Accurate finite-difference time-domain simulation of anisotropic media by subpixel smoothing.

Finite-difference time-domain methods suffer from reduced accuracy when discretizing discontinuous materials. We previously showed that accuracy can be significantly improved by using subpixel smoothing of the isotropic dielectric function, but only if the smoothing scheme is properly designed. Using recent developments in perturbation theory that were applied to spectral methods, we extend this idea to anisotropic media and demonstrate that the generalized smoothing consistently reduces the errors and even attains second-order convergence with resolution.

Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backward-wave structures.

We demonstrate that the ratio of group to phase velocity has a simple relationship to the orientation of the electromagnetic field. In nondispersive materials, opposite group and phase velocity corresponds to fields that are mostly oriented in the propagation direction. More generally, this relationship (including the case of dispersive and negative-index materials) offers a perspective on the phenomena of backward waves and left-handed media. As an application of this relationship, we demonstrate and explain an irrecoverable failure of perfectly matched layer absorbing boundaries in computer simulations for constant cross-section waveguides with backward-wave modes and suggest an alternative in the form of adiabatic isotropic absorbers.

Zero-group-velocity modes in chalcogenide holey photonic-crystal fibers.

We demonstrate that a holey photonic-crystal fiber with chalcogenide-glass index contrast can be designed to have a complete gap at a propagation constant beta = 0 that also extends into the non-zero beta region. This type of bandgap (previously identified only at index contrasts unattainable in glasses) opens up a regime for guiding zero-group-velocity modes not possible in holey fibers with the more common finger-like gaps originating from beta-->infinity. Such modes could be used to enhance nonlinear and other material interactions, such as for hollow-core fibers in gas-sensor applications.

The failure of perfectly matched layers, and towards their redemption by adiabatic absorbers.

Although perfectly matched layers (PMLs) have been widely used to truncate numerical simulations of electromagnetism and other wave equations, we point out important cases in which a PML fails to be reflectionless even in the limit of infinite resolution. In particular, the underlying coordinate-stretching idea behind PML breaks down in photonic crystals and in other structures where the material is not an analytic function in the direction perpendicular to the boundary, leading to substantial reflections. The alternative is an adiabatic absorber, in which reflections are made negligible by gradually increasing the material absorption at the boundaries, similar to a common strategy to combat discretization reflections in PMLs. We demonstrate the fundamental connection between such reflections and the smoothness of the absorption profile via coupled-mode theory, and show how to obtain higher-order and even exponential vanishing of the reflection with absorber thickness (although further work remains in optimizing the constant factor).