. The difference between two images with THz field on and off gives the THz distribution [9
9. Q. Wu, T.D. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996). [CrossRef]
10. Z.G. Lu, P. Campbell, and X.-C. Zhang, “Free-space electro-optic sampling with a high-repetition- rate regenerative amplified laser,” Appl. Phys. Lett. 71, 593–595 (1997). [CrossRef]
The CCD imaging system is capable of measuring 2D THz field distribution in real-time. However, it suffers low SNR because it can not use lock-in amplifier that is very powerful in depressing noise. Nevertheless, in Fig. 1
by using the dynamic subtraction technique, which is in principle the same with the phase-sensitive detection used in a lock-in amplifier, we are able to increase SNR dramatically. The frequency of the synchronization signal of the CCD camera is cut in half and sent to an EO modulator. Therefore the THz signal appears in the CCD picture every other frame. With the CCD operating at high frame rate mode and all the frames sent to the computer, the subtraction between two successive frames gives THz signal, and the accumulation increases the SNR. In the experiment, a Pentamax camera (Roper Scientific) that has 384×288 pixels, 12 bit dynamic range and 69 frames/s is used. With 1000 averages, the SNR is improved by 2 orders and it is possible to measure the modulation depth as small as 5×10-5
Fig. 1. Experimental setup of THz imaging with dynamic subtraction.
In the experiment, the laser used is the Coherent Ti:sapphire amplifier RegA 9000, which produces pulses with 0.8 W average power, 250 fs pulse duration, 830 nm wavelength, and repetition rate of 250 kHz. The emitter is a 2-mm <110> ZnTe crystal with a silicon ball attached to it to collimate the radiation. The nonlinear optical rectification effect is used as the mechanism to radiate THz. The EO crystal is a 4 mm thick <110> ZnTe crystal.
3. Experimental Results
Two THz focusing configurations are used in the experiments. The first one (Fig. 2
(a)) consists of 4 parabolic mirrors. This configuration is used in the point scanning THz imaging system, the first two parabolic mirrors collimate and focus thee THz pulse into a small spot and another two parabolic mirrors refocus the THz pulse onto the EO sensor plane. In the second geometry (Fig.2
(b)), one single polyethylene lens is used. If both the emitter-to-lens distance d
and lens-to-EO sensor distance d
is the focal length of the lens, then it is a focal plane imaging geometry.
Fig. 2. Two configurations used in this proposal. (a) Point scanning system. THz is focused by 4 parabolic mirrors; (b) Single lens system.
3.1 Spatio-temporal distribution near the focal plane
shows the spatio-temporal distribution of the THz pulse at the focal plane (Fig. 2
(a)). This is a combined picture from 200 frames with each frame for one time delay. As expected, the wavefront is flat because at the waist a Gaussian beam has flat wavefront. The wavefront is slightly tilted due to the small angle between the THz beam and the probe beam. Several reasons are responsible for the oscillations: dispersion inside the emitter and sensor, group velocity mismatch between the THz pulse and the probe pulse, strong spatio-temporal coupling of the THz pulse, and water absorption in the air.
Fig. 3. Spatio-temporal distribution at (a) the focal plane; (b) 1.5 cm away from the focal plane.
If the sensor is moved away from the focal plane, then the observed wavefront is curved because the beam is divergent now (Fig. 3
(b)). This is the first direct observation of the 2D focused THz field distribution from a weak optical rectification emitter.
3.2 Spatio-temporal distribution at the imaging plane
In a second set of experiments, THz pulses generated from the same emitter is imaged onto the EO sensor by a polyethylene lens (see Fig. 2
(b)). This configuration gives very different results than in Fig. 3
. For the 2f-2f imaging geometry (both d
in Fig. 2
(b)), the measured spot is Gaussian-like only at the main peak (Fig. 4
(a)). At all other times, it has typical ring structure (Fig. 4
(b)). The sizes of the rings are time dependent. When the time delay between the THz pulses and the probe beam is scanned, the rings are first contracting, then expanding after the main peak. The figure in Fig. 4
(b) also shows the dynamic evolution of the 2D spatial distribution.
2D spatial distribution at (a) t
=0 and (b) t
≠0. Click (b) to see the dynamic evolution of the 2D spatial distribution, the number in the figure is time delay. (345 kB
Fig. 5. The X-shape spatio-temporal distribution obtained with the 2f-2f imaging system, showing strong space-time coupling in the propagation of few-cycle pulses.
Since the system is circularly symmetric, the spatio-temporal distribution in x - t
plane gives all the information (Fig. 5
). Fig. 5
is obtained from the movie by combining 75 frames with each frame be the 2D distribution at one time. At the spatial center of the pulse, the temporal waveform is still of typical bipolar structure. However, unlike the conventional pulses that have time invariant spatial distribution, the spatial profile, dimension, and even the wave front are time dependent in Fig. 5
. The spatio-temporal structure is of striking x-shape, indicating that the spatial and temporal coordinates are not long separable. This phenomenon has not been reported previously with the propagation of few-cycle pulses. It is due to the pure propagation effect, because it does not exist in Fig. 3
, which uses the same emitter.
We also measured the location dependence of the emitter. In Fig. 2
(b), the pump laser beam is collimated, therefore when the emitter location is scanned along the optical axis, the THz generation remains the same. Any change comes from the propagation. With the focal length f
=5 cm, the emitter-to-lens distance d
is scanned from 32 cm to 7 cm with step size of 0.5 cm, the video in Fig. 6
shows the dynamic evolution of the 2D spatial distribution versus emitter position. The rings come from curved wavefront.
Dynamic evolution of the measured 2D distribution when the emitter-to-lens distance d
is scanned from 31.5 cm to 7.5 cm with step size of 0.5 cm. (399 kB
4. Discussions and simulation
4.1 Amplitude Imaging
A 2f-2f system is perfect for intensity imaging, however it is not a perfect imaging system because it brings up a quadratic phase term. Actually for an optical system described by the propagation matrix ABCD, when B=0 the system is an imaging system. The field distribution E
1 at the imaging plane can be expressed as
0 is the field at the source plane, k is the wave number. E
1 is a perfect image of E
0 only when C=0. The quadratic phase term exists for most cases, which explains for the rings.
4.2 X-shaped spatio-temporal structure
is the propagation equation for one frequency. Simple calculation shows that Eq. (1)
can not be used to explain the x-shaped spatio-temporal distribution in Fig. 5
. The reason is that it does not take the finite aperture size of the imaging lens into consideration. Due to very long wavelength, the diffraction of the THz pulse is very severe, and the cutoff by the imaging lens can not be neglected. A complete simulation includes two diffraction integrals: one is from the emitter to the lens plane and the other is from the lens plane to the sensor plane. To consider the aperture effect of the lens, the integral area is that of the lens. Both time-domain and frequency domain diffraction integrals might be used. Fig. 7
shows the simulated result. The main feature (i.e. the x-shaped spatio-temporal structure) is in good agreement with the experimental result in Fig. 5
. Detailed simulation and analysis will be published elsewhere.
Simulated spatio-temporal distribution. (Refer to Fig. 5
for experimental result)
In conclusion, the improved CCD THz imaging system has been used to measure 2D THz distribution. For the first time, the weak THz field distribution can be displayed on the computer screen in real-time. This system is an ideal tool to study THz pulse shaping in free space.
In contrast to the long pulse, the spatial distribution of which is time independent, the spatial distribution of few-cycle pulses shows dramatic change with time. This is explained as the cutoff effect of the imaging lens. The simulation is in good agreement with the experiment. This phenomenon is the result of strong spatio-temporal coupling. Similar phenomenon should exist in optical frequency range as well. It provides a means to manipulate the spatio-temporal structure of ultrashort pulses, and may find applications in nonlinear optics, optical information processing and optical communication.
In addition, the x-shaped spatio-temporal structure is mainly due to the finite size of the lens. That is, the mask is only a circular aperture. It is expected that if a more complicated mask is used as in optical pulse shaping [11
11. A.M. Weiner, “Femtosecond optical pulse shaping and processing,” Progress in Quantum Electronics , 19. 161–237 (1995). [CrossRef]
], one would have more freedom to control the spatio-temporal structure of an ultrashort pulse. The simulation and the design of such masks are underway.
We thank Paul Campbell for his technical assistance. This is supported by the Army Research Office, and the Department of Energy.
References and links
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E. Budiarto, P. Nen-Wen, J. Seongtae, and J. Bokor, “Near-field propagation of terahertz pulses from a large-aperture antenna,” Opt. Lett. 23, 213–215 (1998). [CrossRef]
J. Bromage, S. Radic, G.P. Agrawal, C.R. Stroud Jr., P.M. Fauchet, and R. Sobolewski, “Spatiotemporal shaping of terahertz pulses,” Opt. Lett. 22, 627–629 (1997). [CrossRef] [PubMed]
J. Bromage, S. Radic, G.P. Agrawal, C.R. Stroud Jr., P.M. Fauchet, and R. Sobolewski, “Spatiotemporal shaping of half-cycle terahertz pulses by diffraction through conductive apertures of finite thickness,” J. Opt. Soc. Am. B 15, 1953–1959 (1998). [CrossRef]
Q. Wu, T.D. Hewitt, and X.-C. Zhang, “Two-dimensional electro-optic imaging of THz beams,” Appl. Phys. Lett. 69, 1026–1028 (1996). [CrossRef]
Z.G. Lu, P. Campbell, and X.-C. Zhang, “Free-space electro-optic sampling with a high-repetition- rate regenerative amplified laser,” Appl. Phys. Lett. 71, 593–595 (1997). [CrossRef]
A.M. Weiner, “Femtosecond optical pulse shaping and processing,” Progress in Quantum Electronics , 19. 161–237 (1995). [CrossRef]