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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Outside of a photonic band gap, some of the light can be transmitted or refracted,
propagating at some angle (of the group velocity) within the crystal. And,
depending upon the frequency, the interface periodicity, and the band structure,
a y ωa/2πc = 0.276 contours 1 x incident additional refracted waves? 0.5 M θ Γ X
re Λ θ -1 -0.5 0 0.5 refle c te d -0.5 M M crystal −θ kx -1 (2π/a) refracted 1 incident
diffractive reflections? refracted 0 flecte d air Figure 14: Left: Schematic of ...
(The amplitudes of the refracted and reflected waves, on the other hand, depend
on the surface termination and require a more detailed solution of the Maxwell
equations.) The procedure is depicted in figure 14(right). For a chosen frequency,
For instance, notice that many of the contours in figure 15 exhibit fairly sharp
corners (such as the fourth contour around the M point in the band 1). For
refracted waves near these corners, as the angle or frequency is slightly changed
, we can ...
Finally, we already observed in figure 14 a behavior quite different from ordinary
refraction: negative refraction, where a single incident beam couples to a single
refracted beam on the same side of the normal. By appropriately designing the ...