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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Results 15 of 6
(9) Electromagnetism as an Eigenvalue Problem As discussed in the previous
section, the heart of the Maxwell equations for a harmonic mode in a mixed
dielectric medium is a differential equation for H(r), given by equation (7). The
content of ...
In both cases, the modes of the system are determined by a Hermitian
eigenvalue equation. In quantum mechanics, the frequency ω is related to the
eigenvalue via E = ω, which is meaningful only up to an overall additive constant
V0.20 In ...
However, not all values of ky yield different eigenvalues. Consider two modes,
one with wave vector ky and the other with wave they have the same TˆR vector
ky +2π/a. A quick insertion into (7) shows that eigenvalues. In fact, all of the
modes ...
(13) Because of this periodic boundary condition, we can regard the eigenvalue
problem as being restricted to a single unit cell of the photonic crystal. As was
discussed in the section Discrete vs. Continuous Frequency Ranges of chapter 2,
...
(15) Hkn Hkn We see that OˆR Hkn also satisfies the master equation, with the
same eigenvalue as Hkn. same This means that frequency. We can the rotated
mode further prove that is the itself state an OˆR allowed Hkn the Bloch state with
...