Optical Networks, 3rd Edition

APPENDIX F

Nonlinear Polarization

THE LINEAR EQUATION (2.7) for the relationship between the induced polarization P and the applied electric field E holds when the power levels and/or bit rates are moderate. When this is not the case, this must be generalized to include higher powers of E(r, t). For an isotropic medium and an electric field polarized along one direction so that it has a single component E(r, t), this relationship can be written as follows:

(F.1)

Now X⁽¹⁾(r,t) is called the linear susceptibility to distinguish it from X⁽¹⁾(r,t), i = 2,3, …, which are termed the higher-order nonlinear susceptibilities. Owing to certain symmetry ...