Numerical Modeling of the Transformation of Whispering Gallery Modes of Photonic Crystal Lasers into Lattice Modes

The current paper focuses on the study of 2-D photonic crystal lasers. The effect of changing of the photonic crystal laser structure on the eigenfrequencies, eigenmodes and thresholds of lasing is analyzed numerically. We show that as the capillary diameter of the photonic crystal laser structure increases, the thresholds can decrease. As the capillary diameter increases, some of the whispering gallery modes can be transformed into lattice modes. We demonstrate that at certain frequencies the lattice modes of photonic crystal lasers can have lower thresholds than the whispering gallery modes. Our numerical modeling is based on the reduction of the original lasing eigenvalue problem for the Helmholtz operator on the plane to a nonlinear eigenvalue problem for the system of Muller boundary integral equations and its solution by the Galerkin method with trigonometric basis.