Photonic bandgaps of periodic multilayers with diffuse interfaces

The photonic bandgap of periodic multilayers with diffuse interface 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 structure with 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 to say determining experimentally the ratio of width of the different Bragg peaks on a reflectivity curve, can allow estimating the thickness of the interdiffusion layer.