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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Resonant Scattering and Generation of Waves: Cubically Polarizable Layers

Resonant Scattering and Generation of Waves: Cubically Polarizable Layers

Yatsyk, Vasyl V.
Angermann, Lutz

Hardcover

Series: Mathematical Engineering

Technology & EngineeringGeneral ComputersPhysics

ISBN10: 3319963007
ISBN13: 9783319963006
Publisher: Springer
Published: Aug 7 2018
Pages: 208
Weight: 1.10
Height: 0.56 Width: 6.14 Depth: 9.21
Language: English
The mathematical model.- Maxwell's equations and wave propagation in media withnonlinear polarizability.- The reduced frequency-domain model.- The condition of phase synchronism.- Packets of plane waves.- Energy conservation laws.- Existence and uniqueness of a weak solution.- Weak formulation.- Existence and uniqueness of a weak solution.- The equivalent system of nonlinear integral equations.- The operator equation.- A sufficient condition for the existence of a continuous solution.- A sufficient condition for the existence of a unique continuous solution.- Relation to the system of nonlinear Sturm-Liouville boundary value problems.- Spectral analysis.- Motivation.- Eigen-modes of the linearized problems.- Spectral energy relationships and the quality factor of eigen-fields.- Numerical solution of the nonlinear boundary value problem.- The finite element method.- Existence and uniqueness of a finite element solution.- Error estimate.- Numerical treatment of the system of integral equations.- Numerical quadrature.- Iterative solution.- Numerical spectral analysis.- Numerical experiments.- Quantitative characteristics of the fields.- Description of the model problems.- The problem with the Kerr nonlinearity.- The self-consistent approach.- A single layer with negative cubic susceptibility.- A single layer with positive cubic susceptibility.- A three-layered structure.- Conclusion and outlook.- A Cubic polarization.- A.1 The case without any static field.- A.2 The case of a nontrivial static field.- B Tools from Functional Analysis.- B.1 Poincar e-Friedrichs inequality.- B.2 Trace inequality.- B.3 Interpolation error estimates.- Notation.- References.- Index.

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