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 $8.2 \mathit{\mu }\mathrm{m}\times 13.3 \mathit{\mu }\mathrm{m}$ 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.