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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The smallest region within the Brillouin zone for which the ωn (k) are not related
by symmetry is called the irreducible Brillouin zone. For example, a photonic
crystal with the symmetry of a simple square lattice has a square Brillouin zone ...
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
Right: periodic waveguide of figure 2(b), including twice the irreducible Brillouin
zone. Blue shaded region is light cone (extended states propagating in air).
Discrete guided bands are labelled even or odd according to the y=0 mirror
Write the harmonic modes in Bloch form: (r)eik·r. Hk(r) = uk What are the
nonredundant values for the wave vector k? They lie in the irreducible Brillouin
zone in reciprocal space. They lie in the irreducible Brillouin zone in reciprocal
The reciprocal lattice is a body-centered cubic (bcc) lattice, and the Brillouin zone
is a truncated octahedron with center at r. Also shown are some of the labels that
are traditionally given to the special points in the zone. The irreducible Brillouin ...