Algorithm for reconstruction of terahertz pulse field from electro-optic measurement without phase matching

Abstract

With the rapid growth of the application of Terahertz time-domain spectroscopy (THz-TDS) in many scientific fields, the accurate temporally-resolved THz electric field oscillation is required. However, distortion occurs in electro-optic sampling (EOS) measurements of THz pulse field. In this paper, a time-domain analysis of the distortion in the electro-optic sampling measurement of THz pulses is made with the convolution theory, in which frequency-dependent reflection and electro-optic (EO) effect, dispersive propagation of the THz pulse in the EO crystal, and the phase mismatching between the THz pulse and the sampling lase pulse in the EO crystal are taken into account. And then, a retrieval algorithm for high accurate THz pulse field reconstruction is proposed and numerically demonstrated. Since the reconstruction of the THz pulse field is an ill-posed inverse problem caused by noise, the iterative Tikhonov regularization is adopted in our retrieval algorithm to convert this ill-posed problem to a related well-posed problem. Gallium phosphide (GaP) is used as the EO crystal to reduce the sensitivity of this ill-posed problem, for the complex-dielectric function of GaP is flat within a broader THz range than that of commonly used ZnTe crystal. Phase mismatching arises when GaP crystal is utilized, our proposed retrieval algorithm is demonstrated to have a good performance even when a 0.5-mm-thick GaP crystal (with severe phase mismatching) is used.