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
Results 15 of 5
A given crystal might also be left invariant after a rotation, a mirror reflection, or an
inversion is performed. To begin, we examine the conclusions we can draw
about the modes of a system with rotational symmetry. Suppose the operator (3 ×
3 ...
If rotation by R leaves the system invariant, then we conclude (as before) that [卷,ˆ
OˆR] = 0. Therefore, we may carry out the following manipulation:卷(ˆOˆR ) = OˆR
(卷Hˆkn) = ( ωnc(k) ) 2 (OˆR ). (15) Hkn Hkn We see that OˆR Hkn also satisfies ...
All of the degenerate pairs, regardless of the complexity of their field patterns,
have the same dipole symmetry: the degenerate partner differs by a 90◦ rotation,
they transform the same way under the x = 0 and y = 0 mirror planes as well as ...
For instance, in the defects of figures 14 and 15, we see that our defects have
been chosen to preserve the threefold rotation symmetry of the crystal.13 We
could still classify the modes, including the new localized modes, by how they ...
Here, due to the large index contrast and sixfold symmetry, the two orthogonal
modes are neither purely linearly polarized nor are they exactly related by a 90◦
rotation.6 For larger values of kz, three additional guided bands are localized.