Full-Wave Computational Model of Electromagnetic Scattering by Arbitrarily Rotated 1-D Periodic Multilayer Structure

Abstract

A full-wave computational model of electromagnetic scattering of conically incident plane waves by arbitrarily rotated 1-D periodic multilayer structure is proposed. Each layer in the structure (overall sandwiched between two half-spaces) consists of a dielectric material within which an infinite chain of periodically arranged and arbitrarily orientated circular cylinders is embedded. The orientations of the cylinder arrays in different layers are arbitrary with respect to one another, offering full generality. The above is a model of fiber-reinforced composite laminates as in industry but also of multilayered photonic crystals. Combining Rayleigh’s method and mode-matching produces scattering matrices for each layer cascaded from the top to the bottom in order to relate the reflection/transmission coefficients to the incident field. Power reflection and transmission coefficients follow from Poynting’s theorem. The mathematical derivation insists on modal representations and building up proper S-matrices. Numerical simulations show that the model is accurate, known results on woodpile structures in photonics are in particular recovered. The model is also versatile in terms of illuminations, geometries, and material parameters. The results could also be used as benchmarks in view of lack of data in present-day literature on such arbitrarily orientated layerings. Calculations of pertinent dyadic Green functions is one of possible extensions in view of the imaging methods of possibly damaged multilayer structures.