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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... homogeneous along the third axis. A typical specimen, consisting of a square
lattice of dielectric columns, is shown in figure 1. We imagine the columns to be
infinitely tall; the case of a finite extent in the third direction is treated in chapter 8.
They are not “twodimensional” photonic crystals, despite the resemblance: the
finite thickness in the vertical (z) direction introduces qualitatively new behavior,
just as the periodic dielectric waveguides of the previous chapter differed from ...
Third, we can now predict whether the kz → ∞ limit will yield a finite or an infinite
number of guided modes. Again, we suppose δε = 0, for simplicity. If the low-
index (Aε) regions completely surround the core, then in the scalar limit the field ...
Broadly speaking, there are three categories of problems in computational
photonics: • Frequency-domain eigenproblems: find the band structure ω(k) and
the associated fields, by expressing the problem as a finite matrix eigenproblem
fields at every point in space) to a finite number (N) of discretized unknowns. Four
important classes of discretization schemes are • Finite differences: represent
unknown functions f(x) by their values fn ≈ f(nAx) at discrete points on a grid, and