Transfer Matrix Method-Compatible Model for Metamaterial Stacks

Mean-field theory-based effective refractive index models are widely used to design optical metamaterials and interpret their optical properties. However, emerging applications where metamaterials are embedded into layered device architectures require a detailed consideration of the metamaterial's dispersive properties and interfacial boundary conditions, which are beyond the scope of the mean-field theory for homogeneous bulk media. Here, we describe an approach to calculate the optical transfer function for one-dimensional optical metamaterials that includes the dispersive properties of the effective index as well as the effective interfacial impedance. We address the boundary conditions at a metamaterial interface by a complex-valued effective interfacial impedance. Combined with the effective refractive index, the effective interfacial impedance enables a description of the optical transfer for 1D optical metamaterials with the transfer matrix method. This opens up scalable design of one-dimensional multilayered structures that include metamaterial layers. We illustrate the approach with the design of a metamaterial-based antireflection coating for a thin-film photodetector.