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

Kazuaki Sakoda, Kazuo Ohtaka
1996 Physical Review B (Condensed Matter)  
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 the
more » ... ng to the propagating electric field. We have applied this method to the treatments of sum frequency generation, dipole radiation, and free induction decay.
doi:10.1103/physrevb.54.5732 pmid:9986538 fatcat:cswuqyzylrdsjflihsfjvovqim