Bond Model of Second-and Third-Harmonic Generation in Body- and Face-Centered Crystal Structures

In this work, we describe the third- and fourth-rank tensors of body- and face-centered cubic systems and derive the s- and p-polarized SHG far field using the simplified bond-hyperpolarizability model. We also briefly discuss bulk nonlinear sources in such structures: quadrupole contribution, spatial dispersion, electric-field second-harmonic generation, and third-harmonic generation, deriving the corresponding fourth rank tensor. We show that all the third- and fourth-rank tensorial elements require only one independent fitting parameter.