Two-dimensional complex source point solutions: application to propagationally invariant beams, optical fiber modes, planar waveguides, and plasmonic devices

Abstract

Highly convergent beam modes in two dimensions are considered based on rigorous solutions of the scalar wave (Helmholtz) equation, using the complex source point formalism. The modes are applicable to planar waveguide or surface plasmonic structures and nearly concentric microcavity resonator modes in two dimensions. A novel solution is that of a vortex beam, where the direction of propagation is in the plane of the vortex. The modes also can be used as a basis for the cross section of propagationally invariant beams in three dimensions and bow-tie-shaped optical fiber modes.