Transfer Matrix Method-Compatible Model for Metamaterial Stacks

Abstract

Mean-fieldtheory-based effective refractive index modelsare widelyused to design optical metamaterials and interpret their optical properties.However, emerging applications where metamaterials are embedded intolayered device architectures require a detailed consideration of themetamaterial's dispersive properties and interfacial boundaryconditions, which are beyond the scope of the mean-field theory forhomogeneous bulk media. Here, we describe an approach to calculatethe optical transfer function for one-dimensional optical metamaterialsthat includes the dispersive properties of the effective index aswell as the effective interfacial impedance. We address the boundaryconditions at a metamaterial interface by a complex-valued effectiveinterfacial impedance. Combined with the effective refractive index,the effective interfacial impedance enables a description of the opticaltransfer for 1D optical metamaterials with the transfer matrix method.This opens up scalable design of one-dimensional multilayered structuresthat include metamaterial layers. We illustrate the approach withthe design of a metamaterial-based antireflection coating for a thin-filmphotodetector.