A theoretical study is presented of transmission spectra formation of perfect two dimensional (2D) photonic crystals (PCs) composed of dielectric cylinders arranged parallel to the electromagnetic wave's electric vector in the square lattice. Layer-by-layer transmission spectra are computed on the basis of a Riccati equation for the matrix wave reflection coefficient from a 2D PC slab and Poynting theorem, regarding 2D PCs as a stack of conservative gratings (layers of non-absorptive rods). The lowest (main) and high-order Mie resonances in a single cylinder and the Bragg-like multiple scattering of electromagnetic waves are determined as three mechanisms of formation and frequency position of two opaque bands, with narrow peaks in one of the bands in the transmission spectra of 2D PCs. It is argued that higher-order Mie resonances are responsible for the transmission peaks within the additional band of a perfect crystal. The possibility of opaque band engineering is discussed. In particular, it is demonstrated that filling fraction of volume occupied by cylinders as small as under half a percent does not destroy the opaque band of 2D PCs.

Date Published: 10 June 2006
PDF: 9 pages
Proc. SPIE 6260, Micro- and Nanoelectronics 2005, 62600B (10 June 2006); doi: 10.1117/12.677023

Published in SPIE Proceedings Vol. 6260:
Micro- and Nanoelectronics 2005
Kamil A. Valiev; Alexander A. Orlikovsky, Editor(s)