Density of states of a one-dimensional disordered photonic crystal

An analytic theory of the density of states in one-dimensional disordered photonic crystals is proposed. It is shown that the problem of the density of optical modes can be reduced in the small dielectric contrast approximation to solving a generalized Fokker-Planck equation for the distribution function of the logarithmic derivative of the electric field (the wave phase). The exact analytic solution and density-of-states asymptotics deep in the band gap of the photonic crystal and close to the band gap edge are derived. The results obtained agree well with the empirical relations derived earlier from numerical experiments

Analytic model for the complex effective index of the leaky modes of tube-type anti-resonant hollow core fibers

Abstract Due to their promising applications, hollow-core fibers, in particular, their anti-resonant versions, have recently attracted the attention of the photonics community. Here, we introduce a model that approximates, using the reflection of a wave on a single planar film, modal guidance in tube-type anti-resonant waveguides whose core diameters are large compared to the wavelength. The model yields analytic expressions for the real and imaginary parts of the complex effective index of the leaky modes supported, and is valid in all practically relevant situations, excellently matching all the important dispersion and loss parameters. Essential principles such as the fourth power dependence of the modal loss on the core radius at all wavelengths and the geometry-independent transition refractive index, below which modal discrimination favors the fundamental mode are discussed. As application examples, we use our model for understanding higher-order mode suppression in revolver-type fibers and for uncovering the tuning capabilities associated with nonlinear pulse propagation