- 标题
- 摘要
- 关键词
- 实验方案
- 产品
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Propagation of Electromagnetic Waves in an Open Planar Dielectric Waveguide Filled with a Nonlinear Medium II: TM Waves
摘要： A nonlinear eigenvalue problem on an interval is considered. The nonlinearity in the equation is specified by a nonnegative monotonically increasing function, and the boundary conditions nonlinearly depend both on the sought-for functions and on the spectral parameter. The discrete eigenvalues are defined using an additional (local) condition at one end of the interval. This problem describes the propagation of monochromatic (polarized) electromagnetic TM waves in a planar dielectric waveguide filled with a nonlinear medium. The nonlinearity covers a wide range of laws of nonlinear optics corresponding to self-interaction effects. Results on the solvability of the problem and the properties of the eigenvalues are obtained.
关键词： Maxwell’s equations,nonlinear eigenvalue problem,nonlinear permittivity,nonlinear Sturm–Liouville problem,planar dielectric waveguide,asymptotics of eigenvalues,comparison theorem
更新于2025-09-23 15:21:01
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[IEEE 2019 Photonics & Electromagnetics Research Symposium - Fall (PIERS - Fall) - Xiamen, China (2019.12.17-2019.12.20)] 2019 Photonics & Electromagnetics Research Symposium - Fall (PIERS - Fall) - Efficient Characterization of Topological Photonics Using the Broadband Greena??s Function
摘要： A novel method is developed in this paper to characterize the band diagram and modal ?elds of gyromagnetic photonic crystals that support topolgoical one-way edge states. We exploy an integral equation based method that utilizes the broadband Green’s function as the kernel. The broadband Green’s function is a hybrid representation of the periodic lattice Green’s function that includes an imaginary wavenumber component represented in exponentially decaying spatial series and a reminder in fast converging Floquet plane wave expansions. Special boundary conditions govern the ?elds across the interface of the gyromagnetic scatterers, leading to surface integral equations (SIEs) that involve three components including the pilot ?eld, its normal derivative and its tangential derivative. To reduce the independent number of unknowns, roof-top basis functions and the Garlerkin’s method are used to discretize the SIEs into matrix equations. The broadband Green’s function allows converting the discretized SIEs into a linear eigenvalue problem of a small size. The eigenvalues and eigenvectors of the linear eigenvalue problem are directly related to the band solutions and modal ?elds of the photonic crystal. The proposed approach is an e?ective method to characterize wave interactions with periodic scatterers using integral equations. The solutions of the presented approach are compared against Comsol simulations for various cases to show its accuracy and e?ciency.
关键词： topological photonics,surface integral equations,broadband Green’s function,linear eigenvalue problem,gyromagnetic photonic crystals
更新于2025-09-23 15:21:01
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Eigenwaves in Sommerfeld–Goubau Line: Spectrum
摘要： The problem on normal waves in an inhomogeneous metal-dielectric waveguide structure is reduced to a boundary value problem for the longitudinal components of the electromagnetic field in Sobolev spaces. Nonhomogeneous filling and entering of spectral parameter in transmission conditions leads to necessity of special definition of solution of the problem. We formulate the definition of solution using variational relation. The variational problem is reduced to the study of an operator function. We investigate properties of the operators of the operator function needed for the analysis of its spectral properties. We prove theorem of discrete spectrum and theorem of localization of eigenvalues of the operator-function on complex plane.
关键词： operator-function,inhomogeneous waveguide,Maxwell’s equations,non-linear eigenvalue problem,spectrum,Non-polarized azimuthal-symmetric electromagnetic waves
更新于2025-09-19 17:15:36
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Nonlinear propagation of coupled surface TE and leaky TM electromagnetic waves
摘要： Propagation of the coupled electromagnetic wave, which is a superposition of TE surface and TM leaky waves, in the Goubau line (a perfectly conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium is studied (if the permittivity is linear, the coupled wave does not exist). Nonlinear coupled TE–TM wave is characterised by two (independent) frequencies and two (coupled) propagation constants (propagation constants). The physical problem is reduced to a nonlinear two-parameter transmission eigenvalue problem for Maxwell’s equations. Existence of coupled TE–TM waves is proved. Intervals of localisation of propagation constants are found.
关键词： nonlinear waveguide,Nonlinear coupled TE–TM waves,Kerr nonlinearity,Maxwell’s equations,two-parameter eigenvalue problem,coupled propagation constants
更新于2025-09-16 10:30:52
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Optical solitons and stability analysis with coupled nonlinear schrodinger’s equations having double external potentials
摘要： We consider coupled nonlinear Schrodinger equation (CNLSE) of the Gross-Pitaevskii-type, with linear mixing and nonlinear cross-phase modulation. Motivated by the study of matter waves in Bose-Einstein condensates and multicomponent (vectorial) nonlinear optical systems, we investigate the eigenvalue problem of the CNLSE with double external potentials in a self-defocusig Kerr medium. For this system, we obtain different kinds of wave structures induced by two injected beams, of physical relevance in nonlinear optics and Bose-Einstein condensation. Exact solutions are found by the extended unified method. The linear stability of these solutions is analyzed through the formulation of an eigenvalue problem. The spectral problem is constructed by perturbing the frequency of stationary solutions and by linearizing the resulting equations near the stationary (or steady) states. Our study may simulate experimental work on multiple injected laser beams in a medium with Kerr-type nonlinearity.
关键词： Coupled NLS equation,double external potentials,stability,the eigenvalue problem
更新于2025-09-16 10:30:52
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Slender-body theory for plasmonic resonance
摘要： We develop a slender-body theory for plasmonic resonance of slender metallic nanoparticles, focusing on a general class of axisymmetric geometries with locally paraboloidal tips. We adopt a modal approach where one first solves the plasmonic eigenvalue problem, a geometric spectral problem which governs the surface-plasmon modes of the particle; then, the latter modes are used, in conjunction with spectral-decomposition, to analyse localized-surface-plasmon resonance in the quasi-static limit. We show that the permittivity eigenvalues of the axisymmetric modes are strongly singular in the slenderness parameter, implying widely tunable, high-quality-factor, resonances in the near-infrared regime. For that family of modes, we use matched asymptotics to derive an effective eigenvalue problem, a singular non-local Sturm–Liouville problem, where the lumped one-dimensional eigenfunctions represent axial voltage profiles (or charge line densities). We solve the effective eigenvalue problem in closed form for a prolate spheroid and numerically, by expanding the eigenfunctions in Legendre polynomials, for arbitrarily shaped particles. We apply the theory to plane-wave illumination in order to elucidate the excitation of multiple resonances in the case of non-spheroidal particles.
关键词： slender-body theory,plasmonic eigenvalue problem,localized-surface-plasmon resonance
更新于2025-09-12 10:27:22
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Mathematical and Numerical Modeling of On-Threshold Modes of 2-D Microcavity Lasers with Piercing Holes
摘要： This study considers the mathematical analysis framework aimed at the adequate description of the modes of lasers on the threshold of non-attenuated in time light emission. The lasers are viewed as open dielectric resonators equipped with active regions, ?lled in with gain material. We introduce a generalized complex-frequency eigenvalue problem for such cavities and prove important properties of the spectrum of its eigensolutions. This involves reduction of the problem to the set of the Muller boundary integral equations and their discretization with the Nystrom technique. Embedded into this general framework is the application-oriented lasing eigenvalue problem, where the real emission frequencies and the threshold gain values together form two-component eigenvalues. As an example of on-threshold mode study, we present numerical results related to the two-dimensional laser shaped as an active equilateral triangle with a round piercing hole. It is demonstrated that the threshold of lasing and the directivity of light emission, for each mode, can be e?ciently manipulated with the aid of the size and, especially, the placement of the piercing hole, while the frequency of emission remains largely intact.
关键词： Nystr?m method,active microcavity,eigenvalue problem,boundary integral equation,microcavity laser
更新于2025-09-11 14:15:04
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Electromagnetic field behavior of 3D Maxwell's equations for chiral media
摘要： This article focuses on numerically studying the eigenstructure behavior of generalized eigenvalue problems (GEPs) arising in three dimensional (3D) source-free Maxwell’s equations with magnetoelectric coupling effects which model 3D reciprocal chiral media. It is challenging to solve such a large-scale GEP efficiently. We combine the null-space free method with the inexact shift-invert residual Arnoldi method and MINRES linear solver to solve the GEP with a matrix dimension as large as 5,308,416. The eigenstructure is heavily determined by the chirality parameter γ. We show that all the eigenvalues are real and finite for a small chirality γ. For a critical value γ = γ?, the GEP has 2 × 2 Jordan blocks at infinity eigenvalues. Numerical results demonstrate that when γ increases from γ?, the 2 × 2 Jordan block will first split into a complex conjugate eigenpair, then rapidly collide with the real axis and bifurcate into positive (resonance) and negative eigenvalues with modulus smaller than the other existing positive eigenvalues. The resonance band also exhibits an anticrossing interaction. Moreover, the electric and magnetic fields of the resonance modes are localized inside the structure, with only a slight amount of field leaking into the background (dielectric) material.
关键词： anticrossing eigencurves,Maxwell’s equations,shift-invert residual Arnoldi method,three-dimensional chiral medium,resonance mode,null-space free eigenvalue problem
更新于2025-09-10 09:29:36
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MIXED FINITE ELEMENT METHOD FOR 2D VECTOR MAXWELL'S EIGENVALUE PROBLEM IN ANISOTROPIC MEDIA
摘要： It is well known that the conventional edge element method in solving vector Maxwell’s eigenvalue problem will lead to the presence of nonphysical zero eigenvalues. This paper uses the mixed ?nite element method to suppress the presence of these nonphysical zero eigenvalues for 2D vector Maxwell’s eigenvalue problem in anisotropic media. We introduce a Lagrangian multiplier to deal with the constraint of divergence-free condition. Our method is based on employing the ?rst-order edge element basis functions to expand the electric ?eld and linear nodal element basis functions to expand the Lagrangian multiplier. Our numerical experiments show that this method can successfully remove all nonphysical zero and nonzero eigenvalues. We verify that when the cavity has a connected perfect electric boundary, then there is no physical zero eigenvalue. Otherwise, the number of physical zero eigenvalues is one less than the number of disconnected perfect electric boundaries.
关键词： mixed finite element method,Lagrangian multiplier,2D vector Maxwell’s eigenvalue problem,nonphysical zero eigenvalues,anisotropic media
更新于2025-09-09 09:28:46
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[IEEE 2018 Days on Diffraction (DD) - St.Petersburg, Russia (2018.6.4-2018.6.8)] 2018 Days on Diffraction (DD) - Propagation of electromagnetic waves in a shielded dielectric layer with cubic nonlinearity
摘要： An eigenvalue problem describing propagation of transverse magnetic waves in a shielded dielectric layer with cubic nonlinearity is studied. It is proved that even for small value of the nonlinearity coefficient, the nonlinear problem has infinitely many nonperturbative solutions (eigenvalues and eigenfunctions), whereas the corresponding linear problem always has a finite number of solutions.
关键词： eigenvalue problem,shielded dielectric layer,nonperturbative solutions,cubic nonlinearity,transverse magnetic waves
更新于2025-09-09 09:28:46