Retrieving the undistorted terahertz time-domain electric-field vector from the electro-optic effect

We formulate and experimentally demonstrate a method to retrieve the undistorted temporal profile of an elliptically polarized terahertz pulse from the electric-field (E-field) vector waveform detected by electro-optic (EO) sampling. This method takes into account the distortion effects due to pulse width of the probe laser, absorption by the EO crystal, and frequency-dependent phase mismatch between the probe and terahertz pulses inside the EO crystal. Even with this distortion, the detected elliptically polarized terahertz vector waveform can be simply interpreted as that at the center of the EO crystal for detection. This interpretation enables us to retrieve the undistorted terahertz E-field vector waveform in front of the EO crystal by analyzing the detected EO signals in the frequency domain and then reconstructing those in the time domain. In order to verify our method, we experimentally demonstrate that the same elliptically polarized terahertz waveform can be retrieved even when we use different EO crystals for detection. Although the terahertz E-field vector waveforms measured by different EO crystals are significantly different due to the distortions, the retrieved waveforms show a good agreement without need for additional corrections.