Optical simulation of coupled defect cavities in photonic crystal vertical-cavity surface-emitting lasers

Abstract

We simulated the cold-cavity optical modes of coupled defect cavities in photonic crystal (PhC) vertical-cavity surface-emitting lasers (VCSELs). Holes were etched into the top distributed Bragg reflector of the COST benchmark structure in hexagonal pattern, leaving 2×1 or 2×2 positions intact. A lattice constant of 4 μm was selected, the hole diameter-to-lattice-constant ratio was varied from 0.5 to 0.7 outside the defect region and from 0.15 to 0.7 between the cavities. We used finite volume method to discretize the scalar Helmholtz equation, and finite element method to solve the vectorial Helmholtz equation, both in three dimensions. Prism elements were selected that fit the complicated contours of the PhC-VCSEL. In-phase and out-of-phase couplings were specified with different symmetry boundary conditions. The complex eigenvalues and optical field distributions were obtained with an in-house developed iterative algorithm. The real part of the eigenvalue determined the wavelength, its imaginary part was proportional to the cold-cavity modal loss. In-phase and out-of-phase coupled modes possessed almost equal properties when all holes had relatively large diameters, indicating uncoupled behavior. For a narrower hole between the defect cavities, the in-phase coupled mode exhibited slightly larger mode area than its out-of-phase counterpart due to its extending tails, but also showed considerably larger optical loss. This predicted out-of-phase operation. If one etched very small holes into the coupling region of the 2×2 PhC-VCSEL array, an additional lobe appeared between the holes, which resulted in enhanced overlap with the gain region. This confirmed in-phase operation.