Permissions for ReuseOptical constants such as complex permittivity have been measured for various materials since the development of terahertz time-domain spectroscopy (THz-TDS) using a femtosecond (fs) laser.1,2,3,4,5,6,7,8 This method allows simultaneous determination of both the real and imaginary parts of the optical constant across a spectral range from a few tens of gigahertz to several terahertz because it allows measurement of the change due to the optical constant in the amplitude and phase of a terahertz electric field.
THz-TDS is based on a pump-probe method. A fs optical pulse is first divided into two beams. One (pump) is used to generate a terahertz field pulse, which, for example, is emitted from a semiconductor such as InAs by irradiating its surface with the pump pulse. In measurements using the electro-optic (EO) effect, the other (probe) is overlapped with the terahertz field pulse within an EO crystal such as ZnTe, and the magnitude of the Pockels effect proportional to the amplitude of the terahertz field is obtained from measurement of the intensity of the probe pulse subject to the birefringence in the crossed-polarizer configuration. The temporal waveform of the terahertz field is measured by changing the time interval between the pump and probe pulses with an optical delay line. Thus, THz-TDS is not applicable to single-shot measurement of the temporal waveform of a terahertz field pulse.
A method that allows single-shot measurement of a terahertz field waveform was proposed by Jiang and Zhang.9 In the method, a fs probe pulse is linearly chirped and overlapped with a terahertz field pulse within the EO crystal. The chirped probe pulse is modulated by the terahertz field and dispersed onto a multichannel detector combined with a spectrometer. Since the wavelength axis can be converted to the time axis using the value of the chirp rate, the temporal waveform of the terahertz field is derived from the two spectra of the probe pulses with and without terahertz field modulation. They used a chirped pulse with a temporal width of approximately 30 ps and obtained a terahertz field pulse three times broader than the original pulse width measured by THz-TDS. Moreover, severely distorted terahertz field waveforms were observed even for chirp probe pulses with a time width of several picoseconds.10,11,12 Sun et al.13 analyzed the dependence of the temporal resolution of electro-optic detection using a chirped probe pulse (EODCP) on the chirp rate by assuming that the temporal widths of the chirped pulse and the terahertz field are much longer than the oscillation period of the optical beam and that the stationary phase method is applicable. The EODCP-derived terahertz field pulse waveform in their analysis was monocyclic for a monocyclic original terahertz field. It has recently been demonstrated that the temporal resolution of EODCP can be significantly enhanced by combination with an interferometric retrieval algorithm; the original terahertz field waveform is reproduced well by the algorithm.11,12
Single-shot measurement of the terahertz field pulse has been achieved by overlapping the terahertz radiation and the fs optical probe beam noncollinearly within an EO crystal, where the time window is determined by the spot size of the probe beam and the crossing angle between the two beams.14 Further, it has been demonstrated that for a time window of about 5 ps, the terahertz field waveform obtained from the single-shot measurement almost coincides with that from THz-TDS.
Complex systems such as liquids and proteins show low-frequency vibrations in the terahertz spectral range, and such vibrations are believed to play an important role in the dynamics of chemical reactions in solutions and proteins. Further, the origin of the boson peak observed in the low-frequency vibrational spectrum of the complex system is under debate.15,16 Thus, the low-frequency dynamics of the complex system has been extensively investigated by means of a variety of experimental methods such as due to inelastic neutron17,18,19 and light scatterings,20 as well as by THz-TDS.2,3,4,5,6,7,8 Most of the measurements, however, have been made for systems in thermal equilibrium. It is considered necessary to study how such low-frequency vibrations change during a reaction in order to explore the mechanism of the reaction in solutions and proteins.
This can be achieved by optical pump-terahertz probe (OPTP) spectroscopy. In dye solutions, the solvation dynamics after optical excitation of the dye molecule have been probed by a terahertz field pulse, and it has been suggested that librational modes localized close to the solute occur owing to the abrupt change caused by the excitation in the dipole moment of the dye molecule.21 In liquid hexane, the transient photoconductivity and recombination dynamics of quasifree electrons generated by two-photon ionization induced by the irradiation with a fs UV pulse have been probed by the terahertz pulse.22
THz-TDS is mostly adopted for the terahertz probe in OPTP spectroscopy. In such a case, a fs laser pulse is first divided into two beams, and one is used for exciting the sample. The other is used for THz-TDS; that is, it is further divided into two beams: one for the generation of the probe terahertz field pulse and the other for sampling the terahertz field. Hence, two optical delay lines are employed among the three fs pulses thus divided. OPTP spectroscopy with THz-TDS has several drawbacks. An intense fs laser such as that generated from a chirped-pulse-amplification system is often used in pump-probe spectroscopy to excite as many molecules as possible in the sample. The shot-to-shot fluctuation of such an intense laser deforms the terahertz field waveform obtained from THz-TDS. Even if the shot-to-shot fluctuation is small, the terahertz field pulse shape is deformed if the system under study does not relax within the period of pulse repetition or undergoes an irreversible process. Further, the use of two optical delay lines makes measurement overly time consuming. In fact, in the above mentioned OPTP studies, the amplitude of the terahertz field pulse was measured only at the specified detection delay time at which the waveform had its peak while the pump-probe delay time was scanned, but its temporal waveform was not measured.21,22 These measurements do not provide the so-called time-resolved terahertz spectrum. If EODCP is employed for the terahertz probe in OPTP spectroscopy, these drawbacks can be overcome.23,24 However, no experimental investigation has been performed to determine how the terahertz field waveform measured by EODCP depends on the chirp rate and spectral resolution of the spectrometer, although the chirp rate dependence of the terahertz field waveform has been analyzed under limited conditions using the stationary phase method.13 Such dependence determines the parameters such as the spectral resolution and bandwidth of terahertz spectroscopy using EODCP.
Thus, in this study, we measured the terahertz field waveform by EODCP as a function of the chirp rate and the spectral resolution of the spectrometer, and derived an expression for the temporal shape of the terahertz field pulse obtained from EODCP without using the stationary phase method. The experimental results were compared with the theoretical predictions. Further, in this paper, we examine the experimental conditions such as the chirp rate and the spectral resolution of the spectrometer in the application of EODCP to terahertz spectroscopy.