Semi-analytic method for slow light photonic crystal waveguide design

TL;DR

This paper introduces a semi-analytic approach to efficiently compute dispersion and group velocity in photonic crystal waveguides, enabling rapid exploration of design parameters for slow light applications.

Contribution

The method models waveguides as homogeneous strips with photonic crystal mirrors, incorporating multiple diffraction orders for accurate dispersion calculations.

Findings

Efficient computation of dispersion curves and group velocities.

Ability to scan large parameter spaces rapidly.

Discovery of novel waveguide solutions.

Abstract

We present a semi-analytic method to calculate the dispersion curves and the group velocity of photonic crystal waveguide modes in two-dimensional geometries. We model the waveguide as a homogenous strip, surrounded by photonic crystal acting as diffracting mirrors. Following conventional guided-wave optics, the properties of the photonic crystal waveguide may be calculated from the phase upon propagation over the strip and the phase upon reflection. The cases of interest require a theory including the specular order and one other diffracted reflected order. The computational advantages let us scan a large parameter space, allowing us to find novel types of solutions.