Photonic bandgaps of periodic multilayers with diffuse interfaces

Abstract

The photonic bandgap of periodic multilayers with diffuse interfaces is calculated by considering an empirical model for the interdiffusion profile. The model for the diffuse profile is based on the error function Erf and a characteristic parameter σ. The model is valid for multilayer structures with an arbitrary layer thickness. It is shown that the width of the bandgap varies with the value of σ and the Brillouin zone boundary. Numerical examples are presented. It is suggested that measuring the ratio of the width of the bandgaps at different orders, that is, determining experimentally the ratio of the widths of the different Bragg peaks on a reflectivity curve, can allow estimation of the thickness of the interdiffusion layer.

Sequences of exact analytical solutions for plane waves in graded media

“…This offers a new modelling tool for complex 1D photonic crystals. Indeed, this entails a new type of solutions for the Hill's equation (in contrast to those presented in [14]- [18] which are based on trigonometric functions, the new one would be based on hyperbolic and linear functions of the optical-thickness) and a new avenue for studying the photonic bandgaps of periodic smooth multilayers [60].…”

“…When addressing modulated index profiles, other classical methods are the perturbation-based methods among them the coupled-mode method (see for example [47], [60], [78], [80]). A systematic starting hypothesis is that the index variations are of small amplitude.…”