Scattering Matrix Research Articles

Multimode wave scattering problems in layered dissipative solids

A GENERAL SCHEME within the frequency domain is elaborated for the scattering of obliquely-incident waves at a stratified, anisotropic, viscoelastic solid. Existence and uniqueness of the asymptotic wave propagator is established. Possible nonexistence of the scattering matrix at specific values of the incident field is then shown. Conditions for nonuniqueness or incompatibility of the direct scattering problem are provided.

Semiclassical Representation of the Scattering Matrix by a Feynman Integral

We study the scattering problem for one-dimensional Schrodinger equations in the semiclassical limit when the energy level is close to the quadratic maxima of the potential. Starting from the formula of the scattering matrix obtained by the exact WKB method, we represent its principal term in a reduced form of the Feynman integral, an absolutely convergent sum of suitably defined probability amplitudes over countably many trajectories on ℝ generated by classical trajectories and tunneling effects.

Scattering matrices of imperfect hexagonal ice crystals

Scattering matrices of perfect and imperfect hexagonal ice crystals are presented and compared to those of so-called polycrystals, proposed by Macke et al. [1]. Scattering matrices of imperfect hexagonal crystals are calculated using statistical deviations of ray paths during the ray tracing in perfect hexagonal crystals. At a certain degree of deviation, the resulting scattering matrix becomes similar to that of polycrystals. Therefore, this method forms a link between perfect hexagonal columns and polycrystals. The optical properties of these imperfect crystals are sensitive to the aspect ratio (and thus to particle size) as well as to the allowed deviation from the perfect shape. This approach to simulate imperfect ice crystals introduces new possibilities for interpretation of satellite measurements.

Discrete Schrodinger operators and topology

This work is a continuation and extension of the note published in the Russian Math Surveys 1997 n 6. For any pair of solutions of the spectral problem for the second order selfadjoint real Schrodinger Operator on the graph their Symplectic Wronskian is a 1-cycle in the graph. This is a vector-valued symplectic 2-form on the space of solutions. This construction was applied to the Scattering Theory on the graphs with finite number of tails. The asymptotic values of solutions is a Lagrangian Plane of half dimension. This property determines all unitary properties of Scattering Matrix, which is also symmetric. All higher order discrete operators and operators on higher dimensional simplicial complexes are included in this scheme. Nonlinear analog of that was invented by the present author in collaboration with A.S.Schwarz.

Nonlinear Schrödinger Model with Boundary, Integrability and Scattering Matrix Based on the Degenerate Affine Hecke Algebra

The δ-function interacting many-body systems (nonlinear Schrödinger models) on an infinite interval and with boundary are studied by use of the integrable differential-difference operators, so-called Dunkl operators. These models are related with the classical root systems of type A and BC, and we give a systematic method to construct these integrable operators. This method is based on the infinite-dimensional representation for solutions of the classical Yang–Baxter equation and the classical reflection equation. In addition the scattering matrices of the boundary nonlinear Schrödinger model are investigated.

Scattering matrix elements of fractal-like soot agglomerates: erratum

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text Sivakumar Manickavasagam and Mustafa P. Menguc, "Scattering matrix elements of fractal-like soot agglomerates: erratum," Appl. Opt. 36, 7008-7008 (1997) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

Scattering matrices with block symmetries

Scattering matrices with block symmetry, which correspond to a scattering process in cavities with geometrical symmetry, are analyzed. The distribution of the transmission coefficient is computed for a different number of channels in the case of a system with or without the time-reversal invariance. An interpolating formula for the case of gradual time reversal symmetry breaking is proposed.

Quantum Mechanical Time-Delay Matrix in Chaotic Scattering

We calculate the probability distribution of the matrix $Q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}i\ensuremath{\Elzxh}{S}^{\ensuremath{-}1}\ensuremath{\partial}S/\ensuremath{\partial}E$ for a chaotic system with scattering matrix $S$ at energy $E$. The eigenvalues ${\ensuremath{\tau}}_{j}$ of $Q$ are the so-called proper delay times, introduced by Wigner and Smith to describe the time dependence of a scattering process. The distribution of the inverse delay times turns out to be given by the Laguerre ensemble from random-matrix theory.

Generalized scattering matrix and symmetry principles for infinite planar structures

This paper presents a technique for determining the scattering coefficients of the Generalized Scattering Matrix (GSM) for an infinite planar structure whose operation is prescribed. The technique is partly a synthesis tool in that it allows to identify some geometrical properties of the structure from the relationships between various coefficients of the GSM. These relationships are cast into a formalism that simplifies and generalizes the development of many previously reported results. We also apply the technique to various structures for the purpose of demonstrating its use and validity. When this technique is applied to Linear or circular polarizers with the GSM incorporating only the dominant mode, we find that ideal polarizers are possible only at normal incidence, regardless of their specific physical realizations. Similarly, we find that a structure corresponding to the reciprocal circular polarization selective surface must satisfy the property of 2-fold rotational symmetry, except in a limited neighborhood of the normal incidence where the property of reciprocity suffices, and must not satisfy the property of longitudinal reflection symmetry.

Regarding the article “scattering matrix resonances and quasi-levels”

Regarding the article “scattering matrix resonances and quasi-levels”

Semiclassical approach to the hydrogen-exchange reaction Reactive and transition-state dynamics

Scattering matrix elements and symmetric transition-state resonances for the collinear H 2 + H → H + H 2 reaction are obtained using a time-dependent approach. The correlation function between reactant channel wavepackets and product channel wavepackets is used to determine the S-matrix elements. In a similar fashion, autocorrelation functions are used to extract the positions and widths of transition-state resonances. The time propagation of the wavepackets is performed by the improved semiclassical frozen Gaussian method of Herman and Kluk, which is an initial value, uniformly converged method. The agreement between the quantum and semiclassical results is far better than that obtained previously for this system by other semiclassical methods.

Generalized scattering matrix and symmetry principles for infinite planar structures

This paper presents a technique for determining the scattering coefficients of the Generalized Scattering Matrix (GSM) for an infinite planar structure whose operation is prescribed. The technique is partly a synthesis tool in that it allows to identify some geometrical properties of the structure from the relationships between various coefficients of the GSM. These relationships are cast into a formalism that simplifies and generalizes the development of many previously reported results. We also apply the technique to various structures for the purpose of demonstrating its use and validity. When this technique is applied to Linear or circular polarizers with the GSM incorporating only the dominant mode, we find that ideal polarizers are possible only at normal incidence, regardless of their specific physical realizations. Similarly, we find that a structure corresponding to the reciprocal circular polarization selective surface must satisfy the property of 2-fold rotational symmetry, except in a limited neighborhood of the normal incidence where the property of reciprocity suffices, and must not satisfy the property of longitudinal reflection symmetry.

A new application of absorbing boundary conditions for computing collinear quantum reactive scattering matrix elements

Scattering matrix ( S-matrix) elements are calculated using absorbing boundary conditions (ABC) together with the channel packet method (CPM). Using the CPM, we compute a time dependent correlation function between reactant and product Møller states. As the Møller states evolve in time, they will be attenuated by the ABC which are placed outside the interaction region of the potential. This permits the use of a smaller grid and leads to an order of magnitude improvement in the time required to calculate the correlation function for the H + H 2 reaction. The resulting S-matrix elements are in excellent agreement with previous calculations.

Wave packet correlation function approach to H2(ν)+H→H+H2(ν′): semiclassical implementation

Scattering matrix elements for the collinear H2(ν)+H→H+H2(ν′) reaction are obtained using a recently developed time-dependent approach to scattering. The correlation function between reactant channel wave packet and product channel wave packet is used to determine the S-matrix elements. The time propagation of the reactant wave packet is performed by the semiclassical method of Herman and Kluk, which is an initial value, uniformly converged method. The agreement between the quantum and semiclassical results is far better than that obtained previously for this system by other semiclassical methods.

Transfer matrix of a spherical scatterer.

We derive the off-shell scattering matrix for a spherical scatterer. The result obtained generalizes the off-on-shell matrix commonly used in the theory of scalar waves propagation in random media. \textcopyright{} 1996 The American Physical Society.

Normalization of the Fox?Goodwin algorithm to calculate scattering matrices in an adiabatic basis at low and high collision energies

Scattering matrices in an adiabatic basis were calculated for a model two-state atomic collision using a simple modification (normalization of the wave function) of the Fox—Goodwin three-point recurrence relation. Unlike the previous application of this method to scattering the present algorithm was able to precisely calculate the scattering matrix not only at low collision energies (eV), but also at high energies (keV). An analysis of the convergence of the modified Fox—Goodwin algorithm is also discussed for several angular momenta and for several energies where the results were compared to the renormalized Numerov method. © 1996 by John Wiley & Sons, Inc.

Testing scattering matrices: A compendium of recipes

Scattering matrices describe the transformation of the Stokes parameters of a beam of radiation upon scattering of that beam. The problems of testing scattering matrices for scattering by one particle and for single scattering by an assembly of particles are addressed. The treatment concerns arbitrary particles, orientations and scattering geometries. A synopsis of tests that appear to be the most useful ones from a practical point of view is presented. Special attention is given to matrices with uncertainties due, e.g., to experimental errors. In particular, it is shown how a matrix E mod can be constructed which is closest (in the sense of the Fröbenius norm) to a given real 4 × 4 matrix E such that E mod is a proper scattering matrix of one particle or of an assembly of particles, respectively. Criteria for the rejection of E are also discussed. To illustrate the theoretical treatment a practical example is treated. Finally, it is shown that all results given for scattering matrices of one particle are applicable for all pure Mueller matrices, while all results for scattering matrices of assemblies of particles hold for sums of pure Mueller matrices.

Diffusion of classical waves in random media with microstructure resonances

The diffusion constant of classical waves propagating in random media with microstructure resonances is obtained. Renormalizations of D that are due to expansions in transferred momentum q and frequency ω in the Bethe–Salpeter equation are taken into account. The diffusion constant is estimated for scalar waves propagating in the medium with randomly distributed dielectric spheres with the use of the nondiagonal off-shell transition matrix for penetrable scatterers. A detailed comparison of different sources of renormalization is made. Differences between previous calculations based on the on-shell scattering matrix and new results implementing the off-shell scattering matrix are discussed.

Bill Martin'sMatrix and Line

Bill Martin's<i>Matrix and Line</i>

Full-wave design and realization of multicoupled dual-mode circular waveguide filters

A new full-wave method for the design and realization of dual-mode circular waveguide filters is presented. The rigorous CAD is a combination of the mode-matching and the finite-element techniques, which permits obtaining the Generalized Scattering Matrix for all the blocks that compose the structure (rectangular slots, cross-irises, and screws). The finite thickness of the irises, the higher order mode interaction, as well as the coupling and tuning screws are rigorously taken into account. A systematic design process for the different elements is described. A full prediction of resonant out-of-band spurious modes is accomplished prior to the filter construction. Special attention is devoted to the circuital model in order to save a great deal of computational effort in the final adjustment. A four-pole elliptic circular waveguide cavity filter has been designed and constructed. The experimental filter results show excellent agreement with theory. >