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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We conclude this section by showing what it means for an operator to be
Hermitian. First, in analogy with the inner product of two wave functions, we
define the inner product of two vector fields F(r) and G(r) as (F,G) ∫ d3rF∗(r) ·G(r)
, (12) where ...
that Ó is Hermitian," we perform an integration by parts" twice: a 3. Tok 1 (F, GG)
= | dor F : V × iv x G – sarov. F. v. G (14) F so sy X (ov X r)| : G = (ÖF,G). In
performing the integrations by parts, we neglected the surface terms that involve
It is a simple matter to convert this into an ordinary eigenproblem by dividing (26)
by ε, but then the operator is no longer Hermitian. If we stick to the generalized
eigenproblem, however, then simple theorems analogous to those of the
considerably by allowing for small nonlinearities and material absorption, using
the well-developed perturbation theory for linear Hermitian eigenproblems. More
generally, we may be interested in many types of small deviations from an initial ...
We proved the variational theorem for the Maxwell eigenproblem, but the same is
true of any Hermitian eigenproblem, and in particular for our finite eigenproblem
Ax = ω2Bx. That is, the smallest eigenvalue ω20 satisfies x†Ax ω20 = minx ...