Tight focusing of electromagnetic fields by large-aperture mirrors

We derive nonparaxial input conditions for simulations of tightly focused electromagnetic fields by means of unidirectional nonparaxial vectorial propagation equations. The derivation is based on the geometrical optics transfer of the incident electric field from significantly curved reflecting surfaces such as parabolic and conical mirrors to the input plane, with consideration of the finite thickness of the focusing element and large convergence angles, making the propagation vectorial and nonparaxial. We have benchmarked numerical solutions of propagation equations initiated with the nonparaxial input conditions against the solutions of Maxwell equations obtained by vectorial diffraction integrals. Both transverse and longitudinal components of the electric field obtained by these methods are in excellent agreement.