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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2 Figure 4: For a flat interface between two dielectrics ε1 and ε2, light can be
described by a ray with an incident angle θ1 and a refracted angle θ2 given by
Snell's law. When ε2 < ε1, we can have no solution θ2 for certain θ1, and the light
Similarly, if we include off-axis wave vectors, we obtain states that are localized in
the z direction, but that propagate (are guided) along the interface (kz = iκ,k = 0).
These guided modes, forming a planar waveguide, can differ markedly from the ...
In this section, we digress to briefly review a few of these phenomena, and to
relate their underlying principles to the foundations established in the preceding
chapters. Consider the case where an incident plane wave strikes an interface of
The group velocity direction at various k points is shown as arrows (black/blue/
red for incident/reflected/refracted waves). Because the wave vector component
parallel to the interface is conserved, all reflected and refracted solutions (blue
Then, to select modes with the same k, we draw a dashed line through the
incident k and perpendicular to the interface (here, along the r–M direction). The
place(s) where this dashed line intersects the photonic-crystal contours
determines the ...