Systematic design, optimization, and sensitivity analysis methods for photonic crystal devices

Photonic crystals (PC) are a promising medium for constructing extremely compact integrated optical components. However, the difficulty of modeling PC structures, and the limitations in commonly used electromagnetic simulation and modeling tools, are impeding the research and development of better device designs and new functionalities. In this work, I will develop a set of new modeling methods and design optimization algorithms for PC structures. I will introduce the extended Hamiltonian method for analyzing beam propagation in a non-uniform PC for frequencies within the frequency band. We will describe the method and use it to design beam steering devices. While the method represents one of the most efficient ways of analyzing and designing beam propagation, the shortcomings and limitations of the method lead us to the development of a second class of methods based on Wannier basis field expansion and efficient matrix analysis techniques. We describe the Wannier basis design method, and show that it is ∼1000X faster than the standard finite-difference time domain (FDTD) method for searching through a large number of similar device designs. To enable the optimization process, we develop a sensitivity analysis technique to analyze both refractive index perturbations and dielectric boundary shift perturbations. 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 discuss the advantages of our methods thorough several design examples. We start with a very compact mode separator (8.2 x 13.3 um), which demultiplexes 3 modes of a multimode waveguide into 3 single mode output waveguides. Next, we use our design method complementarily with coupled mode analysis to design a frequency demultiplexer. Finally, using a broadband low crosstalk waveguide intersection design example, we show that our design method can overcome performance barriers caused by limitations in previous modeling tools. 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 verify our method with FDTD calculations. The new method will enable the systematic design of many compact waveguiding devices with complex and novel functionalities.