Arbitrary-order three-point finite difference method for the modal analysis of chiral waveguides

A three-point finite difference method with an arbitrary order of accuracy is proposed for the modal analysis of chiral planar waveguides. The elaborate application of a nonuniform grid, compact finite difference technique, and boundary conditions results in an efficient, easily implemented, and versatile tool for the modal analysis of chiral planar waveguides with an arbitrarily discontinuous profile of permittivity, permeability, and chirality. In particular, this method efficiently resolves the fine structures in plasmon and photonic crystal waveguides. For the test model of a chiral-metallic plasmon waveguide, stable convergence up to a sixteenth order of accuracy can be obtained, which produces a relative error on the effective index that approaches the machine precision with only eighty grid points.

Efficient full-vectorial modal analysis based on immersed interface method for dielectric chiral optical fibers

This paper presents the application of an immersed interface method in efficient modal analysis of dielectric chiral optical fibers. Under the easily implemented finite-difference framework, the second- and fourth-order accuracy formulations are developed, which in principle are applicable for automatically computing various types of modes in dielectric chiral optical fibers with an arbitrary, electromagnetic parameters piecewise constant profile. To validate the developed formulations, numerical examples are given for the guided, leaky, and surface modes in dielectric chiral step-profile and Bragg fibers.

Radiation in bent asymmetric coupled waveguides

A numerical study of the radiation in coupled bent waveguides is presented. Such arrangements of curved waveguides in reduced radiation-loss configurations can be used to enhance the quality factor of integrated microresonators. 3D full vector computations of the complex modal fields (and propagation constants) and the transient propagation effects have been performed. The results obtained agree qualitatively with former 2D finite-difference time-domain (FDTD) analyses. At the same time, the calculations presented meet the accuracy requirements for the design of practical implementations that are unattainable with 2D approaches.

Arbitrary truncation order three-point finite difference method for optical waveguides with stepwise refractive index discontinuities

An exact finite difference (FD) representation of the second-order derivative on three nodes is presented and used to obtain an FD algorithm that allows achieving an arbitrary truncation order. The FD weights are calculated analytically using the series that expresses the field value at a given FD node in terms of the field value and its derivatives at a neighboring node, when a stepwise discontinuity in the refractive index distribution is present between the nodes. The results obtained confirm that the proposed algorithm is accurate, efficient, and achieves the predicted improved performance.