Abstract:
Using the exact theory of multipole expansions, we construct the two-dimensional Green’s function for
photonic crystals, consisting of a finite number of circular cylinders of infinite length. From this Green’s
function, we compute the local density of states (LDOS), showing how the photonic crystal affects the
radiation properties of an infinite fluorescent line source embedded in it. For frequencies within the photonic
band gap of the infinite crystal, the LDOS decreases exponentially inside the crystal; within the bands, we find
‘‘hot’’ and ‘‘cold’’ spots. Our method can be extended to three dimensions as well as to treating disorder and
represents an important and efficient tool for the design of photonic crystal devices.
