Quantifying bound and leaky states of resonant optical lattices by Rytov-equivalent homogeneous waveguides

The properties of periodic optical lattices are generally investigated with rigorous numerical methods. For physical insight and understanding of the complex processes underlying observed spectra, simple analytical models are needed. Accordingly, we show that by applying full Rytov effective-medium formalisms, the bound and leaky states of resonant photonic lattices can be quantified with high precision. Thus, all key properties are embodied in Rytov-equivalent homogeneous waveguides. The symmetric effective-medium theory (EMT) model quantifies rigorously computed guided-mode resonance (GMR) reflectance loci defining the leaky states. The asymmetric EMT formula similarly quantifies the bound state in the continuum (BIC) loci. Even with the period and wavelength on similar scales, the analytical EMT refractive index solutions agree exactly with rigorous solutions. We apply the Rytov formulas to explain the resonant leaky band structure including appearance of GMR and BIC states as well as band transitions and band closure points. The wavenumbers of the equivalent waveguides represent the BIC embedded eigenvalues as quantified here.