Hankel transform-domain analysis of scattered fields in multilayer planar waveguides and lasers with circular gratings

Radiation patterns of scattered fields with arbitrary azimuthal orders in multilayer planar waveguides and laser cavities with circularly symmetric gratings are formulated based on the volume current method. Full-wave Greenʹs function analysis based on the integral transform method lies at the heart of this approach. Unlike the conventional approach, the dyadic Greenʹs function relates some auxiliary fields to some auxiliary sources in the spectral domain. These auxiliary functions are defined to facilitate the spectral domain formulation in the cylindrical coordinate system and the use of transfer matrix method for obtaining a closed-form solution of the spectral Greenʹs function in multilayer planar structures. More importantly, it is shown that the far-field pattern of the scattered field can be expressed directly in terms of the auxiliary fields in the Hankel transform domain.