Efficient Numerical Method for Analyzing Coupling Structures of Photonic Crystal Waveguides

Efficient coupling of light into and out of photonic crystal (PhC) waveguides is important for applications in photonic integrated circuits. An efficient numerical method is presented for analyzing two-dimensional structures that connect PhC waveguides with conventional waveguides (or free space). The method relies on rigorous boundary conditions for terminating both types of waveguides to obtain small computation domains. These boundary conditions are derived from square root operators for conventional waveguides and Bloch mode expansions in PhC waveguides.