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Sergei V. Shabanov

Publications and source records attributed to Sergei V. Shabanov.

At least 19 recordsLinked to original sources
arXiv2012

The resonant nonlinear scattering theory with bound states in the radiation continuum and the second harmonic generation

A nonlinear electromagnetic scattering problem is studied in the presence of bound states in the radiation continuum. It is shown that the solution is not analytic in the nonlinear susceptibility and the conventional perturbation theory fails. A non-perturbative approach is proposed and applied to the system of two parallel periodic arrays of dielectric cylinders with a second order nonlinear susceptibility. This scattering system is known to have bound states in the radiation continuum. In particular, it is demonstrated that, for a wide range of values of the nonlinear susceptibility, the conversion rate of the incident fundamental harmonic into the second one can be as high as 40% when the distance between the arrays is as low as a half of the incident radiation wavelength. The effect is solely attributed to the presence of bound states in the radiation continuum.

math-ph↗
arXiv2011

Electromagnetic Siegert states for periodic dielectric structures

The formalism of Siegert states to describe the resonant scattering in quantum theory is extended to the resonant scattering of electromagnetic waves on periodic dielectric arrays. The excitation of electromagnetic Siegert states by an incident wave packet and their decay is studied. The formalism is applied to develop a theory of coupled electromagnetic resonances arising in the electromagnetic scattering problem for two such arrays separated by a distance 2h (or, generally, when the physical properties of the scattering array depend on a real coupling parameter h). Analytic properties of Siegert states as functions of the coupling parameter h are established by the Regular Perturbation Theorem which is an extension the Kato-Rellich theorem to the present case. By means of this theorem, it is proved that if the scattering structure admits a bound state in the radiation continuum at a certain value of the coupling parameter h, then there always exist regions within the structure in which the near field can be amplified as much as desired by adjusting the value of h. This establishes a rather general mechanism to control and amplify optical nonlinear effects in periodically structured planar structures possessing a nonlinear dielectric susceptibility.

math-ph↗
arXiv2010

Electromagnetic bound states in the radiation continuum for periodic double arrays of subwavelength dielectric cylinders

Electromagnetic bound states in the radiation continuum are studied for periodic double arrays of subwavelength dielectric cylinders in TM polarization. They are similar to localized waveguide mode solutions of Maxwell's equations for metal cavities or defects of photonic crystals, but, in contrast to the latter, their spectrum lies in the radiation continuum. The phenomenon is identical to the existence of bound sates in the radiation continuum in quantum mechanics, discovered by von Neumann and Wigner. In the formal scattering theory, these states appear as resonances with the vanishing width. For the system studied, the bound states are shown to exist at specific distances between the arrays in the spectral region where one or two diffraction channels are open. Analytic solutions are obtained for all bound states (below the radiation continuum and in it) in the limit of thin cylinders (the cylinder radius is much smaller than the wavelength). The existence of bound states is also established in the spectral region where three and more diffraction channels are open, provided the cylinders' dielectric constant and radius are fine-tuned. The near field and scattering resonances of the structure are investigated when the distance between the arrays varies in the neighborhood of its critical values at which the bound states are formed. In particular, it is shown that the near field in the scattering process becomes significantly amplified in specific regions of the array as the distance approaches its critical values. The effect may be used to control optical non-linear effects by varying the distance between the arrays near its critical values.

math-ph↗
arXiv2010

Absorption tomography of laser induced plasmas with a large aperture

An emission tomography of laser-induced plasmas employed in the laser induced breakdown spectroscopy (LIBS) requires long signal integration times during which the plasma cannot be considered stationary. To reduce the integration time, it is proposed to measure a plasma absorption in parallel rays with an aperture that collects light coming from large fractions of the plasma plume at each aperture position. The needed spatial resolution is achieved by a special numerical data processing. Another advantage of the proposed procedure is that inexpensive linear CCD or non-discrete (PMT, photodiode) detectors can be used instead of costly 2-dimensional detectors.

physics.plasm-ph↗
arXiv2005

Wave packet propagation by the Faber polynomial approximation in electrodynamics of passive media

Maxwell's equations for propagation of electromagnetic waves in dispersive and absorptive (passive) media are represented in the form of the Schrödinger equation $i\partial Ψ/\partial t = {H}Ψ$, where ${H}$ is a linear differential operator (Hamiltonian) acting on a multi-dimensional vector $Ψ$ composed of the electromagnetic fields and auxiliary matter fields describing the medium response. In this representation, the initial value problem is solved by applying the fundamental solution $\exp(-itH)$ to the initial field configuration. The Faber polynomial approximation of the fundamental solution is used to develop a numerical algorithm for propagation of broad band wave packets in passive media. The action of the Hamiltonian on the wave function $Ψ$ is approximated by the Fourier grid pseudospectral method. The algorithm is global in time, meaning that the entire propagation can be carried out in just a few time steps. A typical time step is much larger than that in finite differencing schemes, $Δt_F \gg \|H\|^{-1}$. The accuracy and stability of the algorithm is analyzed. The Faber propagation method is compared with the Lanczos-Arnoldi propagation method with an example of scattering of broad band laser pulses on a periodic grating made of a dielectric whose dispersive properties are described by the Rocard-Powels-Debye model. The Faber algorithm is shown to be more efficient. The Courant limit for time stepping, $Δt_C \sim \|H\|^{-1}$, is exceeded at least in 3000 times in the Faber propagation scheme.

physics.comp-ph↗
arXiv2004

Electromagnetic Pulse Propagation in Passive Media by the Lanczos Method

Maxwell's equations are cast in the form of the Schrödinger equation. The Lanczos propagation method is used in combination with the fast Fourier pseudospectral method to solve the initial value problem. As a result, a time-domain, unconditionally stable, and highly efficient numerical algorithm is obtained for the propagation and scattering of broad-band electromagnetic pulses in dispersive and absorbing media. As compared to conventional finite-difference time-domain methods, an important advantage of the proposed algorithm is a dynamical control of accuracy: Variable time steps or variable computational costs per time step with error control are possible. The method is illustrated with numerical simulations of extraordinary transmission and reflection in metal and dielectric gratings with rectangular and cylindrical geometry.

physics.comp-ph↗
arXiv2004

Lanczos Pseudospectral Propagation Method for Initial-Value Problems in Electrodynamics of Passive Media

Maxwell's equations for electrodynamics of dispersive and absorptive (passive) media are written in the form of the Schrödinger equation with a non-Hermitian Hamiltonian. The Lanczos time-propagation scheme is modified to include non-Hermitian Hamiltonians and used, in combination with the Fourier pseudospectral method, to solve the initial-value problem. The time-domain algorithm developed is shown to be unconditionally stable. Variable time steps and/or variable computational costs per time step with error control are possible. The algorithm is applied to study transmission and reflection properties of ionic crystal gratings with cylindric geometry in the infra-red range.

physics.comp-ph↗
arXiv2003

Applications of the wave packet method to resonant transmission and reflection gratings

Scattering of femtosecond laser pulses on resonant transmission and reflection gratings made of dispersive (Drude metals) and dielectric materials is studied by a time-domain numerical algorithm for Maxwell's theory of linear passive (dispersive and absorbing) media. The algorithm is based on the Hamiltonian formalism in the framework of which Maxwell's equations for passive media are shown to be equivalent to the first-order equation, $\partial Ψ/\partial t = {\cal H}Ψ$, where ${\cal H}$ is a linear differential operator (Hamiltonian) acting on a multi-dimensional vector $Ψ$ built of the electromagnetic inductions and auxiliary matter fields describing the medium response. The initial value problem is then solved by means of a modified time leapfrog method in combination with the Fourier pseudospectral method applied on a non-uniform grid that is constructed by a change of variables and designed to enhance the sampling efficiency near medium interfaces. The algorithm is shown to be highly accurate at relatively low computational costs. An excellent agreement with previous theoretical and experimental studies of the gratings is demonstrated by numerical simulations using our algorithm. In addition, our algorithm allows one to see real time dynamics of long leaving resonant excitations of electromagnetic fields in the gratings in the entire frequency range of the initial wide band wave packet as well as formation of the reflected and transmitted wave fronts.

physics.comp-ph↗
arXiv2003

Electromagnetic pulse propagation in passive media by path integral methods

A novel time domain solver of Maxwell's equations in passive (dispersive and absorbing) media is proposed. The method is based on the path integral formalism of quantum theory and entails the use of ({\it i}) the Hamiltonian formalism and ({\it ii}) pseudospectral methods (the fast Fourier transform, in particular) of solving differential equations. In contrast to finite differencing schemes, the path integral based algorithm has no artificial numerical dispersion (dispersive errors), operates at the Nyquist limit (two grid points per shortest wavelength in the wavepacket) and exhibits an exponential convergence as the grid size increases, which, in turn, should lead to a higher accuracy. The Gauss law holds exactly with no extra computational cost. Each time step requires $O(N\log_2 N)$ elementary operations where $N$ is the grid size. It can also be applied to simulations of electromagnetic waves in passive media whose properties are time dependent when conventional stationary (scattering matrix) methods are inapplicable. The stability and accuracy of the algorithm are investigated in detail.

math.NA↗
arXiv2003

An application of interpolating scaling functions to wave packet propagation

Wave packet propagation in the basis of interpolating scaling functions (ISF) is studied. The ISF are well known in the multiresolution analysis based on spline biorthogonal wavelets. The ISF form a cardinal basis set corresponding to an equidistantly spaced grid. They have compact support of the size determined by the underlying interpolating polynomial that is used to generate ISF. In this basis the potential energy matrix is diagonal and the kinetic energy matrix is sparse and, in the 1D case, has a band-diagonal structure. An important feature of the basis is that matrix elements of a Hamiltonian are exactly computed by means of simple algebraic transformations efficiently implemented numerically. Therefore the number of grid points and the order of the underlying interpolating polynomial can easily be varied allowing one to approach the accuracy of pseudospectral methods in a regular manner, similar to high order finite difference methods. The results of numerical simulations of an H+H_2 collinear collision show that the ISF provide one with an accurate and efficient representation for use in the wave packet propagation method.

physics.atom-ph↗
arXiv2001

The wave packet propagation using wavelets

It is demonstrated that the wavelets can be used to considerably speed up simulations of the wave packet propagation in multiscale systems. Extremely high efficiency is obtained in the representation of both bound and continuum states. The new method is compared with the fast Fourier algorithm. Depending on ratios of typical scales of a quantum system in question, the wavelet method appears to be faster by a few orders of magnitude.

physics.comp-ph↗
arXiv2001

Infrared Yang-Mills theory as a spin system. A lattice approach

To verify the conjecture that Yang-Mills theory in the infrared limit is equivalent to a spin system whose excitations are knot solitons, a numerical algorithm based on the inverse Monte Carlo method is proposed. To investigate the stability of the effective spin field action, numerical studies of the renormalization group flow for the coupling constants are suggested. A universality of the effective spin field action is also discussed.

hep-lat↗
arXiv2000

Geometry of the physical phase space in quantum gauge models

The physical phase space in gauge systems is studied. Effects caused by a non-Euclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac gauge invariant states is used to derive a necessary modification of the Hamiltonian path integral in gauge theories of the Yang-Mills type with fermions that takes into account the non-Euclidean geometry of the physical phase space. The new path integral is applied to resolve the Gribov obstruction. Applications to the Kogut-Susskind lattice gauge theory are given. The basic ideas are illustrated with examples accessible for non-specialists.

hep-th↗
arXiv1999

Yang-Mills theory as an Abelian theory without gauge fixing

A general procedure to reveal an Abelian structure of Yang-Mills theories by means of a (nonlocal) change of variables, rather than by gauge fixing, in the space of connections is proposed. The Abelian gauge group is isomorphic to the maximal Abelian subgroup of the Yang-Mills gauge group, but not its subgroup. A Maxwell field of the Abelian theory contains topological degrees of freedom of original Yang-Mills fields which generate monopole-like and flux-like defects upon an Abelian projection. 't Hooft's conjecture that ``monopole'' dynamics is projection independent is proved for a special class of Abelian projections. A partial duality and a dynamical regime in which the theory may have massive excitations being knot-like solitons are discussed.

hep-th↗
arXiv1999

An effective action for monopoles and knot solitons in Yang-Mills theory

By comparision with numerical results in the maximal Abelian projection of lattice Yang-Mills theory, it is argued that the nonperturbative dynamics of Yang Mills theory can be described by a set of fields that take their values in the coset space SU(2)/U(1). The Yang-Mills connection is parameterized in a special way to separate the dependence on the coset field. The coset field is then regarded as a collective variable, and a method to obtain its effective action is developed. It is argued that the physical excitations of the effective action may be knot solitons. A procedure to calculate the mass scale of knot solitons is discussed for lattice gauge theories in the maximal Abelian projection. The approach is extended to the SU(N) Yang-Mills theory. A relation between the large N limit and the monopole dominance is pointed out.

hep-th↗
arXiv1999

Towards a Nonperturbative Path Integral in Gauge Theories

We propose a modification of the Faddeev-Popov procedure to construct a path integral representation for the transition amplitude and the partition function for gauge theories whose orbit space has a non-Euclidean geometry. Our approach is based on the Kato-Trotter product formula modified appropriately to incorporate the gauge invariance condition, and thereby equivalence to the Dirac operator formalism is guaranteed by construction. The modified path integral provides a solution to the Gribov obstruction as well as to the operator ordering problem when the orbit space has curvature. A few explicit examples are given to illustrate new features of the formalism developed. The method is applied to the Kogut-Susskind lattice gauge theory to develop a nonperturbative functional integral for a quantum Yang-Mills theory. Feynman's conjecture about a relation between the mass gap and the orbit space geometry in gluodynamics is discussed in the framework of the modified path integral.

hep-th↗