Photonic Crystals: Molding the Flow of Light (Second Edition)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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... Fourier modes). From these building blocks, we develop all of the needed mathematical and physical tools. We hope that interested undergraduates will find the text approachable, and that professional researchers will find our heuristics ...
... Fourier analysis that we can build any solution with an appropriate combination of these harmonic modes. Often we will refer to them simply as modes or states of the system. For mathematical convenience, we employ the standard trick of ...
... Brillouin zone, or alternatively by picking the k + G corresponding to the largest Fourier component. Care must be taken in interpreting such a quantity, however. 1 Interestingly, in Lord Rayleigh's first attack on the problem 42 CHAPTER 3.
... Fourier transform of the time-varying field in the cavity has a squared amplitude (L0/2Q)2], and that is a Lorentzian peak, proportional to 1/[(L − L0)2 + 1/Q is the peak's fractional width at half-maximum. Finally, Q plays a critical ...
... Fourier transform of such a pattern yields a Lorentzian-like peak centered at the Brillouin-zone edge, k = 7/a. The radiation losses come from the tails of this Fourier peak that lie within the light cone. As the substrate index is ...
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Photonic Crystals: Innovative Systems, Lasers and Waveguides Alessandro Massaro Limited preview - 2012 |