Simple binary stack analysis via a phase space transformation

A simple phase-based technique is presented for the analysis and design of binary layered optical media operating at effective refractive indices below the lowest index of the layers - relevant for devices such as hollow-core Bragg fiber and on-chip waveguides, radial Bragg resonators, VCSEL cavities, multilayer mirrors or antireflection coatings. For a given binary stack of layers, the phase accumulation in each layer type, rather than the frequency and effective index of the incident wave, are considered as the fundamental system parameters. Applications to Bloch wave analysis are given.