Two-dimensional coupled wave theory for square-lattice photonic-crystal lasers with TM-polarization

Abstract

We present a useful framework based on the coupled-wave theory, through which we can survey the resonant modes of TM polarization in 2D photonic-crystal lasers and understand their properties in detail. Through numerical calculations, we clarify their threshold gains, deviations from the Bragg frequency and field distributions. We find that the lasing mode can be selected by manipulating the hole-filling factor or the boundary reflection.

Coupled Mode Theory of Photonic Crystal Lasers

“…These methods are meant to effectively support the design process of such lasers. They are based on a coupled mode theory ; Vurgaftman & Meyer (2003)) and focused on square and triangular lattice photonic crystals (Koba & Szczepanski (2010); Koba, Szczepanski & Kossek (2011); Koba, Szczepanski & Osuch (2011); Sakai et al (2007;). …”

“…The Sakai et al (2007; works contain a mathematical description and numerical results of the threshold analysis of two-dimensional (2-D) square lattice photonic crystal laser with TM and TE polarization. They introduce general coupled mode relations for a threshold gain, a Bragg frequency deviation and field distributions, and give calculation results for some specific values of coupling coefficients.…”

“…They introduce general coupled mode relations for a threshold gain, a Bragg frequency deviation and field distributions, and give calculation results for some specific values of coupling coefficients. Additionally, in (Sakai et al (2007)) the effect of boundary reflections has been investigated, and it has been shown that the mode properties can be adjusted by changing refractive index or boundary conditions. In Sakai et al (2008) paper, the analytical description of triangular lattice photonic crystal cavity for TE polarization has been given.…”

“…In Sakai et al (2007; works threshold analysis has been conducted for specific values of coupling coefficient and TM polarization for triangular has not been considered.…”

“…In the derivation of Equations 13 and 14 following e.g. (Sakai et al (2007)), we set α ≪ β ≡ 2πε 1/2 0 λ , ε G =0 ≪ ε 0 , and α G ≪ β. In these equations the periodic variation in the refractive index is included as a small perturbation and appears in the third term through the coupling constant κ (G) of the form:…”