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.

• Maxwell's equations.- Diffraction grating theory.- Variational formulations.- Adaptive finite element methods.- Inverse scattering problems.- Near-field imaging.- Related topics.

“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)