arXiv subjects

Alexander B. Samokhin

Publications and source records attributed to Alexander B. Samokhin.

5 recordsLinked to original sources

arXiv2006

Essential state of the electromagnetic field and the double-slit experiment

A new class of generalized solutions related to the essential spectrum of linear Maxwell's equations is presented. The essential modes are given in terms of normalized singular Weyl's sequences, whose square represents Dirac's delta functions in spatial and angular frequency domains. The action integral associated with essential modes is well-defined. We claim that these modes represent the collapsed state of the electromagnetic field and, with some additional assumptions on the conservation of action, are suitable for describing the double-slit experiment in accordance with the orthodox point of view.

quant-ph↗

arXiv2006

Collapsing Solutions of the Maxwell Equations

We derive the essential space-time spectrum of the Maxwell equations in linear isotropic inhomogeneous media together with the corresponding essential modes. These modes represent the collapse of the electromagnetic field into a single point in space at a single angular frequency. The location and frequency of the essential mode are random variables obeying the Born statistical postulate.

physics.class-ph↗

arXiv2006

Singular Modes of the Electromagnetic Field

We show that the mode corresponding to the point of essential spectrum of the electromagnetic scattering operator is a vector-valued distribution representing the square root of the three-dimensional Dirac's delta function. An explicit expression for this singular mode in terms of the Weyl sequence is provided and analyzed. An essential resonance thus leads to a perfect localization (confinement) of the electromagnetic field, which in practice, however, may result in complete absorption.

physics.class-ph↗

arXiv2005

Classification of electromagnetic resonances in finite inhomogeneous three-dimensional structures

We present a simple and unified classification of macroscopic electromagnetic resonances in finite arbitrarily inhomogeneous isotropic dielectric 3D structures situated in free space. By observing the complex-plane dynamics of the spatial spectrum of the volume integral operator as a function of angular frequency and constitutive parameters we identify and generalize all the usual resonances, including complex plasmons, real laser resonances in media with gain, and real quasi-static resonances in media with negative permittivity and gain.

physics.class-ph↗

arXiv2005

Spectrum of the volume integral operator of electromagnetic scattering

Spectrum of the volume integral operator of the three-dimensional electromagnetic scattering is analyzed. The operator has both continuous essential spectrum, which dominates at lower frequencies, and discrete eigenvalues, which spread out at higher ones. The explicit expression of the operator's symbol provides exact outline of the essential spectrum for any inhomogeneous anisotropic scatterer with Holder continuous constitutive parameters. Geometrical bounds on the location of discrete eigenvalues are derived for various physical scenarios. Numerical experiments demonstrate good agreement between the predicted spectrum of the operator and the eigenvalues of its discretized version.

math-ph↗