Propagation of Arbitrary Non-Paraxial Beams by Expansion in Spherical Functions

While the paraxial approximation is applicable to many, even most, optical systems, the highly non-paraxial regime, where the paraxial approximation and simple corrections to it fail, is becoming increasingly important with the development of intrinsically non-paraxial optical devices and structures such as nano/micro-cavities, photonic crystals, VCSELs, and others of sizes comparable to, or smaller than, the optical wavelength. We calculate the propagation of a highly non-paraxial beam by expansion into spherical functions, which can be considered as fundamental non-paraxial modes. This method is applicable to arbitrary beams