Waves in Periodic and Random Media.

Intro -- Contents -- Preface -- Spectral properties of absorptive photonic crystals -- Regularity properties for the density of states of random Schrödinger operators -- Spectral properties of Schrödinger operators with a strongly attractive δ interaction supported by a surface -- Absolute continuity of the spectra of periodic waveguides -- The Anderson metal-insulator transport transition -- Theory and computation of scattering resonances of photonic microstructures -- 1. Introduction and outline -- 2. Maxwell's equations in a wave guide and the scalar approximation -- 3. The resonance problem for microstructure waveguides -- 4. Scattering resonances of the Schrödinger equation for high contrast and oscillatory potentials -- 5. Multiple scales and homogenization expansion -- 6. Numerical simulations for selected structures -- 7. Implementation of homogenization expansion -- 8. Summary and discussion -- Appendix A. Calculations for simple layered structures -- References -- Asymptotic formulas for eigenvalues and eigenfunctions of periodic magnetic Schrödinger operators -- On guided waves in photonic crystal waveguides -- The design and photofabrication of random achromatic optical diffusers for uniform illumination -- Resonance optical switch: calculation of resonance eigenvalues -- High energy asymptotics of the density of states for certain periodic pseudo-differential operators in dimension one -- On discrete spectrum in the gaps of a two-dimensional periodic elliptic operator perturbed by a decaying potential -- On the principal eigenvalue of the Schrödinger operator with a scaled random potential.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.