Demonstration of systematic photonic crystal device design and optimization by low-rank adjustments: an extremely compact mode separator.

We present a powerful design and optimization method for devices in a photonic crystal. The method is based on a Wannier basis field expansion and efficient matrix analysis techniques for searching through a vast number of designs. The method permits the design of many compact optical devices with complex and novel functions. We present a design example of a very compact mode separator that is 8.2 microm x 13.3 microm in size that demultiplexes the three modes of an input photonic crystal multimode waveguide into three single-mode output waveguides. We verify the method with finite-difference time-domain calculations.