Efficient and quantitative analysis of photon density of states for two-dimensional photonic crystals with omnidirectional light propagation

Abstract

Omnidirectional light propagation in two-dimensional (2D) photonic crystals (PCs) has been investigated by extending the formerly developed 2D finite element analysis (FEA) of in-plane light propagation in which the corresponding band structure (BS) and photon density of states (PDOS) of 2D PCs with complex geometry configurations had been calculated more accurately by using an adaptive FEA in real space for both the transverse electric (TE) and transverse magnetic (TM) modes. In this work, by adopting a waveguiding theory under the consideration of translational symmetry, the omnidirectional PDOS corresponding to both the radiative and evanescent waves can be calculated accurately and efficiently based on the in-plane dispersion relations of both TE and TM modes within the irreducible Brillouin zone. We demonstrate that the complete band gaps shown by previous work considering only the radiative modes will be closed by including the contributions of the evanescent modes. These results are of general importance and relevance to the spontaneous emission by an atom or to dipole radiation in 2D periodic structures. In addition, it may serve as an efficient approach to identifying the existence of a complete photonic band gap in a 2D PC instead of using time-consuming 3D BS calculations. * mclin@hanyang.ac.kr; Also at the Institute for Pulsed Power and Microwave Technology, Karlsruhe Institute of Technology, Germany as a visiting scholar.

Quantitative Analysis of Photon Density of States for One-Dimensional Photonic Crystals in a Rectangular Waveguide

“…In this work, light propagation in 1D PCs enclosed in a rectangular waveguide or quasi-1D PCs is investigated in order to achieve a complete PBG while avoiding the difficulty in fabricating 3D PCs. This work complements two previous articles [15,16] that quantitatively analyzed omnidirectional light propagation in 1D and 2D PCs, respectively, both showing that a complete PBG cannot exist if an evanescent wave propagation is involved. The transfer matrix method is extended to study the transmittance of the quasi-1D PCs for both TE and TM polarization modes [34].…”

“…This indicates that a tremendous computational effort is still needed to find a complete PBG in spite of the approach with a closed form developed is very efficient for the quasi-1D PCs. A better way to identify PBGs more accurately and efficiently is to perform the BS calculation and further compute the PDOS [15,16]. Figure 4 shows the band structures of (a) TE 10 and (b) TM 11 modes for the quasi-1D PC with the dielectric constants ε 1 = 3.8, ε 2 = 1 and the thicknesses t 1 = 1.00 mm, t 2 = 3.30 mm, corresponding to the case presented in Figures 2 and 3 in a black solid line with a filling ratio of 23.26%.…”

“…It was proposed that the emission of EM radiation can be modified by the environment [6,7]. Several environments such as metallic cavities [8], dielectric cavities [9], superlattices [10][11][12][13][14][15], and 2D PCs [16] have been studied. The environmental effects have been described by the photon density of states (PDOS), which is related to the transition rate of the Fermi golden rule.…”