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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The key to a quantitative understanding of the large-kz limit is to realize that this
regime is asymptotically described by a scalar wave equation that is independent
of kz. Consequently, for large kz, the modes approach kz-independent “linearly ...
We may therefore use the scalar approximation (3) in the regions where Aε = 0,
and simply set ψ = 0 where Aε = 0.9 ... Second, each mode ψ in the scalar limit, a
so-called LP mode (Gloge, 1971), corresponds toseveralvectorial solutions of the
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 ...
In this limit, as described in the subsection The scalar limit and LP modes of
chapter, the system is again equivalent to a two-dimensional system—one in
which the holes are replaced by perfect-metal rods and only an analogue of the
These were precisely the conditions in which the scalar limit applies. In this limit,
we can describe the mode as a linear polarization multiplied by a scalar
amplitude ψ(x,y) that is zero in the cladding. In reality, there is some small