Optical response of three-dimensional photonic lattices: Solutions of inhomogeneous Maxwell’s equations and their applications

We have formulated a Green's function method for the radiation field in an arbitrary three-dimensional photonic lattice to deal with the source term of an extrinsic polarization field Pₑₓ(r,t). It is shown that the induced field is expressed as a superposition of Pₑₓ(r,t) itself and the photonic-band eigenmodes of a nonzero frequency. The longitudinal eigenmodes of zero frequency, which are important for the closure relation of photonic bands, is shown to contribute nothing to the propagating electric field. We have applied this method to the treatments of sum frequency generation, dipole radiation, and free induction decay. {} 1996 The American Physical Society.