Characterization of tight focused vector fields formed by an off-axis parabolic mirror

We present a systematic investigation of the characterization of tight focused vector fields formed by an off-axis parabolic mirror. Based on the Stratton-Chu integral of Green’s theorem, the rigorous diffraction integrals that generate vector fields within and outside of the focus arising from a collimated beam incident on an idealized parabolic mirror are derived in detail. And the explicit analytical expressions of the far-field vector diffraction electric and magnetic fields suitable for an off-axis parabolic mirror are also obtained. It is shown that there are significant differences of vector diffraction characterizations between on- and off-axis parabolic mirrors. When the off-axis rate is greater than four, the longitudinal field is predominant, and the maximum peak intensity ratio between the longitudinal field and the transverse field at the focus is about 10³. This property is very valuable for all applications where a strong longitudinal field component is desirable. The effective focal length increases with increasing the off-axis rate, and the depth of the focus and the convergence angle of the focused beam are strongly dependent on f´/2ω: smaller values of f´/2ω lead to shorter focal depth and larger beam convergence (or more tightly focusing).