Maxwell's equations in periodic structures / Gang Bao, Peijun Li.

Bao, Gang [Browse]
Singapore : Springer ; Beijing : Science Press, [2022]
xi, 355 pages : illustrations (some color) ; 25 cm


  • Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 208. [More in this series]
  • Applied mathematical sciences, 0066-5452 ; volume 208
Summary note
This book addresses recent developments in mathematical analysis and computational methods for solving direct and inverse problems for Maxwells equations in periodic structures. The fundamental importance of the fields is clear, since they are related to technology with significant applications in optics and electromagnetics. The book provides both introductory materials and in-depth discussion to the areas in diffractive optics that offer rich and challenging mathematical problems. It is also intended to convey up-to-date results to students and researchers in applied and computational mathematics, and engineering disciplines as well.
Bibliographic references
Includes bibliographical references and index.
  • Maxwellʼs Equations
  • Electromagnetic Waves
  • Jump and Boundary Conditions
  • Two Fundamental Polarizations
  • References
  • Diffraction Grating Theory
  • Perfectly Conducting Gratings
  • Dielectric Gratings
  • Biperiodic Gratings
  • Perfect Electric Conductors
  • Dielectric Media
  • Variational Formulations
  • The Dirichlet Problem
  • The Transmission Problem
  • Biperiodic Structures
  • Function Spaces
  • The Transparent Boundary Condition
  • The Variational Problem
  • Finite Element Methods
  • The Finite Element Method
  • Finite Element Analysis for TE Polarization
  • Finite Element Analysis for TM Polarization
  • Adaptive Finite Element PML Method
  • The PML Formulation
  • Transparent Boundary Condition for the PML Problem
  • Error Estimate of the PML Solution
  • The Discrete Problem
  • Error Representation Formula
  • A Posteriori Error Analysis
  • Numerical Results
  • Adaptive Finite Element DtN Method
  • TM Polarization
  • Adaptive Finite Element PML Method for Biperiodic Structures
  • Convergence of the PML Solution
  • Inverse Diffraction Grating
  • Uniqueness Theorems
  • The Helmholtz Equation
  • Local Stability
  • Numerical Methods
  • Near-Field Imaging
  • Near-Field Data
  • An Analytic Solution
  • Convergence of the Power Series
  • The Reconstruction Formula
  • Error Estimates
  • Far-Field Data
  • The Reduced Problem
  • Transformed Field Expansion
  • A Nonlinear Correction Scheme
  • The Reduced Model Problem
  • The Zerolh Order Term
  • The First Order Term
  • Related Topics
  • Method of Boundary Integral Equations
  • Model Problems
  • Quasi-periodic Greenʼs Function
  • Boundary Integral Operators
  • Boundary Integral Equations
  • Integral Formulas for Rayleighʼs Coefficients
  • Time-Domain Problems
  • Problem Formulation
  • Time-Domain Transparent Boundary Condition
  • A Priori Estimates
  • Nonlinear Gratings
  • SHG Model
  • TE-TE Polarization
  • TM-TE Polarization
  • Optimal Design Problems
  • The Model Problem
  • The Optimal Design Problem
  • Homogenization of the Design Problem
  • The Relaxed Problem
  • Appendices
  • Index.
  • 9789811600609 ((hardback))
  • 9811600600 ((hardback))
  • 9789811600630 ((pbk.))
  • 9811600635
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