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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sinusoidally (harmonically) with time. This is no great limitation, since we know by
Fourier analysis that we can build any solution with an appropriate combination
of these harmonic modes. Often we will refer to them simply as modes or states ...
In addition, the Hermiticity of 卷ˆ forces any two harmonic modes H1(r) and H2(r)
with different frequencies ω1 and ω 2 to have an inner product of zero. Consider
two normalized modes, H1(r) and H2(r), with frequencies ω1 and ω 2: ω21(H2 ...
But the notion that orthogonal modes of different frequency have different
numbers of spatial nodes holds rather generally. In fact, a given harmonic mode
will generally contain more nodes than lowerfrequency modes. This is
analogous to the ...
In a harmonic mode, the physical energy is periodically exchanged between the
electric and magnetic fields, and one can show that UE = UH.14 The physical
energy and the energy functional are related, but there is an important difference.
Suppose, for example, we have an electromagnetic eigenmode H(r) of frequency
ω in a dielectric configuration ε(r). We recall the master equation (7): ∇ × ( 1ε(r) )
= ( ω c )2 H(r). (31) Now suppose we are curious about the harmonic modes in ...