OPTICAL-RESPONSE OF 3-DIMENSIONAL PHOTONIC LATTICES - SOLUTIONS OF INHOMOGENEOUS MAXWELLS EQUATIONS AND THEIR APPLICATIONS

We have formulated a Green's function method for the radiation field i n an arbitrary three-dimensional photonic lattice to deal with the sou rce term of an extrinsic polarization field P-ex(r,t). It is shown tha t the induced field is expressed as a superposition of P-ex(r,t) itsel f and the photonic-band eigenmodes of a nonzero frequency. The longitu dinal eigenmodes of zero frequency, which are important for the closur e relation of photonic bands, is shown to contribute nothing to the pr opagating electric held. We have applied this method to the treatments of sum frequency generation, dipole radiation, and free induction dec ay.