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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(a) (b) (c) a a R Figure 1: Three examples of photonic-crystal fibers. (a) Bragg
fiber, with a one-dimensionally periodic cladding of concentric layers. (b) Two-
dimensionally periodic structure (a triangular lattice of air holes, or “holey fiber”),
Then, for photonic-bandgap fibers, we start with the case of two-dimensional
periodicity and follow with onedimensional periodicity. The reason for this
reversal is not only that the holey bandgap fibers are closely related to their index
However, as first pointed out by Birks et al. (1997), this need not be true of
photonic-crystal fibers: they can remain endlessly single-mode, regardless of
wavelength (limited only by the material properties). In figure 2, we saw that our
holey fiber ...
This scale-invariant ratio tells us the size of the mode relative to the “natural
diameter” of half a wavelength in the dielectric; it also lets us compare effective
areas for the case where we keep λ fixed and vary a. In both the holey fiber and
2 photonic crystal light cone 1.9 1.8 1.7 1.6 1.5 1.4 k ω = c z 0 max Intensity 1.3
1.4 1.5 1.6 1.7 1.8 1.9 2 Wave vector k z a/2π c Figure 12: Band diagram and
mode intensity patterns (insets) of a hollow-core holey fiber with a larger air core