Detailed study of transient anomalous electric field vector focused by parabolic mirror

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.