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 higherdimensional PCs become accessible.

We demonstrate that the infiltration of individual pores of certain two-dimensional photonic crystals with liquid crystals and (or) polymers provides an efficient platform for the realization of integrated photonic crystal circuitry. As an illustration of this principle, we present designs for monomode photonic crystal wave-guides and certain functional elements, such as waveguide bends, beam splitters, and waveguide intersections. These devices exhibit very low reflection over broad frequency ranges. In addition, we discuss the inherent tunability of these devices that originates in the tunability of the infiltrated material.

We outline a theoretical framework that allows qualitative as well as quantitative analysis of the optical properties of Photonic Crystals (PCs) and which is derived from solid state theoretical concepts. Starting from photonic bandstructure computations which allow us to obtain dispersion relations and associated Bloch functions, we show how related physical quantities such as densities of states and group velocities can be calculated. In addition, defect structures embedded in PCs can be efficiently treated with the help of photonic Wannier functions that are derived from photonic Bloch functions by means of a lattice Fourier transform. Nonlinear PCs may be investigated by an appropriate multi‐scale analysis utilizing Bloch functions as carrier waves together with an adaptation of k · p‐perturbation theory. This leads to a natural generalization of the slowly varying envelope approximation to the case of nonlinear wave propagation in PCs.

No abstract

No abstract