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
We have shown that our system is symmetric under inversion only if the inversion
operator commutes with 卷;ˆ that is, we ... Continuous Translational Symmetry
Another symmetry that a system might have is continuous translation symmetry.
A generalization of this result follows from translational symmetry, which tells us
that k is conserved. In this section, we will describe this familiar phenomenon with
the symmetry language developed earlier in this chapter. We will see that, in a ...
Photonic crystals, like traditional crystals of atoms or molecules, do not have
continuous translational symmetry. Instead, they have discrete translational
symmetry. That is, they are not invariant under translations of any distance, but
rather, ...
In addition, the system has discrete translational symmetry in the xy plane.
Specifically, ε(r) = ε(r+R), as long as R is any linear combination of the primitive
lattice vectors aˆx and aˆy. By applying Bloch's theorem, we can focus our
attention on ...
All of the degenerate pairs, regardless of the complexity of their field patterns,
have the same dipole symmetry: the ... A system with a linear defect still has one
direction within the plane for which discrete translational symmetry is preserved.