Abstract
We review our recent works on polarization-sensitive electro-optic (PS-EO) sampling, which is a method that allows us to measure elliptically-polarized terahertz time-domain waveforms without using wire-grid polarizers. Because of the phase mismatch between the employed probe pulse and the elliptically-polarized terahertz pulse that is to be analyzed, the probe pulse senses different terahertz electric-field (E-field) vectors during the propagation inside the EO crystal. To interpret the complex condition inside the EO crystal, we expressed the expected EO signal by “frequency-domain description” instead of relying on the conventional Pockels effect description. Using this approach, we derived two important conclusions: (i) the polarization state of each frequency component can be accurately measured, irrespective of the choice of the EO crystal because the relative amplitude and phase of the E-field of two mutually orthogonal directions are not affected by the phase mismatch; and, (ii) the time-domain waveform of the elliptically-polarized E-field vector can be retrieved by considering the phase mismatch, absorption, and the effect of the probe pulse width. We experimentally confirm the above two conclusions by using different EO crystals that are used for detection. This clarifies the validity of our theoretical analysis based on the frequency-domain description and the usefulness of PS-EO sampling.
Highlights
Terahertz time-domain spectroscopy (THz-TDS) is a powerful tool to obtain coherent electric-field (E-field) time-domain waveforms in the terahertz frequency range [1,2], and it is an emerging spectroscopic technique for determining the low-energy dielectric and conductive properties of materials
We confirmed that the correction by appropriately considering the phase mismatch is quite important for the retrieval, and the time-domain waveforms that were retrieved from EO signals recorded using different EO crystals show good agreement
In order to account for the velocity mismatch, this description considers that the EO crystal comprises many thin layers, and the probe pulse is affected by a different refractive index ellipsoid in each layer as a result of the changing terahertz E-field vector
Summary
Terahertz time-domain spectroscopy (THz-TDS) is a powerful tool to obtain coherent electric-field (E-field) time-domain waveforms in the terahertz frequency range [1,2], and it is an emerging spectroscopic technique for determining the low-energy dielectric and conductive properties of materials. The effects of frequency-dependent phase-mismatch (corresponding to the velocity mismatch in the Pockels effect description), the absorption coefficient, the nonlinear optical coefficient, and the effect of the finite pulse width of the probe pulse are straightforwardly included Because of these benefits, the frequency-domain description has been used to describe the EO signals in different types of EO sampling setups, such as single-shot [85,87,88,89], nonellipsometric noncollinear [90], heterodyne [91], energy-sensitive [92], and shot-noise reduced [22] EO samplings. We confirmed that the correction by appropriately considering the phase mismatch is quite important for the retrieval, and the time-domain waveforms that were retrieved from EO signals recorded using different EO crystals show good agreement These results strongly support the effectiveness of the frequency-domain description for the PS-EO sampling.
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