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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Electromagnetic Energy and the Variational Principle Although the harmonic
modes in a dielectric medium can be quite complicated, there is a simple way to
understand some of their qualitative features. Roughly, a mode tends to
This is most easily seen after rewriting the energy functional in terms of E.
Beginning with an eigenmode H that minimizes Uf, we rewrite the numerator of (
20) using (11), (8), and (9), and we rewrite the denominator using (17) and (8).
In a harmonic mode, the physical energy is periodically exchanged between the
electric and magnetic fields, and one can show that UE = UH.14 The physical
energy and the energy functional are related, but there is an important difference.
The numerator (with the co/2a factor) is in fact 2/110 times the average
electromagnetic energy flux: that is, it is (2/110) s S = (2/uo) Res dor E. × H/2 (the
integral of the Poynting vector S from equation (25) of chapter 2). This can be
seen by ...
Since the units of A can be chosen arbitrarily, we make the convenient choice
that |A|2 is the electromagnetic energy stored in the cavity. We express the fields
in the waveguide as the sum of incoming and outgoing waveguide modes, which