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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 P ex (r,t). It is shown that the induced field is expressed as a superposition of P ex (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 thedoi:10.1103/physrevb.54.5732 pmid:9986538 fatcat:cswuqyzylrdsjflihsfjvovqim