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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We will use the former name.5 One key fact about Bloch states is that the Bloch
state with wave vector ky and the Bloch state ... As explained in appendix B, the
vectors (a1, a2 ,a3) give rise to three primitive reciprocal lattice vectors (b1 ,b2 ,
b3) ...
Those vectors q such that exp(iq · R) = 1, or, equivalently, q · R = 2πN (N an
integer), are called reciprocal lattice vectors and are usually designated by the
letter G. They form a lattice of their own; for example, adding two reciprocal lattice
...
One way to do this is to exploit a feature of the cross product. Remembering thatx·
(x×y) = 0 for any vectors xand y, we can construct the primitive reciprocal lattice
vectors with the following recipe: 2πa2 3 2π a3 1 b3 = 2πa1 × a2 . (5) b1 = a1 ...
The dotted line is the perpendicular bisector of the line joining two reciprocal
lattice points (blue). If we choose the left point as the origin, any lattice vector (
such as k) that reaches to an arbitrary point on the other side (red) can be
expressed as ...
In the middle is the corresponding reciprocal lattice, which in this case is arotated
version of the original. On the right is the ... The square lattice vectors, its
reciprocal lattice vectors, and its Brillouin zone are shown in figure 2. We can
handle ...