An effect of excitation of a transverse magnetic creeping wave when a transverse electric wave crosses the line of the coincidence of propagation constants

Andronov, I. V.; Zaika, D. Yu.; Perel, M. V.

doi:10.1134/s1064226911070035

Cited by 7 publications

(10 citation statements)

References 4 publications

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“…As is evident from (C7), (C8), the expansions are not valid whenever β j , j = 1, 2, degenerate, and they do degenerate in x = 0 according to our assumption (11).…”

Section: Perturbed Eigenproblem In the Vicinity Of The Degeneracy Pointmentioning

confidence: 89%

“…At first time, the equation ( 6) was applied to an anisotropic electromagnetic waveguide in the monography [9], where the operator K was a matrix differential operator with respect to variables transverse to x. Equation ( 6) has been already used by the some of us in several applied problems dealing with asymptotics near degeneracy points of different types: for Maxwell equations in the Earth-ionosphere waveguide [10] (with a non-invertible Γ), Maxwell equations in curvilinear coordinates near the smooth boundary of the convex body [11], the Timoshenko beam equations [12], and elastic wave equations [13]. It was also applied to investigation of liquid crystals [14].…”

mentioning

confidence: 99%

“…This is the method we apply in the present paper. The same method was used in our previous papers [10], [12], [13], [11] (although it was not always written explicitly), where different asymptotic situations for waveguide problems were considered.…”

mentioning

confidence: 99%

“…It is crucial whether there are two independent eigenfunctions at x = 0 (in other words if the restriction of the operator Γ −1 K to invariant subspace corresponding to β 1 (x * ) = β 2 (x * ) is diagonalizable) or an eigenfunction and its associated. Particular cases of the treatment of the degeneracy points with linear independent eigenfunctions were presented in [11,12,34], and ones with linear dependent eigenfunctions in [13]. Here we consider the former case.…”

mentioning

confidence: 99%

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Modes transformation for a Schroedinger type equation: avoided and unavoidable level crossings

Fialkovsky,

Perel

2019

Preprint

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An asymptotic approach for a Schroedinger type equation with a non selfadjoint slowly varying Hamiltonian of a special type is developed. The Hamiltonian is assumed to be the result of a small perturbation of an operator with a twofold degeneracy (turning) point, which can be diagonalized at this point. The non-adiabatic transformation of modes is studied in the case where two small parameters are dependent: the parameter characterizing an order of the perturbation is a square root of the adiabatic parameter. The perturbation of the Hamiltonian produces a close pair of simple degeneracy points. Two regimes of mode transformation for the Schroedinder type equation are identified: avoided crossing of eigenvalues, corresponding to complex degeneracy points, and an explicit unavoidable crossing (with real degeneracy points).Both cases are treated by a method of matched asymptotic expansions in the context of a unifying approach. An asymptotic expansion of the solution near a crossing point containing the parabolic cylinder functions is constructed, and the transition matrix connecting the coefficients of adiabatic modes to the left and to the right of the degeneracy point is derived.Results are illustrated by an example: fermion scattering governed by the Dirac equation.

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“…As is evident from (C7), (C8), the expansions are not valid whenever β j , j = 1, 2, degenerate, and they do degenerate in x = 0 according to our assumption (11).…”

Section: Perturbed Eigenproblem In the Vicinity Of The Degeneracy Pointmentioning

confidence: 89%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Modes transformation for a Schroedinger type equation: avoided and unavoidable level crossings

Fialkovsky,

Perel

2019

Preprint

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show abstract

“…We use a curvilinear system associated with geodesics, such coordinate system is standard for ray method; see, for example, [20]. This coordinate system has been applied recently in electromagnetic problems in [21,22]. Then we rewrite the Maxwell equation in matrix form by analogy with [23].…”

Section: Introductionmentioning

confidence: 99%

Asymptotics of surface plasmons on curved interface

Perel

Zaika

2011

Proceedings of the International Conference Days on Diffraction 2011

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Surface plasmon polaritons (SSP), moving along a smooth curved interface between two isotropic media with slowly varying dielectric permittivities and magnetic permeabilities and supporting SSP, are studied theoretically. Solutions of Maxwell equations are investigated within a small wavelength limit in the boundary layer of the wavelength order near the surface. An explicit asymptotic formula for an EM wave traveling along geodesics on the surface is obtained. An exponential factor reflects the distinction between the planar and curved cases. The curvature-dependent correction term in the exponent demonstrates a strong dependence on the transverse curvature and a weak dependence on the longitudinal curvature. The closer the parameters to the resonance case, the more pronounced this tendency. It is found that the attenuation of the SPP in the case of lossy media may be reduced by changing the curvature. If the signs of the magnetic permeability of the medium on both sides of the interface are opposite, the surface magnetic plasmon polariton may propagate. Its short-wavelength asymptotics is found.

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Mode transformation for a Schrödinger type equation: Avoided and unavoidable level crossings

Fialkovsky

Perel

2020

Journal of Mathematical Physics

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Methods elaborated in quantum mechanics for the Landau–Zener problem are generalized to study the non-adiabatic transitions in a wide class of problems of wave propagation, in particular in the waveguide problems. If the properties of the waveguide slowly vary along its axis and the phase velocities of two modes have a degeneracy point or are almost degenerate near some point, the transformation of modes may occur. The conditions are formulated under which we can find formal asymptotic expansions of modes outside the vicinity of the degeneracy point and write out explicitly the transition matrix. The starting point is rewriting the governing equations in the form of the Schrödinger type equation. The Hamiltonian is assumed to be the result of a small perturbation of an operator with a degeneracy point of the crossing types of two eigenvalues. The perturbation of the Hamiltonian produces a close pair of simple degeneracy points. Two regimes of mode transformation for the Schrödinger type equation are identified: avoided crossing of eigenvalues (corresponding to complex degeneracy points) and an explicit unavoidable crossing (with real degeneracy points).

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An effect of excitation of a transverse magnetic creeping wave when a transverse electric wave crosses the line of the coincidence of propagation constants

Cited by 7 publications

References 4 publications

Modes transformation for a Schroedinger type equation: avoided and unavoidable level crossings

Modes transformation for a Schroedinger type equation: avoided and unavoidable level crossings

Asymptotics of surface plasmons on curved interface

Mode transformation for a Schrödinger type equation: Avoided and unavoidable level crossings

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