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Field name	Details
Dewey Class	518
Title	Scattering Theory for Diffraction Gratings ([EBook] /) / by Calvin H. Wilcox.
Author	Wilcox, Calvin H.
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : : Springer New York : : Imprint: Springer, , 1984.
Physical Details	180 p. : online resource.
Series	Applied mathematical sciences 0066-5452 ; ; 46
ISBN	9781461211303
Summary Note	The scattering of acoustic and electromagnetic waves by periodic sur faces plays a role in many areas of applied physics and engineering. Opti cal diffraction gratings date from the nineteenth century and are still widely used by spectroscopists. More recently, diffraction gratings have been used as coupling devices for optical waveguides. Trains of surface waves on the oceans are natural diffraction gratings which influence the scattering of electromagnetic waves and underwater sound. Similarly, the surface of a crystal acts as a diffraction grating for the scattering of atomic beams. This list of natural and artificial diffraction gratings could easily be extended. The purpose of this monograph is to develop from first principles a theory of the scattering of acoustic and electromagnetic waves by periodic surfaces. In physical terms, the scattering of both time-harmonic and transient fields is analyzed. The corresponding mathematical model leads to the study of boundary value problems for the Helmholtz and d'Alembert wave equations in plane domains bounded by periodic curves. In the formal ism adopted here these problems are intimately related to the spectral analysis of the Laplace operator, acting in a Hilbert space of functions defined in the domain adjacent to the grating.:
Contents note	1. Physical Theory -- 1. The Physical Problem -- 2. The Mathematical Formulation -- 3. Solution of the Initial-Boundary Value Problem -- 4. The Reference Problem and Its Eigenfunctions -- 5. Rayleigh-Bloch Diffracted Plane Waves for Gratings -- 6. Rayleigh-Bloch Surface Waves for Gratings -- 7. Rayleigh-Bloch Wave Expansions -- 8. Wave and Scattering Operators for Gratings -- 9. Asymptotic Wave Functions for Gratings -- 10. The Scattering of Signals from Remote Sources -- 2. Mathematical Theory -- 1. Grating Domains and Grating Propagators -- 2. Rayleigh-Bloch Waves -- 3. The Reduced Grating Propagator Ap -- 4. Analytic Continuation of the Resolvent of Ap -- 5. Proofs of the Results of §4 -- 6. The Eigenfunction Expansion for Ap -- 7. Proofs of the Results of §6 -- 8. The Rayleigh-Bloch Wave Expansions for A -- 9. Proofs of the Results of §8 -- 10. The Initial-Boundary Value Problems for the Scattered Fields -- 11. Construction of the Wave Operators for AP and Ao,p -- 12. Construction of the Wave Operators for A and Ao -- 13. Asymptotic Wave Functions and Energy Distributions -- 14. Construction and Structure of the S-Matrix -- 15. The Scattering of Signals by Diffraction Gratings -- References.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4612-1130-3
Links to Related Works	Subject References: Mathematics . Numerical Analysis . Authors: Wilcox, Calvin H. . Corporate Authors: SpringerLink (Online service) . Series: Applied mathematical sciences . Classification: 518 .

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Scattering Theory for Diffraction Gratings

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