1. Overview

Our research focuses on terahertz time-domain spectroscopy and ultrafast carrier dynamics in semiconductors using femtosecond lasers. Major activities are:

- Development of new schemes to manipulate teraherz (THz) pulses using optical rectification in nonlinear crystals (LiNbO₃ , ZnTe, and GaAs)

- Optical and THz measurements at cryogenic temperature to investigate exciton dynamics in semiconductor quantum wells (QWs) under strong THz fields

- Study of large amplitude motions in proteins via THz time-domain spectroscopy (THz-TDS) investigating the feasibility of using THz spectroscopy for biosensing and analysis.

2. THz pulse manipulation

We have developed novel schemes to control the basic properties of THz waves: pulse shape, polarization and propagation. THz technology has made great progresses recently, but the successful realization of the potential of THz technology still needs effective control devices of THz fields. The THz devices we developed—pulse shapers, wave plates, high reflectors, and resonant cavities—could be basic tools in any THz laboratories as such devices in the optical regime are indispensable in optics laboratories. The THz devices can make contributions to promising applications in high-speed switching, demultiplexing, and wavelength conversion of optical signals. Effective THz control is also essential for the potential application to ultrahigh-speed wireless digital interconnects for computer chips of the ultrahigh clock rates (>10 GHz). Several research groups are exploring the potential of THz time-domain imaging for medical diagnosis. The THz imaging techniques can benefit from the THz devices. A wide range of new experiments would be enabled if THz sources with controlled and adjustable elliptical polarization states were available. Examples for which the THz ellipticity is critical include the control of excitons in semiconductor nanostructures and of molecular rotational wavepackets. Elliptically polarized THz is also potentially important to study macromolecular chiral structures such as proteins and DNA because of strong absorption in the THz regime due to collective vibrational modes.

2.1. Multi-cycle THz pulse generation in poled lithium niobate crystals

The scheme of the multi-cycle THz waveform generation is shown in Fig. 1, which illustrates optical rectification in the pre-engineered domain structure of a PLN crystal. The second order nonlinear susceptibility (c⁽²⁾) of the crystal reverses sign between neighboring domains. The green (down) and purple (up) shades in Fig. 1 indicate the direction of the optic axis. When a femtosecond optical pulse propagates through a PLN crystal with such a domain structure, a THz nonlinear polarization is generated via optical rectification. Each domain in the crystal contributes a half cycle to the radiated THz field. Since the length of the half-cycle pulse is proportional to the corresponding domain length, the resulting THz pulse directly corresponds to the crystal domain structure as illustrated in Fig. 1.

Figure 2.1. Schematic diagram of the multi-cycle THz pulse generation in a PLN crystal. The green (down) and purple (up) shade indicates the direction of the domain optic axis.

When the domain structure is periodic, narrow-band multi-cycle THz pulses can be generated. Figure 2 shows the THz waveforms and the respective spectra from a periodically-poled lithium niobate (PPLN) crystal when the domain width is 30, 40, 50, and 60 mm at T =115 K.¹ The frequency of the THz wave is determined as n_THz = c/2d(n_T  - n_O) where c is the light velocity, d is the domain-width, and n_T (n_O) is the group refractive index at THz (optical) frequency. Tuning of the THz frequency is accomplished simply by scanning the sample laterally to the beam propagation direction.

Figure 2.2. (a) THz waveforms and (b) power spectra at T = 115 K when the PPLN domain-width is 30, 40, 50, and 60 mm. The sample is a laterally chirped z-cut PPLN crystal: multiple domain structures of slightly different domain width are fabricated side by side at a regular distance from one to another. The THz frequency is inversely proportional to the domain width.

It is interesting to note that, since the THz waveform is essentially a direct manifestation of the crystal domain structure, the multi-cycle THz generation method provides a novel approach to characterizing the domain structure of poled materials. Figure 3(a) shows an optical image of the electrode pattern of a PPLN crystal, magnified to exaggerate the domain lengths.³ It is clearly seen that the sample is wedged. The domain structure of the sample is supposed to match with the electrode pattern, but in reality each domain suffers width fluctuations due to the strong coercive electric fields and field leakage out of the electrodes. To probe the entire domain structure of the PPLN, the PPLN sample was scanned laterally with respect to the fixed excitation beam. The THz waveform image of the PPLN domain structure is shown in Fig. 3(b), which indicates that the domain structure is fairly periodic, which is consistent with the electrode pattern.³ In the narrower region of the crystal, the effective optical beam path is shorter, thus the THz waves arrive earlier than in the wider region. The slanted domain interfaces to the sample surfaces are also well reproduced in the THz waveform image.

Figure 2.3. (a) Optical microscope image of electrode patterns (magnified in the direction of 1.2 mm) and (b) two dimensional image of THz waveforms of a 6.5 mm ´ 1.2 mm PPLN crystal (THz field amplitude corresponds to the color-bar).

2.2. THz pulse shaping

Arbitrary THz waveforms can be obtained using non-periodic PLN crystals.  Figure 4 shows experimental results and numerical simulations for three different types of PLN structures, which demonstrates the feasibility and versatility of the THz pulse shaping scheme.⁴ First, the zero-area double pulse (Fig. 4(a)) consisting of two pulses with a p phase shift is generated from a domain structure in which a single domain (100-mm) is placed between two sets of multiple domains (50 mm). The corresponding spectrum (Fig. 4(a)) clearly shows the signature of the interference fringes of two coherent pulses. The phase-locked double pulses can be applied to coherent control experiments ranging from chemical reactions to semiconductor carrier dynamics. Second, a chirped THz waveform is shown in Fig. 4(b). The domain structure for the chirped pulse includes multiple domains ranging from 20 to 90 mm with 1 mm gradual increment. The broad band spectrum is shown in Fig. 4(b). Chirped pulses in the optical regime have been used in the control of atomic wavepackets via adiabatic transfer. Similarly, chirped THz pulses are applicable to adiabatic transfer between excitonic wavepackets in semiconductor nanostructures or between rotational and vibrational modes of molecules. Third, Fig. 4(c) shows the waveform from a structure of alternating domain length (30 and 60 mm). Narrow and broad half-cycle pulses appear alternately. Figure 4(c) shows the narrow band spectrum corresponding to the 90-mm period. In general, the results clearly show that shaped THz pulses can be generated in PLN structures.

Figure 2.4. Experimental data and numerical solution of (a) zero-area double pulse from a domain structure in which a single domain (100-mm) is placed between two sets of periodic multiple domains (50-mm), (b) chirped pulse from a domain structure which includes multiple domains ranging from 20 to 90-mm with 1 mm gradual increment, and (c) pulse with alternating period from a structure of alternating domain length (30 and 60-mm). THz waveforms and corresponding spectra from poled lithium niobate structures are shown. Diagrams of the three domain structures are included: green (down) and purple (up) indicates the alternating direction of the crystal optic axis.

We can substantially improve the flexibility of THz pulse shaping by optical-THz hybrid systems. We demonstrate a simple scheme that a pair of temporally separated optical pulses can synthesize THz waveforms by adjusting the relative time-delay and intensity between the two optical pulses.

Figure 2.5. (a) Schematic diagram for THz pulse shape control using two optical pulses.  (b)  Relative phase (2pnt=2pn+Df) dependent THz waveforms and (c) corresponding spectra.

2.3. Generation of THz pulses with arbitrary elliptical polarization

We have demonstrated two techniques to generate elliptically polarized THz pulses. One utilizes optical rectification in nonlinear crystals using two temporally separated optical pump pulses. We control the THz ellipticity adjusting the relative time delay and polarization of the two optical pulses. We generate mixed polarization states of single-cycle THz pulses using ZnTe, and elliptically-polarized multi-cycle THz pulses in PPLN crystals. The second is essentially a broad-band THz wave-plate using a combination of a wire-grid THz polarizer and a mirror to transform linearly-polarized multi-cycle THz pulses into elliptical polarization. The wire-grid THz wave-plate is applicable to the entire THz spectral range. In general, the wave-plate method should be more practical than the two-pulse technique because the set-up is simpler and the polarization control is more flexible. We expect that THz ellipticity control techniques may be useful for coherent control of carrier dynamics in semiconductor nanostructures and of molecular dynamics. For example, single-cycle THz pulses of spiral polarization might be useful for exploring quantum chaos of the transiently kicked quantum rotor. This problem has been rigorously studied theoretically, but only a few experimental studies have been done in atomic systems. A spirally-polarized single-cycle THz pulse could be used as a transient rotational impact on gas phase heteropolar molecules, which are nearly ideal quantum rotors. THz time-domain spectroscopy, which can measure not only the amplitude of the rotational motion but also the phase, would be an excellent experimental scheme to investigate the quantum wavepacket dynamics.

Figure 2.6. Mixed polarization states of single-cycle THz pulses. (a) Optical and THz electric fields in ZnTe (110) plane. (b) Waveforms of two linearly-polarized THz pulses: the measured angle between the two THz fields is 51°. (c) Polarization trajectories of the superposed THz fields.

Figure 2.7. Schematics of the THz wave plate and elliptically polarized THz pulses.

3. THz control of quantum coherence in semiconductor quantum-wells

4. THz-TDS on Large Amplitude Motion in Proteins

The use of THz spectroscopy for biosensing has only recently emerged in the development of biological sensors. THz radiation is non-invasive, non-ionizing, and highly sensitive, and it is therefore ideal for biological applications. The collective modes in large complex molecules manifest themselves in the THz frequency range, i.e., THz fields directly interact with large dipole moments represented by the collective motions in proteins. The response is linear, and the thus required radiation field is minimal. In contrast, other techniques involving optical or X-rays depend on indirect processes such as nonlinear effects, the very nature of which requires high power radiations. Moreover, nonlinear processes are also plagued by complications. THz-TDS measures the actual electric field of THz pulses including both the amplitude and the phase, thus it can directly map out the collective motion in time. In bioimaging, the phase sensitivity of THz-TDS has been demonstrated in the sharp spatial and temporal contrasts of the obtained images

Figure 4.1. Illustarion of  THz interaction with a myoglobin molecule

We have measured the absorption spectra of Mb in the powder form using a BWO based spectrometer. Because of their tight binding nature in free space, powder samples of Mb are expected to show a different response upon THz radiation from their water solutions. Nevertheless, it is worthwhile to have the spectral information in hand for comparisons with the spectral data from water solutions.

4.2 Absorption spectrum of 1-mm thick dry Mb. The exponential growth (solid line) fits well with the experimental data (solid circles).

We have built and tested a terahertz time-domain spectrometer to measure the transmission of Mb water solutions. Figure 4.3 shows the schematic diagram. We use optical rectification for the emission of single-cycle THz pulses and electro-optic sampling for the detection of the electric-field in the time-domain. The dotted line in the figure indicates the purged region so to prevent absorption by the moisture in the air. The waveform of the single-cycle THz pulse and the corresponding power spectrum are also shown in the figure. The spectral tuning range is from 0.1 to 2.7 THz, and the signal to noise ratio is in the vicinity of ~10⁶.

4.3 Schematic diagram of the terahertz time-domain spectroscopy setup for the transmission measurement of Mb water solution. and THz single-cycle waveform and the corresponding power spectrum on a logarithmic scale.