Chebychev Response of Thin Film Optical Filters

Abstract

The power reflection coefficient (reflectance) of linear, periodically homogenous, isotropic, nonabsorbing stack filters is derived using full wave analysis. The well-known ABCD characteristic matrix is used to assess the spectral response of the stack filters. Adopting this method requires a huge number of matrix multiplications as the number of layers increases. An alternative approach of evaluating the whole matrix is suggested which is shown to save computational time. Band reject response far from ideal characteristics, due to the presence of unwanted ripples surrounding the stopband, is obtained. Equating these ripples without changing the length of the structure is undertaken by varying some design parameters related to the layers constituting the filter. Namely, the index of refraction and the physical thickness of individual layers are used as optimization variables. This process requires evaluating the derivative of the reflectance with respect to each design variable while leaving other parameters unchanged. The sensitivity of the derivatives to various design parameters is also addressed, which is sometimes required in manufacturing multilayered dielectric thin films.