Photonic Crystals: Molding the Flow of Light - Second Edition
Princeton University Press, Oct 30, 2011 - Science - 304 pages
Since it was first published in 1995, Photonic Crystals has remained the definitive text for both undergraduates and researchers on photonic band-gap materials and their use in controlling the propagation of light. This newly expanded and revised edition covers the latest developments in the field, providing the most up-to-date, concise, and comprehensive book available on these novel materials and their applications.
Starting from Maxwell's equations and Fourier analysis, the authors develop the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory. They then investigate the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions. This new edition includes entirely new chapters describing important hybrid structures that use band gaps or periodicity only in some directions: periodic waveguides, photonic-crystal slabs, and photonic-crystal fibers. The authors demonstrate how the capabilities of photonic crystals to localize light can be put to work in devices such as filters and splitters. A new appendix provides an overview of computational methods for electromagnetism. Existing chapters have been considerably updated and expanded to include many new three-dimensional photonic crystals, an extensive tutorial on device design using temporal coupled-mode theory, discussions of diffraction and refraction at crystal interfaces, and more. Richly illustrated and accessibly written, Photonic Crystals is an indispensable resource for students and researchers.
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The content of the equation is this: perform a series of operations on a function H(
r), and if H(r) is really an allowable electromagnetic mode, the result will be a
constant times the original function H(r). This situation arises often in
operating on a function translationally invariant; f(r), then shifts we have the ˆ
argument by d. Suppose our system is [Tˆd,卷]ˆ under Tˆ = d. 0. The modes of 卷ˆ
Tdε(r) = ε(r−d) = ε(r), or equivalently, can now be classified according to how they
Table 1 Quantum Mechanics in a Electromagnetism in a Periodic Periodic
Potential (Crystal) Dielectric (Photonic Crystal) What is the “key function” that The
scalar wave function, F(r,t). The magnetic vector field H(r,t). contains all of the ...
IN CHAPTER 4, we used Bloch's theorem to express an electromagnetic mode
as a plane wave that is modulated by a periodic function u(r). The function u
shares the same periodicity as the crystal. We also argued that we need only
Here g(q) is the coefficient on the plane wave with wave vector q. An expansion
like this can be performed on any well-behaved function. But our function f is
periodic on the lattice—what information does this tell us about the expansion?