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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For example, since the defect in the left panel of figure 14 is unchanged under 90
◦ rotations, we can immediately predict the symmetry properties of the doubly
degenerate modes that cross the gap for 0 < An < 0.8. They must be a pair of
y x neg pos neg Ey Ex pos Figure 3: Electric-field pattern for the doubly
degenerate fundamental mode of figure 2. Their polarizations are nearly
orthogonal everywhere: the mode pictured at left is mostly Ex, and the mode
pictured at right is ...
There are two possibilities. If ψ is a nondegenerate mode, then we get two
vectorial modes ψˆx and ψˆy, corresponding to a doubly degenerate “linearly
polarized” state. If ψ itself is a doubly degenerate state with two solutions ψ(1)
and ψ(2), ...
ωa/2πc. = 1.68 kza/2π= 1.6 kza/2π = 1.7 0 max Intensity Figure 11: Intensity
patterns (ˆz · Re[E∗ × H]) of three doubly degenerate modes of a hollow-core
holey fiber (ε shaded green), corresponding to the dots on the thick red lines in
PMD arises in an ordinary fiber because the operating mode is doubly
degenerate, with two orthogonal polarizations. Any imperfection or stress in the
fiber, however, can break the symmetry and split these two polarizations into
modes that ...