Transmission in the vicinity of the Dirac point in hexagonal Photonic Crystals

TL;DR

This paper investigates wave transmission near the Dirac point in hexagonal Photonic Crystals, revealing a specific length-dependent scaling law for transmission and establishing criteria for its validity.

Contribution

It demonstrates a scaling law for transmission at the Dirac point in hexagonal Photonic Crystals and relates it to individual channel behavior and maximum length criteria.

Findings

Transmission follows a W/L scaling law at the Dirac point.

No oblique transmission occurs for infinite structures in the Gamma-K direction.

A maximum length criterion for the scaling law is established.

Abstract

We use a scattering matrix approach to simulate the transmission through a hexagonal Photonic Crystal in the vicinity of the Dirac point. If the crystal is oriented so that the propagation direction perpendicular to the surface corresponds to the Gamma-K direction, no oblique transmission is possible for a very long (infinite) structure. For a finite structure with width, W, and length, L, the length dependence of the transmission is given by T_total = Gamma_0 W/L. For T_total all waves with a wavevector parallel to the surface, k_||=n 2pi/W, described by a channel number, n, must be considered. We show the transmission at the Dirac point follows the given scaling law and this scaling law is related to the behavior of the individual channels. This leads to the establishment of a criterion for the maximum length for this scaling behavior when the total transmission reaches a constant value. We also compare this scaling behavior to the results in other frequency regions.