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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Equivalently, if one looks at the Fourier components of the field pattern, the more
delocalized it is in space, the more localized its Fourier transform can be—this
allows most of the Fourier components to lie inside the light cone and not radiate.
Suppose that we have a finitewidth beam of light propagating in the ˆx direction,
and consider its decomposition into different ky components (i.e., its Fourier
transform along the y dimension). An infinitely wide beam (a plane wave)
consists of ...
To see how that works, we begin in one dimension where it corresponds to the
familiar Fourier series. In particular, we are solving (1) for a periodic function uk(x
) = uk(x + a) with period a. It is a remarkable fact, first postulated by Joseph
Fourier ...
Given the transverse Fourierseries representation (6), we now derive a set of
equations to determine the coefficients cG by substituting (6) into the
eigenequation with ∫ e−iG (1). ·r), By we Fourier obtain equations transforming
both sides of ...
Unfortunately, for discontinuous dielectric structures, the corresponding Fourier
transform converges rather slowly (the Fourier coefficients of ε−1 decrease
proportional to 1/G), which leads to problems noted by Sözüer et al. (1992). (
Related ...