Related papers: Solutions to Maxwell's Equations using Spheroidal …
Usual Gaussian beams are particular scalar solutions to the paraxial Helmholtz equation, which neglect the vector nature of light. In order to overcome this inconvenience, Simon et al. (J. Opt. Soc. Am. A 1986, 3, 536-540) found a paraxial…
This paper presents a new approach for the computation of eigenvalues of the generalized spheroidal wave equations. The novelty of the present method is in the use of the analytical derivatives of the eigenvalues to minimize losses in…
We derive and interpret solutions of time-harmonic Maxwell's equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g. graphene sheet, lying between two unbounded isotropic and non-magnetic media.…
We prove Strichartz estimates for solutions to Maxwell equations in three dimensions with rough permittivities, which have less than three different eigenvalues. To this end, Maxwell equations are conjugated to half-wave equations in phase…
We present the applications of variational--wavelet approach for computing multiresolution/multiscale representation for solution of some approximations of Vlasov-Maxwell equations.
We prove that spatial Kerr solitons, usually obtained in the frame of nonlinear Schroedinger equation valid in the paraxial approximation, can be found in a generalized form as exact solutions of Maxwell's equations. In particular, they are…
In this paper we study the eigenvalues of the angular spheroidal wave equation and its generalization, the Coulomb spheroidal wave equation. An associated differential system and a formula for the connection coefficients between the various…
In this paper, we provide an attractive analytic solution for Maxwell's equation for a given set of smooth periodic functions as initial condition with demonstrative examples. The complexity of the solution is comparable to the Fourier…
In a previous paper of ours [Phys. Rev. E64 (2001) 066603, e-print physics/0001039] we have shown localized (non-evanescent) solutions to Maxwell equations to exist, which propagate without distortion with Superluminal speed along…
An asymptotic investigation of monochromatic electromagnetic fields in a layered periodic medium is carried out under the assumption that the wave frequency is close to the frequency of a stationary point of the dispersion surface. We find…
We consider the evolution of ultra-short optical pulses in linear and nonlinear media. For the linear case, we first show that the initial-boundary value problem for Maxwell's equations in which a pulse is injected into a quiescent medium…
The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the…
We present the applications of variational-wavelet approach for computing multiresolution/multiscale representation for solution of some approximations of Vlasov-Maxwell-Poisson equations.
It is shown that three-dimensional nonparaxial beams are described by the oblate spheroidal exact solutions of the Helmholtz equation. For the first time, their beam behaviour is investigated and their corresponding parameters are defined.…
Two-dimensional periodic surface waves propagating under the combined influence of gravity and surface tension on water of finite depth are considered. Within the framework of small-amplitude waves, we find the exact solutions of the…
The spheroidal wave functions are investigated in the case m=1. The integral equation is obtained for them. For the two kinds of eigenvalues in the differential and corresponding integral equations, the relation between them are given…
It is now wellknown that Maxwell equations admit of wavelet-type solutions endowed with arbitrary group-velocities (0 < v_g < infinity). Some of them, which are rigidly moving and have been called localized solutions, attracted large…
The Duffin-Kemmer form of massless vector field (Maxwell field) is extended to the case of arbitrary pseudo-Riemannian space-time in accordance with the tetrad recipe of Tetrode-Weyl-Fock-Ivanenko. In this approach, the Maxwell equations…
In this paper we set forth new exact analytical Superluminal localized solutions to the wave equation for arbitrary frequencies and adjustable bandwidth. The formulation presented here is rather simple, and its results can be expressed in…
The discussion of our recent work concerning the vector solution of boundary-value problems in electromagnetism is extended to the case of no azimuthal symmetry by means of the spin-weighted spherical harmonics.