Optimization of a single defect photonic crystal laser cavity

Abstract

Using nonlinear programing and the geometry projection method, the quality factor of the monopole mode of a single defect photonic crystal laser cavity is improved from 38 000 to 87 000. Beginning with a design that considers only round air holes shifted away from the cavity, the radius of the nearest neighbor and of the surrounding air holes are optimized while satisfying a constraint on the resonant frequency. The total reflectivity of the photonic crystal laser structure is then defined, and it is shown that this quantity correlates strongly to the total quality factor. The reflectivity of the structure is improved by altering the shape of the holes immediately surrounding the cavity, thus leading to an improvement in quality factor. The geometry projection method is used to define the shape of the holes and the finite element and adjoint methods are used to compute the objective function and sensitivities required by the optimizer. This work demonstrates one way to optimize the Q factor of a photonic crystal laser by altering the hole shape.