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We have investigated the spatial distribution of the polarization state of a terahertz electromagnetic wave focused by an off-axis parabolic mirror (OPM) in the focal plane. We employed polarization-resolved terahertz time-domain spectroscopy and found that a steep spatial variation in the polarization state appears slightly distant from the focus when a linearly polarized terahertz wave is focused. The spatial variation includes an abrupt change in the polarization state (states change between circular and linear polarizations) within a wavelength. The observed phenomena are confirmed by numerical calculations and are shown to be intrinsic to the reflection from the OPM.

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This paper provides a detailed theoretical analysis of the unexpected transient divergent and rotational distributions of the focused electric field vector reported in Shibata et al (2015 Phys. Rev. A 92 053806). We reveal the physical origin of these distributions. More quantitatively, we derive the semi-analytic expressions and clarify how these distributions depend on the mirror size, offset angle, and the intensity distribution of the incident parallel light. We compare the formulas with numerical calculations and evaluate the area where linearity holds. If the wavelength and the mirror size are sufficiently shorter than the focal length, the radius of the linear area becomes longer than the wavelength. These formulas and evaluations are useful for studies, which require high spatio-temporal resolution.

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