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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(17) We conclude that when there is rotational symmetry in the lattice, the
frequency bands ωn (k) have additional redundancies within the Brillouin zone.
In a similar manner, we can show that whenever a photonic crystal has a rotation,
By applying Bloch's theorem, we can focus our attention on the values of k that
are in the Brillouin zone. As before, we use the label n (band number) to label the
modes in order of increasing frequency. a z x y Figure 1: A two-dimensional ...
we found that a photonic band gap opens up at the Brillouin-zone edge (ω = c|k|
= cπ/a) even for arbitrarily small values of the dielectric contrast. Given this fact,
one might expect that in three dimensions we could achieve the same property—
Reciprocallattice point B k G Reciprocallattice point A G k Figure 1:
Characterization of the Brillouin zone. The dotted line is the perpendicular
bisector of the line joining two reciprocal lattice points (blue). If we choose the left
point as the origin, ...
On the right is the construction of the first Brillouin zone: taking the center point as
the origin, we draw the lines connecting the origin to the other lattice points (red),
their perpendicular bisectors (blue), and highlight the square boundary of the ...