Introduction to Photonic Crystals: Bloch’s Theorem, Band ...

Introduction to Photonic Crystals: Bloch s Theorem, Band Diagrams, and Gaps(But No Defects)Steven G. Johnson and J. D. Joannopoulos, MIT3rd February 20031 IntroductionPhotonic crystals are periodically structured electromagnetic media, generallypossessingphotonic band gaps: ranges of frequency in which light cannot prop-agate through the structure. This periodicity, whose lengthscale is proportionalto the wavelength of light in the band gap, is the electromagnetic analogue ofa crystalline atomic lattice, where the latter acts on the electron wavefunctionto produce the familiar band gaps, semiconductors, and so on, of solid-statephysics. The study of Photonic crystals is likewise governed by the Bloch-Floquet theorem, and intentionally introduced defects in the crystal (analo-gous to electronic dopants) give rise to localized electromagnetic states: linearwaveguides and point-like cavities.

applied to electromagnetism by casting Maxwell’s equations as an eigenproblem in analogue with Schr¨odinger’s equation. By combining the source-free Fara-day’s and Ampere’s laws at a fixed frequency ω, i.e. time dependence e−iωt, one can obtain an equation in only the magnetic field H~ : ∇×~ 1 ε ∇×~ H~ = ω c 2 H,~ (1)

Tags:

  Laws, Photonics, Electromagnetism

Information

Related search queries