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Register a new userMethod of problem solution of diffraction and scattering theory
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Authors
Valery B. Morozov
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No Arabic abstract
Problem solutions in area of diffraction and of scattering theory are considered from one point of view. The method common for them is based on approximate orthogonality of solution constituents, which oscillate on a body long frontier. Method potentiality is discussed.
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Reflectionless CMV matrices are studied using scattering theory. By changing a single Verblunsky coefficient a full-line CMV matrix can be decoupled and written as the sum of two half-line operators. Explicit formulas for the scattering matrix associated to the coupled and decoupled operators are derived. In particular, it is shown that a CMV matrix is reflectionless iff the scattering matrix is off-diagonal which in turn provides a short proof of an important result of [Breuer-Ryckman-Simon]. These developments parallel those recently obtained for Jacobi matrices.
We study the spectral and scattering theory of light transmission in a system consisting of two asymptotically periodic waveguides, also known as one-dimensional photonic crystals, coupled by a junction. Using analyticity techniques and commutator methods in a two-Hilbert spaces setting, we determine the nature of the spectrum and prove the existence and completeness of the wave operators of the system.
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