Transfer Matrix Method-Compatible Model for Metamaterial Stacks

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.

Automated summary

Mean-field theory-based models are commonly used for designing optical metamaterials. However, for applications involving layered device architectures, the dispersive properties and interfacial boundary conditions of the metamaterials need to be considered. In this study, we propose a method to calculate the optical transfer function for one-dimensional optical metamaterials, taking into account the dispersive properties of the effective index and the effective interfacial impedance.