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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Chapter 4 includes a section on how to best quantify the band gap of a photonic
crystal and a section describing the novel ... new aspects of 3D photonic crystal
structures, including the photonic structure of several well known geometries.
Photonic band gaps appear in the plane of periodicity. For light propagating in
this plane, the harmonic modes can be divided into two independent
polarizations, each with its own band structure. As before, we can introduce
defects in order to ...
Figure 2: The photonic band structure for a square array of dielectric columns
with r = 0.2a. The blue bands represent TM modes and the red bands represent
TE modes. The left inset shows the Brillouin zone, with the irreducible zone
1.5 ω = ck z c 1 0.5 Γbands K bands 0 0 1 2 3 4 5 y en c eq u Fr Γ M K a/2π Γ
lowest photonic band Perpendicular wave vector k z a/2π k z Figure 11: The out-
of-plane band structure of the triangular lattice of air columns for the first few
Figure 20: The projected band structure of the constant-x surface of the square
lattice of alumina rods in air. The shading denotes regions in which light is
transmitted (purple EE states), internally reflected (red DE states), and externally