- 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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Wave Polarization Analyzed by Singular Value Decomposition of the Spectral Matrix in the Presence of Noise
摘要： Analysis of wave polarization provides wave propagation parameters and enables an identification of modes in space plasmas. It is based on measurements of several components of fluctuating electromagnetic fields. This technique has become a conventional part of modern instrumentation onboard scientific spacecraft. A definition of the degree of polarization can be reduced to a very basic form, i.e., the ratio of a signal’s polarized power to its total power. However, this simple definition can have several different realizations which depend mainly on the underlying assumptions about separating the polarized (coherent) part from the unpolarized part (noise). After reviewing polarization of a plane wave in two and three dimensions, we examine the singular value decomposition technique for a complex spectral matrix as well as for a real spectral matrix. The meaning of singular values is explained, and we show to what extent the singular values are able to contribute to a separation between polarized signal and noise. Finally, our theoretical findings are verified with synthetic data as well as with whistler-mode chorus wave observations from the THEMIS spacecraft.
关键词： Singular value decomposition,Wave normal vector,Hermitian spectral matrix,Spectral averaging,Stokes parameters,Degree of polarization,Planarity,Singular values,Ellipticity,Plane wave,Eigenvalues,Polarization analysis
更新于2025-09-19 17:15:36
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Asymptotics of Eigenvalues in Spectral Gaps of Periodic Waveguides with Small Singular Perturbations
摘要： The asymptotics of eigenvalues appearing near the lower edge of a spectral gap of the Dirichlet problem is studied for the Laplace operator in a d-dimensional periodic waveguide with a singular perturbation of the boundary by creating a hole with a small diameter ε. Several versions of the structure of the gap edge are considered. As usual, the asymptotic formulas are di?erent in the cases d ≥ 3 and d = 2, where the eigenvalues occur at distances O(ε2(d?2)) or O(ε2d) and O(| ln ε|?2) or O(ε4), respectively, from the gap edge. Other types of singular perturbation of the waveguide surface and other types of boundary conditions are discussed, which provide the appearance of eigenvalues near both edges of one or several gaps. Bibliography: 51 titles.
关键词： eigenvalues,spectral gaps,periodic waveguides,asymptotics,singular perturbations
更新于2025-09-16 10:30:52
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Finite difference time domain simulation of arbitrary shapes quantum dots
摘要： Utilizing the finite difference time domain (FDTD) method, energy eigenvalues of spherical, cylindrical, pyramidal and cone-like quantum dots are calculated. To do this, by the imaginary time transformation, we transform the schr?dinger equation into a diffusion equation. Then, the FDTD algorithm is hired to solve this equation. We calculate four lowest energy eigenvalues of these QDs and then compared the simulation results with analytical ones. Our results clearly show that simulation results are in very good agreement with analytical results. Therefore, we can use the FDTD method to find accurate results for the Schr?dinger equation.
关键词： Finite difference time domain,Quantum dots,Energy eigenvalues,Schr?dinger equation
更新于2025-09-12 10:27:22
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[IEEE 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Munich, Germany (2019.6.23-2019.6.27)] 2019 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC) - Statistical Properties of Phase and Eigenvalues of Nonlinear Fourier Transform of Second Order Solitons
摘要： Due to the inherently nonlinear nature of optical fibres, the increased demand for transmission capacity means that fibre optic communication systems will reach a limit, known as the Linear Capacity Limit. A radically new solution has received significant attention in the past few years, which is based on Nonlinear Fourier Transform (NFT). Under NFT a signal q(t) in time domain transforms into a continuous, qc(λ), and a discrete, qd(λk), complex spectral part, with continuous and discrete eigenvalues λ, and λk, respectively. Considering only multisolitons (a class of optical signals that have discrete NFT eigenvalues), it is well-known that 1) complex eigenvalues λk are invariant, and 2) the spectral part propagates as: (cid:3031)((cid:1878)) = |(cid:1869)(cid:3038) (cid:1869)(cid:3038) (cid:3031)(0)|(cid:1857)(cid:3037)(cid:2957)((cid:3053)); Φ((cid:1852)) = ∠(cid:1869)(cid:3038) (cid:3031)(0) ? 4(cid:2019)(cid:3038) (cid:2870) (cid:1878), where |(cid:1869)(cid:3038) (cid:3031)(0)| and ∠(cid:1869)(cid:3038) (cid:3031)(0) are the initial spectral amplitude and phase associated with the eigenvalue λk, respectively. In the discrete NFT domain, QPSK modulation has been proposed to encode data on the phase of the NFT spectral components qd(λk). For efficient encoding/decoding of the proposed modulation schemes, it is crucial to have knowledge of NFT noise perturbation on spectral phases and eigenvalues. There are limited reports on correlations among eigenvalues in multi-soliton systems and correlation between eigenvalues and their corresponding phases. However, there is no report with detailed analysis of correlation properties among NFT parameters of multi-soliton signals as a function of initial signal parameters. Here, we investigate correlations of the discrete spectra components in a two-eigenvalue system related to their relative NFT phase differences and distinguish a correlation pattern, which reaches extreme values at a NFT phase difference of π. We show this pattern to be unrelated to the choice of eigenvalues nor their spectral amplitude or constant phase offsets. We show that not only the eigenvalues but also the phases of signals in NFT domain are correlated, approaching a maxima at a NFT phase differences of π. We consider second-order solitons with different eigenvalue pairs, where for each of them, 129 symbols have been defined in the NFT domain with varying initial NFT phase differences Φ1,2=∠qd 2 between 0 and 2π, representing Φ1,2 on discrete positions of propagation over z. For every symbol, 1500 copies have been produced and exposed to white Gaussian noise. Using a combination of the fast inverse NFT algorithm and bidirectional NFT algorithm, each signal is translated into time domain, introduced to Gaussian noise, and translated back into NFT domain. The resulting scattering data has been used to estimate the eigenvalues λ1,2 and corresponding spectral components qd 1,2. The ellipticity (defined as the relative difference of principal axes of the scattering cloud) as a function of phase difference for a range of eigenvalue pairs, Fig.1 a,b, shows almost an ellipse at a phase difference of π and a circle at π/2. While both (Im((cid:79)1),Im((cid:79)2)) and (∠qd 2) are highly correlated at the phase difference of π, |Correlation coefficient|≈1, they are negative of each other, where its reason is under investigation. These correlation properties help to gain deeper physical insight of noise properties of signals in NFT domain, which is crucial for developing efficient NFT communication schemes.
关键词： phase,eigenvalues,Nonlinear Fourier Transform,correlation,solitons
更新于2025-09-11 14:15:04
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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