Topic
Transfer matrix
About: Transfer matrix is a research topic. Over the lifetime, 3516 publications have been published within this topic receiving 64660 citations.
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TL;DR: In this paper, a 2 × 2 matrix method is applied to planar multilayer optical waveguides to satisfy substrate-to-cover field transfer equations that reduce to the equation 0 for bound modes and leaky waves.
Abstract: A standard 2 × 2 matrix method-used in thin-film optics is applied to planar multilayer optical waveguides. All modes are required to satisfy substrate-to-cover field-transfer equations that reduce to the equation γcm11 + γcγsm12 + m21 + γsm22 = 0 for bound modes and leaky waves. Expressions are derived for the field profiles and the power in each medium. A first-order perturbation theory is developed and applied to absorbing multilayer guides and to the reflection of plane waves from the prism-loaded lossy multilayer guide. The latter leads to experimental arrangements for measuring losses in which the gap thickness and propagation constant are accessible parameters.
419 citations
TL;DR: In this article, the authors present a theory of multichannel disordered conductors by directly studying the statistical distribution of the transfer matrix for the full system, based on general properties of the scattering system: flux conservation, time-reversal invariance, and the appropriate combination requirement when two wires are put together.
417 citations
TL;DR: A method is presented by which the wavenumbers for a one-dimensional waveguide can be predicted from a finite element (FE) model, which involves postprocessing a conventional, but low order, FE model, the mass and stiffness matrices of which are typically found using a conventional FE package.
Abstract: A method is presented by which the wavenumbers for a one-dimensional waveguide can be predicted from a finite element (FE) model. The method involves postprocessing a conventional, but low order, FE model, the mass and stiffness matrices of which are typically found using a conventional FE package. This is in contrast to the most popular previous waveguide/FE approach, sometimes termed the spectral finite element approach, which requires new spectral element matrices to be developed. In the approach described here, a section of the waveguide is modeled using conventional FE software and the dynamic stiffness matrix formed. A periodicity condition is applied, the wavenumbers following from the eigensolution of the resulting transfer matrix. The method is described, estimation of wavenumbers, energy, and group velocity discussed, and numerical examples presented. These concern wave propagation in a beam and a simply supported plate strip, for which analytical solutions exist, and the more complex case of a viscoelastic laminate, which involves postprocessing an ANSYS FE model. The method is seen to yield accurate results for the wavenumbers and group velocities of both propagating and evanescent waves.
400 citations
TL;DR: This approach enables to answer questions such as When does ultrarefraction occur?
Abstract: We describe methods of investigating the behavior of photonic crystals. Our approach establishes a link between the dispersion relation of the Bloch modes for an infinite crystal (which describes the intrinsic properties of the photonic crystal in the absence of an incident field) and the diffraction problem of a grating (finite photonic crystal) illuminated by an incident field. We point out the relationship between the translation operator of the first problem and the transfer matrix of the second. The eigenvalues of the transfer matrix contain information about the dispersion relation. This approach enables us to answer questions such as When does ultrarefraction occur? Can the photonic crystal simulate a homogeneous and isotropic material with low effective index? This approach also enables us to determine suitable parameters to obtain ultrarefractive or negative refraction properties and to design optical devices such as highly dispersive microprisms and ultrarefractive microlenses. Rigorous computations add a quantitative aspect and demonstrate the relevance of our approach.
391 citations
TL;DR: Using the algebraic Bethe ansatz method and the solution of the quantum inverse scattering problem for local spins, this article obtained multiple integral representations of the n-point correlation functions of the XXZ Heisenberg spin-1 2 chain in a constant magnetic field.
377 citations