The Wannier function approach to photonic crystal circuits

We introduce a novel approach to the accurate and efficient calculation of the optical properties of defect structures embedded in photonic crystals (PCs). This approach is based on an expansion of the electromagnetic field into optimally adapted photonic Wannier functions, which leads to effective lattice models of the PC structures. Calculations for eigenmode frequencies of simple and complex cavities as well as the dispersion relations for straight waveguides agree extremely well with the results from numerically exact supercell calculations. Similarly, calculations of the transmission through various waveguiding structures agree very well with the results of corresponding finite-difference time domain simulations. Besides being substantially more efficient than standard simulation tools, the Wannier function approach offers considerable insight into the nature of defect modes in PCs. With this approach, design studies and accurate simulation of optical anisotropic and non-linear defects as well as detailed investigations of disorder effects in higher-dimensional PCs become accessible. (topical review)