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.

From inside the book
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The modes of a threedimensional periodic system are Bloch states that can be
labelled by a Bloch wave vector k = k1b1 + k2b2 + k3b3 where k lies in the
Brillouin zone. For example, for a crystal in which the unit cell is a rectangular box
, the ...
As we saw in the previous chapter, this allows us to classify the modes using k, kz
, and n: the wave vector in the plane, the wave vector in the z direction, and the
band number. The wave vectors specify how the mode transforms under ...
The reason why the gap is maximized for a quarterwave stack is related to the
property that the reflected waves from each layer are ... (6) They are just like the
Bloch modes we constructed in equation (1), but with a complex wave vector k +
iκ.
Because the system is homogeneous in the z direction, we know that the modes
must be oscillatory in that direction, with no restrictions on the wave vector kz. In
addition, the system has discrete translational symmetry in the xy plane.
Consider the case where an incident plane wave strikes an interface of a
photonic crystal, as depicted in figure 14(left). ... Here, there is only translational
symmetry along directions parallel to the interface (xz), and so only the wave
vector k ...