Chebychev response of thin film optical filters

The power reflection coefficient (reflectance) of linear, periodically homo genous, isotropic, nonabsorbing stack filters is derived using full wave an alysis. The well-known ABCD characteristic matrix is used to assess the spe ctral response of the stack filters. Adopting this method requires a huge n umber of matrix multiplications as the number of layers increases. An alter native approach of evaluating the whole matrix is suggested which is shown to save computational time. Band reject response far from ideal characteris tics, due to the presence of unwanted ripples surrounding the stopband, is obtained. Equating these ripples without changing the length of the structu re is undertaken by varying some design parameters related to the layers co nstituting the filter. Namely, the index of refraction and the physical thi ckness of individual layers are used as optimization variables. This proces s requires evaluating the derivative of the reflectance with respect to eac h design variable while leaving other parameters unchanged. The sensitivity of the derivatives to various design parameters is also addressed, which i s sometimes required in manufacturing multilayered dielectric thin films.