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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(26) Because there are operators on both sides of this equation, it is referred to
as a generalized eigenproblem. It is a simple matter to convert this into an
ordinary eigenproblem by dividing (26) by ε, but then the operator is no longer
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
Frequency-Domain Eigenproblems A frequency-domain eigensolver solves the
Maxwell eigenproblem for the frequencies of a periodic system (or nonperiodic,
as described below), as given by equation (11) of chapter 3: [ (ik+ ∇) × 1ε(r) ] (ik+
In general, such a discretization yields a finite generalized eigenproblem Ax=
ω2Bx, where A and B are N×N matrices and x is the eigenvector. Since the
original eigenproblem is Hermitian, the discretization can be chosen so that A
and B are ...
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 ...