Full-vectorial mode solver for anisotropic optical waveguides using multidomain spectral collocation method

A Multidomain Pseudospectral Mode Solver for Optical Waveguide Analysis

“…The idea is mimicking the procedure of obtaining the full-vectorial wave equations from the Maxwell equations, which involves taking the partial derivatives of the first-order system of equations and then conducting algebraic eliminations to yield decoupled second-order wave equations. For the present method, we can write (16) and (17) into their continuous representations, and then take derivatives and conduct algebraic eliminations to obtain a system of second-order equations composed of the transverse magnetic field components and the nontransverse electric field component. Thus, the total number of discrete equations is reduced and the computational work can be reduced.…”

“…Hence, these approaches lead to large systems of equations to be solved, which may consume lots of computational resources and time. An approach for overcoming this issue is designing high-order accurate schemes based on spectral/pseudospectral methods [14]- [17]. Generally, these schemes can compute accurate results by using a coarse mesh, compared to low-order methods.…”

Projection methods for computation of spectral characteristics of weakly guiding optical waveguides

“…Many different numerical techniques are applied for computing eigenmodes of dielectric waveguides [1,2] ; namely, Finite-element, Finite-difference, beam propagation, and spline collocation meth ods, as well as multidomain spectral approach. Of ten the authors concentrate on algorithm's features and physical interpretation of the numerical results rather than on fundamental mathematical aspects including the existence, properties, and distribution of the spectra on the complex plane.…”

Vector Mode Analysis of Optical Waveguides by Quadratic Spline Collocation Method

“…Though the idea of collocation is not new in optics [18][19][20][21][22], the spline collocation based on the piecewise polynomials is rarely examined. Most of the available collocation approaches are based on orthogonal collocation [18][19][20][21][22], which use global basis functions that are nonzero throughout the whole computation domain.…”

“…Most of the available collocation approaches are based on orthogonal collocation [18][19][20][21][22], which use global basis functions that are nonzero throughout the whole computation domain. Such global collocation methods have difficulties in dealing with dielectric interfaces where the field or the first-order derivative is discontinuous.…”