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.
What do the field profiles of the electromagnetic modes at these points look like?
The field patterns of the TM modes of the first band (dielectric band) and second
band (air band) are shown in figure 3. For modes at the r point, the field pattern is
D z field at X (TM) band 1 band 2 negative positive Figure 6: Displacement fields
of X-point TM modes for a square array ... Again, we turn to the field patterns of
the modes in the two lowest bands to understand the appearance of the band
This claim is verified by calculating the concentration factors for the field
configurations. ... In the previous two sections, we used the field patterns as our
guide to understand which aspects of two-dimensional photonic crystals lead to
TM and ...
The other two insets suggest the field patterns of the modes, within each column (
red/blue for positive/negative fields). the left inset shows the π-like pattern for
band 3; the right shows the δ-like pattern for the bottom of band 4. We illustrate
radiation pattern from a localized source, it is natural to represent the radiated
field by a multipole expansion.17 Depicted schematically in figure 14, this is a
decomposition of the field into a sum of dipole, quadrupole, hexapole, etc.,