Transmission in the vicinity of the Dirac point in hexagonal photonic crystals

• Published in: Physica. B, Condensed matter Vol. 405; no. 14; pp. 2990 - 2995
• Main Authors: Diem, Marcus, Koschny, Thomas, Soukoulis, C.M.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Kidlington Elsevier B.V 15.07.2010; Elsevier
• Subjects: Channels; Condensed matter; Criteria; Crystal structure; Dirac point; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Law; Mathematical analysis; Optical materials; Optics; Photonic bandgap materials; Photonic crystals; Physics; Scaling; Simulation; Transmittance; Scaling; Dirac point; Transmittance; Photonic crystals; Scattering matrix
• ISSN: 0921-4526; 1873-2135
• DOI: 10.1016/j.physb.2010.01.020

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 Γ 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 = Γ 0 W / L . For T total all waves with a wavevector parallel to the surface, k ∥ = n 2 π / 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.