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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From inside the book
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... Eigenvalue Problem General Properties of the Harmonic Modes Electromagnetic Energy and the Variational Principle Magnetic vs. Electric Fields The Effect of Small Perturbations Scaling Properties of the Maxwell Equations Discrete vs ...
... eigenvalue problem. This brings the electromagnetic problem into a close analogy with the Schrödinger equation, and allows us to take advantage of some well-established results from quantum mechanics, such as the orthogonality of modes ...
... Eigenvalue Problem As discussed in the previous section, the heart of the Maxwell equations for a harmonic mode in a mixed dielectric medium is a differential equation for H(r), given by equation (7). The content of the equation is this ...
... eigenvalue equation by operating on the wave function with the Hamiltonian. A reader familiar with quantum mechanics might recall some key properties of the eigenfunctions of the Hamiltonian: they have real eigenvalues, they are ...
... eigenvalues of 6 must be real numbers. Suppose H(r) is an eigenvector of 6 with eigenvalue (a/c)*. Take the inner product of the master equation (7) with H(r): ÖH(r) = (a,”/co)H(r) = (H, ÖH) = (a,”/co)(H, H) (15) = (H, 6H) = (a,”/co)*(H ...
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Photonic Crystals: Innovative Systems, Lasers and Waveguides Alessandro Massaro Limited preview - 2012 |