Scattering Matrix Method

Scattering Matrix Method

In computational electromagnetics, Scattering Matrix Method (SMM) is a numerical method used to solve the Maxwells equations.

Principles

SMM uses cylinders to model dielectric/metal objects in the domain. The total-field/scattered-field (TF/SF) formalism where the total field is written as sum of incident and scattered at each point in the domain::E_{tot} = E_{inc} + E_{scatt}

By assuming series solutions for the total field, the SMM method transforms the domain into a cylindrical problem. In this domain total field is written in terms of Bessel and Hankel function solutions to the cylindrical Helmholtz equation. SMM method formulation, finally helps compute these coefficients of the cylindrical harmonic functions within the cylinder and outside it, at the same time satisfying EM boundary conditions.

Finally, SMM accuracy can be increased by adding (removing) cylindrical harmonic terms used to model the scattered fields.

SMM, eventually leads to a matrix formalism, and the coefficients are calculated through matrix inversion. For N-cylinders, each scattered field modeled using 2M+1 harmonic terms, SMM requires to solve a N(2M + 1) system of equations.

Advantages

SMM, is a rigorous and accurate method deriving from first principles. Hence, it is guaranteed to be accurate within limits of model, and not show suprious effects of numerical dispersion arising in other technqiues like FDTD.

ee also

*Finite-difference time-domain method
*Finite element method
*Maxwells equations
* Method of Lines

References

* Kiyotoshi Yasumoto, Electromagnetic Theory and Applications for Photonic Crystals, Taylor & Francis, 2006.


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Matrix (mathematics) — Specific elements of a matrix are often denoted by a variable with two subscripts. For instance, a2,1 represents the element at the second row and first column of a matrix A. In mathematics, a matrix (plural matrices, or less commonly matrixes)… …   Wikipedia

  • Method of quantum characteristics — In quantum mechanics, quantum characteristics are phase space trajectories that arise in the deformation quantization through the Weyl Wigner transform of Heisenberg operators of canonical coordinates and momenta. These trajectories obey the… …   Wikipedia

  • Abeles matrix formalism — The Abeles matrix method is a computationally fast and easy way to calculate the specular reflectivity from a stratified interface, as a function of the perpendicular momentum transfer, Qz .Application Q z=frac{4pi}{lambda}sin heta=2k z Where θ… …   Wikipedia

  • Transmission Line Matrix Methode — Viele Probleme der modernen Mikrowellentechnik lassen sich nur durch numerische Verfahren zufriedenstellend lösen. Z. B. lassen sich die technischen Eigenschaften einer Handyantenne wie Abstrahlverhalten nicht mehr mit geschlossenen… …   Deutsch Wikipedia

  • Transmission-Line-Matrix-Methode — Viele Probleme der modernen Mikrowellentechnik lassen sich nur durch numerische Verfahren zufriedenstellend lösen. Zum Beispiel lassen sich die technischen Eigenschaften einer Handyantenne wie Abstrahlverhalten nicht mehr mit geschlossenen… …   Deutsch Wikipedia

  • S-matrix — ▪ quantum mechanics also called  scattering matrix        in quantum mechanics, array of mathematical quantities that predicts the probabilities of all possible outcomes of a given experimental situation. For instance, two particles in collision… …   Universalium

  • Eigendecomposition of a matrix — In the mathematical discipline of linear algebra, eigendecomposition or sometimes spectral decomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and… …   Wikipedia

  • Biological small-angle scattering — Small angle scattering is a fundamental method for structure analysis of materials, including biological materials. Small angle scattering allows one to study the structure of a variety of objects such as solutions of biological macromolecules,… …   Wikipedia

  • Subsurface scattering — (or SSS) is a mechanism of light transport in which light penetrates the surface of a translucent object, is scattered by interacting with the material, and exits the surface at a different point. The light will generally penetrate the surface… …   Wikipedia

  • Convolution for optical broad-beam responses in scattering media — Photon transport theories, such as the Monte Carlo method, are commonly used to model light propagation in tissue. The responses to a pencil beam incident on a scattering medium are referred to as Green’s functions or impulse responses. Photon… …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”