Vector Fourier optics of anisotropic materials

Abstract

The Fourier optics technique is founded on the transfer function derived from the scalar wave equation and thus has traditionally been applied to monochromatic scalar fields propagating paraxially in isotropic lossless materials. We review scalar and vector diffraction theory to show that the scalar Fourier optics technique can be seamlessly extended to the case of time-dependent nonparaxial and evanescent vector fields propagating in anisotropic and/or absorbing materials. The missing piece is shown to be the Fourier-domain vector boundary conditions that have recently been derived from the real-domain vector Rayleigh–Sommerfeld diffraction integral. These boundary conditions, complemented by the anisotropic transfer functions provided by the roots of the Booker quartic, combine the rigor of Green’s function integrals with the intuitive simplicity and general applicability of Fourier optics. We illustrate the power of this technique via analytically simple solutions to traditionally complex problems such as Fresnel transmission between arbitrary media, uniaxial conoscopy, and biaxial conical refraction. The accuracy of vector near-field diffraction is validated via comparison with the finite-difference time-domain method.