2 × 2 anisotropic transfer matrix approach for optical propagation in uniaxial transmission filter structures

Multi-layered metamaterial structures show promise in a wide variety of optical applications such as superlenses, electromagnetic cloaking, tunable filters, sensors, and spatial light modulators. Optical transmission analysis of multilayer metallo-dielectric stacks with overall thickness less than the wavelength of light can be modeled using effective medium theory and the Berreman matrix method. For multilayer anisotropic stacks of arbitrary thickness, a rigorous 4 × 4 transfer matrix embodiment is typically used. In this work, a 2 × 2 anisotropic transfer matrix method is developed to analyze optical propagation through multilayer uniaxial stacks of arbitrary thicknesses. Optical transmission of a multilayer silver-zinc oxide stack deposited on a quartz substrate is modeled with this 2 × 2 anisotropic transfer matrix method and reconciled with experimental observations. Results indicate that this numerical approach is applicable to in situ assessment of the complex refractive indices of constituent metal and dielectric layers. Additionally, the anisotropic 2 × 2 transfer matrix method enables the possibility of modeling the transmission of the same metallo-dielectric structure deposited on an electro-optic, uniaxial substrate. Simulation results predict that adjusting the bias field across the substrate results in an electrically tunable transmission filter.