Electromagnetic energy and energy flows in photonic crystals made of arrays of parallel dielectric cylinders

TL;DR

This paper investigates electromagnetic energy flows in 2D photonic crystals made of dielectric cylinders, comparing direct energy flow calculations with group velocity methods across different frequency regimes.

Contribution

It introduces a direct computation approach for optical energy flows and compares it with traditional group velocity calculations in photonic crystals.

Findings

Group velocity can be accurately obtained by appropriate averaging of energy flows.

Discrepancies between averaging schemes and group velocity are analyzed.

Energy flow behavior varies within passing bands and partial bandgaps.

Abstract

We consider the electromagnetic propagation in two-dimensional photonic crystals, formed by parallel dielectric cylinders embedded a uniform medium. The frequency band structure is computed using the standard plane-wave expansion method, and the corresponding eigne-modes are obtained subsequently. The optical flows of the eigen-modes are calculated by a direct computation approach, and several averaging schemes of the energy current are discussed. The results are compared to those obtained by the usual approach that employs the group velocity calculation. We consider both the case in which the frequency lies within passing band and the situation in which the frequency is in the range of a partial bandgap. The agreements and discrepancies between various averaging schemes and the group velocity approach are discussed in detail. The results indicate the group velocity can be obtained by appropriate averaging method.