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Considered here is an efficient technique to compute approximate profiles of solitary wave solutions of fractional Korteweg-de Vries equations. The numerical method is based on a fixed-point iterative algorithm along with extrapolation…
We present a robust iterative technique for solving complex transcendental dispersion equations routinely encountered in integrated optics. Our method especially befits the multilayer dielectric and plasmonic waveguides forming the basis…
The Semi-Analytical Finite Element (SAFE) method is widely used for computing guided wave dispersion curves in waveguides of arbitrary cross-section. Accurate mode tracking across consecutive wavenumber steps remains challenging,…
We consider the Maxwell's equations with perfect electric conductor boundary conditions in three-dimensional unbounded domains which are the union of a bounded resonator and one or several semi-infinite waveguides. We are interested in the…
Waves are all around us--be it in the form of sound, electromagnetic radiation, water waves, or earthquakes. Their study is an important basic tool across engineering and science disciplines. Every wave solver serving the computational…
We analyze and develop numerical methods for time-harmonic wave scattering in metallic waveguide structures of infinite extent. We show that radiation boundary conditions formulated via projectors onto outgoing modes determine the…
We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach…
In our recent work [AIP Adv. 11, 095006], we presented an efficient numerical method to compute dispersions and spatial mode profiles of spin waves propagating in waveguides with translationally invariant equilibrium magnetization. Using a…
In this work a new generalization of the theory of coupled modes for non-periodic structured waveguide is presented. Based on a set of eigen waves of a homogeneous periodic waveguide, a new basis of vector functions is introduced that takes…
We propose a numerical method for finding solitary wave solutions of generalized Korteweg-de Vries equations by solving the nonlinear eigenvalue problem on an unbounded domain. The artificial boundary conditions are obtained to make the…
In this paper, a general methodology to study rigorously discontinuities in open waveguides is presented. It relies on a full vector description given by Maxwell's equations in the framework of the finite element method. The discontinuities…
We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…
The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…
Characteristic modes are formulated using the scattering dyadic, which maps incident plane waves to scattered far fields generated by an object of arbitrary material composition. Numerical construction of the scattering dyadic using…
Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and optics design of nanostructured components. As has been shown in previous benchmarks some of the presently used…
An important problem that arises in many engineering applications is the boundary value problem for ordinary differential equations. There have been many computational methods proposed for dealing with this problem. The convergence of the…
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
We discuss a quartic eigenvalue problem arising in the context of an optical waveguiding problem involving atomically thick 2D materials. The waveguide configuration we consider consists of a gradient-index (spatially dependent) dielectric…
Semi-analytical methods for the modeling of guided waves in structures of constant cross-section lead to frequency-dependent polynomial eigenvalue problems for the wavenumbers and mode shapes. Solving these eigenvalue problems for a range…
We formulate the definition of eigenwaves and associated waves in a nonhomogeneously filled waveguide using the system of eigenvectors and associated vectors of a pencil and prove its double completeness with a finite defect or without a…