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We present a set of modeling, sensitivity analysis, and design optimization methods for photonic crystal structures based on Wannier basis field expansion and efficient matrix analysis techniques. We develop the sensitivity analysis technique to analyze both refractive index perturbations and dielectric boundary shift perturbations. Our modeling method is ∼1000× faster than finite-difference time-domain (FDTD) for searching through a large number of similar device designs. We show that our optimization techniques, relying on the efficiency of the modeling and sensitivity analysis methods, enable systematic global and local optimizations of integrated optical components. We show that our design method can be controlled to favor designs without high-energy build-ups, potentially making them more fabrication-error tolerant. We present design examples and verify our designs with FDTD calculations.
Date of Publication: March 2006