Selective imaging of terahertz electric field of phonon-polariton in LiNbO$_3$

Coherent phonon-polaritons have attracted a considerable amount of interest owing to their relevance to nonlinear optics and terahertz (THz)-wave emissions. Therefore, it is important to analyze the THz electric-fields of phonon-polaritons. However, in the majority of previous measurements, only a single component of the THz electric field was detected. In this paper, we demonstrate that pump-probe electro-optical imaging measurements using the Stokes parameters of probe polarization enable the phase-resolved selective detection of THz electric-field components that are associated with the phonon-polariton. We experimentally distinguish the mode profiles of ordinary and extraordinary phonon-polaritons, and clarify the excitation mechanism as optical rectification. These results are explained by numerical calculations of Maxwell equations for the THz electric field. The technique of selectively observing the THz electric field components may be useful for designing efficient THz-wave emitters.