An Introduction to Photonic Crystals

Abstract

During the past five years, there has emerged a new class of materials called photonic band gap materials or, more simply, photonic crystals. The underlying concept behind these materials stems from early notions by Yablonovitch [1] and John [2]. In a nutshell, the basic idea is to design materials so they can effect the properties of photons in much the same way ordinary solids or crystals effect the properties of electrons. Now, the properties of electrons are governed by Schroedinger’s equation

$$ \left\{ { - \frac{{{{\nabla }^{2}}}}{2} + V(r)} \right\}\psi (r) = E\psi (r) $$

((1))

and properties of photons by Maxwell’s equations, which can be cast in a form very reminiscent of the Schroedinger equation,

$$ \left\{ {\nabla \times \frac{1}{{\varepsilon (r)}}\nabla \times } \right\}H(r) = {{\omega }^{2}}H(r) $$

((2))

.