arXiv subjects
Publications and source records attributed to Dzmitry M. Shyroki.
Arguments for H and B to be considered `axial', or pseudo vectors, are revisited. As a point against, we examine the complex-coordinate method for numerical grid truncation and mode loss analysis proved very successful in computational electrodynamics. This method is not compatible with convention that H and B are axial.
A widespread, intuitive and computationally inexpensive method to analyze light guidance through waveguide bends is by introducing an equivalent straight waveguide with refractive index profile modified to account for actual waveguide bend. Here we revise the commonly used equivalent-index formula, ending up with its simple extension that enables rigorous treatment of one- and two-dimensionally confined, uniformly bent waveguides, including tightly coiled microstructure fibers, curved ridge waveguides and ring microresonators. We also show that such technique is applicable only to waveguides composed of isotropic or uniaxially anisotropic materials, with anisotropy axis directed perpendicular to the curvature plane.
To simulate open boundaries within finite computation domain, real-function coordinate transformation in the framework of generally covariant formulation of Maxwell equations is proposed. The mapping--realized with arctangent function here--has a transparent geometric meaning of pure squeezing of space, is admissible by classical electrodynamics, does not introduce artificially lossy layers (or `lossy coordinates') to absorb outgoing radiation nor leads to non-Maxwellian fields. At the same time, like for anisotropic perfectly matched layers, no modification (except for transformation of material tensors) is needed to existing nearest-neighbor computation schemes, which makes it well suited for parallel computing implementation.
Intermodal interactions displayed through the phenomena of mode coupling and conversion in optical systems are treated by means of the Lindstedt-Poincare perturbation method of strained parameters more widely known in classical quantum mechanics and quantum chemistry as the stationary perturbation technique. The focus here is on the mode conversion at the points of virtual phase matching (otherwise called anticrossings or avoided crossings) associated with the maximum conversion efficiency. The method is shown to provide a convenient tool to deal with intermodal interactions at anticrossings -- interactions induced by any kind of perturbation in dielectric index profile of the waveguide, embracing optical inhomogeneity, magnetization of arbitrary orientation, and nonlinearity. Closed-form analytic expressions are derived for the minimum value of mode mismatch and for the length of complete mode conversion (the coupling length, or the beat length) in generic waveguiding systems exhibiting anticrossings. Demonstrating the effectiveness of the method, these general expressions are further applied to the case of TE -- TM mode conversion in (i) a multilayer gyrotropic waveguide under piecewise-constant, arbitrarily oriented magnetization, and (ii) an optically-inhomogeneous planar dielectric waveguide -- an example which the standard coupled-mode theory fails to describe.
We analyse theoretically for the first time to our knowledge the perfect phase matching of guided TE and TM modes with a multilayer waveguide composed of linear isotropic dielectric materials. Alongside strict investigation into dispersion relations for multilayer systems, we give an explicit qualitative explanation for the phenomenon of mode matching on the basis of the standard one-dimensional homogenization technique, and discuss the minimum number of layers and the refractive index profile for the proposed device scheme. Direct applications of the scheme include polarization-insensitive, intermodal dispersion-free planar propagation, efficient fibre-to-planar waveguide coupling and, potentially, mode filtering. As a self-sufficient result, we present compact analytical expressions for the mode dispersion in a finite, N-period, three-layer dielectric superlattice.