Photonic Crystals: Molding the Flow of Light - Second Edition
Princeton University Press, Oct 30, 2011 - Science - 304 pages
Since it was first published in 1995, Photonic Crystals has remained the definitive text for both undergraduates and researchers on photonic band-gap 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 up-to-date, 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 solid-state 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, photonic-crystal slabs, and photonic-crystal 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 three-dimensional photonic crystals, an extensive tutorial on device design using temporal coupled-mode 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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Localized. Modes. at. Defects. Now that we understand the band structure of a
perfectly periodic system, we can examine systems in which the translational
symmetry has been broken by a defect. Suppose that the defect consists of a
If a defect does retain a point symmetry, then we can use that symmetry to classify
the defect modes, just as we did in ... However, since we expect a smooth
transition between localized and continuum behavior, the mode still concentrates
We have already seen that defects in photonic crystals can localize light modes.
In one dimension, this meant we could confine light to a single plane. In two
dimensions, we could localize light to a single line, which can also be considered
0.6 Air Defect Dielectric Defect 0.55 Photonic Band Gap y c n e u q e r F 0.5 Air
Defect Dielectric Defect 0.45 0 1 2 3 4 5 6 7 8 Defect Volume (λ/2n)3 Figure 16:
Plotted are the frequencies of the localized modes of Yablonovite as the defect
The simplest case to handle is that of localized modes, such as the waveguide
and cavity modes trapped around line and point defects, respectively. In this case
, we can use a supercell approximation: periodic boundary conditions, but with a