Based on more than 30 years of research on differential theories of gratings, this book describes developments in differential theory for applications in spectroscopy, acoustics, X-ray instrumentation, optical communication, information processing, photolithography, high-power lasers, high-precision engineering, and astronomy. Introducing the Fast Fourier Factorization approach to improve the convergence of a truncated series, the book examines multilayers, stacked gratings, crossed gratings, photonic crystals, and isotropic and anisotropic materials; techniques and examples in grating design; and Maxwell equations in a truncated Fourier space.

chapter 1|35 pages

General Properties

chapter 3|23 pages

Stacks of Gratings

chapter 4|22 pages

Fast Fourier Factorization (FFF) Method

chapter 6|26 pages

Rigorous Coupled-Wave (RCW) Method

chapter 7|35 pages

Coordinate Transformation Methods

chapter 8|7 pages

Gratings Made of Anisotropic Materials

chapter 9|21 pages

Crossed Gratings

chapter 10|37 pages

Photonic Crystals

chapter 11|31 pages

X-Ray Gratings

chapter 12|28 pages

Transmission Gratings

chapter 14|29 pages

Differential Theory of Non-Periodic Media