Analysis of Bragg gratings for long-range surface plasmon polaritons using the bidirectional beam propagation method based on scattering operators

摘要

For realization of highly integrated optical circuits, various metallic nanostructures supporting the propagation of surface plasmon polaritons have been extensively studied experimentally and theoretically in recent years. This paper reports on the development of a numerically stable and accurate finite-difference-based bidirectional beam propagation method (FD-BiBPM) for analyzing piecewise z-invariant plasmonic structures. Our method is developed based on the scattering operators. The adoption of complex coefficient rational approximations to the square root operator allows to correctly model the propagation of evanescent modes excited at discontinuity interfaces. In view of the large index contrast at metal-dielectric interfaces, a fourth-order accurate finite difference formulation for discretization is incorporated to the present method and its fine treatment of these interfaces guarantees accuracy. By using the present method, the reflection and transmission spectra of the Bragg gratings consisting of a thin metal film embedded in dielectric medium and an array of equidistant metal ridges on each side of the film are calculated. The good agreement of our results with the previously reported simulations illustrates the potential of the newly developed FD-BiBPM for the analysis of long-range surface plasmon polariton (LRSPP) waves guided along the described Bragg gratings.