Photonic Crystals: Molding the Flow of Light  Second EditionSince it was first published in 1995, Photonic Crystals has remained the definitive text for both undergraduates and researchers on photonic bandgap 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 uptodate, 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 solidstate 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, photoniccrystal slabs, and photoniccrystal 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 threedimensional photonic crystals, an extensive tutorial on device design using temporal coupledmode 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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It follows that a* = (a,”)”, or that w” is real. By a different argument, we can also
show that w” is always nonnegative for e0. Set F=G=H in the middle equation "
The property that Ó is Hermitian is closely related to the Lorentz reciprocity
theorem, ...
This useful but somewhat vague notion can be expressed precisely through the
electromagnetic variational theorem, which is analogous to the variational
principle of quantum mechanics. In the lowestfrequency mode, particular,
corresponds ...
Table 1 Quantum Mechanics Electrodynamics Discrete translational symmetry V(
r) = V(r+R) ε(r) = ε(r+R) Commutation relationships [H,ˆ TˆR] = 0 [卷,ˆ TˆR ] = 0
Bloch's theorem Fkn (r)eik·r Hkn (r)eik·r (r) = ukn (r) = ukn Quantum mechanics vs.
By applying Bloch's theorem, we can focus our attention on the values of k that
are in the Brillouin zone. As before, we use the label n (band number) to label the
modes in order of increasing frequency. a z x y Figure 1: A twodimensional ...
In contrast, for onedimensional and twodimensional crystals, it typically appears
that even arbitrarily small defects can localize modes. This is the electromagnetic
analogue of a famous theorem of quantum mechanics. The theorem states that ...