ABSTRACT
This chapter analyzes a sharp 90° bend in proposed photonic crystals (PhC). It shows that optimization may render some parts of the PhC very critical or sensitive, which causes problems for the fabrication and may be attractive at the same time when one is interested in tuning or switching. Because few useful design rules are available, the analysis and optimization of PhC structures requires efficient, accurate, and reliable simulations. The chapter presents several techniques based on the multiple multipole program (MMP) for the simulation and optimization of such structures. It highlights more powerful computers and further improvements of the numerical methods will allow people to find various promising structures for ultradense integrated optics based on the concept of PhCs. The chapter outlines the basics of the MMP, which may be considered a semianalytic method. It also shows how MMP can handle all important problems associated with PhC simulations, namely periodic symmetries, eigenvalue problems, and waveguide discontinuity problems.
