Maxwell’s Equations in Periodic Structures

1. Front Matter

   Pages i-xi

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2. Maxwell’s Equations

   • Gang Bao, Peijun Li

   Pages 1-12

3. Diffraction Grating Theory

   • Gang Bao, Peijun Li

   Pages 13-43

4. Variational Formulations

   • Gang Bao, Peijun Li

   Pages 45-85

5. Finite Element Methods

   • Gang Bao, Peijun Li

   Pages 87-161

6. Inverse Diffraction Grating

   • Gang Bao, Peijun Li

   Pages 163-204

7. Near-Field Imaging

   • Gang Bao, Peijun Li

   Pages 205-266

8. Related Topics

   • Gang Bao, Peijun Li

   Pages 267-329

9. Back Matter

   Pages 331-355

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This book addresses recent developments in mathematical analysis and computational methods for solving direct and inverse problems for Maxwell’s 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.

• Maxwell’s Equations
• Diffractive Optics
• Boundary Value Problems
• Variational Problems
• Finite Element Method
• Well-posedness
• Inverse Scattering

“The book is addressed to anybody working in the area of electromagnetic field computation of periodic structures, which is the back bone of modern optics.” (Mircea Dragoman, optica-opn.org, June 16, 2022)

“The book is quite interdisciplinary in nature and provides a balance between analytical and numerical methods. Plenty of references are provided as well.” (Eric Stachura, zbMATH 1484.35001, 2022)

• School of Mathematical Sciences, Zhejiang University, Hangzhou, China

  Gang Bao

• Department of Mathematics, Purdue University, West Lafayette, USA

  Peijun Li

Gang Bao has made fundamental contributions in developing mathematical and computational techniques to a wide array of emerging scientific problems in scattering and inverse scattering theory, ranging from geophysics, material science, optical science, to medical imaging. His research accomplishments include stability theory of inverse problems for the wave equation, mathematical analysis and computational method in electromagnetic scattering and inverse scattering, and mathematical modeling and analysis in diffractive and nano optics. He was awarded the Feng Kang Prize on Scientific Computing in 2003 and was selected as a SIAM Fellow in 2016 and an AMS Fellow in 2021.

Peijun Li’s research area is applied and computational mathematics with an emphasis on modeling, analysis and computation of the direct and inverse scattering problems for acoustic, electromagnetic, and elastic wave propagation in complex and random environments. He has made important contributions to the area of inverse scattering and wave propagation. He was awarded the 5th Calderon Prize by the Inverse Problems International Association in 2015.

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