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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The modes of 卷ˆ Tdε(r) = ε(r−d) = ε(r), or equivalently, can now be classified
according to how they behave A system with under all of the Tˆd continuous 's for
that direction. translation symmetry in the z direction is invariant What sort of
function ...
If the glass extends much farther in the x and y directions than in the z direction,
we may consider this system to be onedimensional: the dielectric function ε(r)
varies in the z direction, but has no dependence on the inplane coordinate P.
This ...
a z Figure 5: A dielectric configuration with discrete translational symmetry. If we
imagine that the system continues forever in the y direction, then shifting the
system by an integral multiple of a in the y direction leaves it unchanged.
The term “onedimensional” is used because the dielectric function ε(z) varies
along one direction (z) only. The system consists of alternating layers of materials
(blue and green) with different dielectric constants, with a spatial period a.
THAT WE HAVE discussed some interesting properties of onedimensional
photonic crystals, in this chapter we will see how the situation changes when the
crystal is periodic in two directions and homogeneous in the third. Photonic band
...