Numerical scheme to determine the photonic properties of tunable crystals

摘要

The dielectric distribution and polarizability of certain materials, e.g., the liquid dielectrics, change in response to the external electromagnetic field. Since their photonic properties can be adjusted by controlling the applied field, these materials can be used to construct tunable photonic band gap crystals. Due to recent advances in tunable photonic bandgap materials technology, it has become necessary to determine the properties of the propagating fields accurately. Numerical methods currently in use are quite cumbersome and place limits on the accuracy of the solutions. A numerical scheme is developed here by expressing the solution in the framework of the Feynman path integral formulation of quantum mechanics. The formulation describes the evolution of the solution in terms of a propagator, which can be determined by the method of fast Fourier transforms. The resulting numerical scheme is more efficient and reliable than other similar methods.