Scattering theory for diffraction gratings

TLDR: In this paper, the S-Matrix was constructed using the Rayleigh-Bloch wave expansion and the reduced Grating Propagator (GRP) for the Scattered Fields problem.

Abstract: 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.