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 6
For now, we restrict our attention to onaxis propagation and consider a mode
with frequency ω in the photonic band gap. There are no extended modes with
frequency ω inside the periodic lattice. Introducing the defect does not change
that ...
For light propagating in this plane, the harmonic modes can be divided into two
independent polarizations, each with its own band structure. As before, we can ...
Inside this gap, no extended states are permitted, and incident light is reflected.
However, at a certain critical thickness (∼1.2a for the holes and ∼2.25a for the
rods), a higherorder mode is pulled into the ... The extended modes of the crystal
are in the dark blue region, and the band gap appears in the light blue region.
The guided band is shown as a red line, and extended modes of the crystal are
shown in shaded dark blue, with the band gap(s) shaded yellow. Left: TM mode
of twodimensional crystal (uniform in z, kz =0) with a TM gap. Middle: TMlike ...
This is done in figure 2. We have defined Aω such that it is positive for an index
guided mode. We can calculate the light line in the same way we did previously
when considering the continua of extended modes for linear defects or surface ...