| Photonic crystals (PhCs) have been of great interest in a variety of fields in the past decade due to their great capability for manipulating photons in a manner similar to how electrons are controlled in a semiconductor material. In particular, PhCs are expected to revolutionize such fields as optical signal processing and optical communication by allowing the development of novel optical devices for high-density photonic integrated circuits (PICs). The development of PhC devices will be greatly accelerated by systematic designs. In this dissertation, I developed several procedures to systematically engineer the dispersion properties of PhCs. Using these procedures, I presented a variety of novel applications intended for use in future high-density PICs. These were achieved through efficient implementations of the finite-difference time-domain (FDTD) method and the plane wave method (PWM). Specifically, by combining these efficient electromagnetic tools with the direct binary search (DBS) method or simulated annealing (SA), I developed very efficient synthesis processes and used them to optimize absolute photonic band gaps (PBGs) of PhC structures and a beam steering device based on a PhC with PBG(s). I also presented another novel PhC device working in PBG, namely a PhC ring drop filter. On the other hand, I utilized the FDTD method and the PWM to shape dispersion surfaces and/or contours of PhC structures for manipulating light propagation. In particular, I engineered PhCs with square- and circle-shaped equi-frequency contours (EFCs) and presented several applications using these two unique PhCs. These applications include optical beam routing, coupling and splitting a wide beam into multiple narrow self-guiding beams, a unidirectional emitter, and an in-plane lens coupler. I also explored negative refraction and left-handed behavior in PhCs and presented a flat lens using a PhC exhibiting negative refraction and left-handed behavior. |
