Second-order nonlinear polarization matter

Second-Order Nonlinear Polarization of Matter and Second-Order NLO Effects... 

The TPA cross section (7>) is proportional to the second-order nonlinear polarizability y. This is derived by consideration of interactions of light with matter causing a change in the dipole moment that is the induced dipole moment /iirld. Induced polarization Pind is proportional to /(ind and the field strength E of the incident light, Eq. (7) [50, 73] ... 

Owing to the coherence, we need to consider the macroscopic evolution of the field in a medium that shows a macroscopic polarization induced by the field-matter interaction. This will be done in three steps. First, the polarization induced by an arbitrary field will be calculated and expanded in power series in the field, the coefficients of the expansion being the material susceptibilities (frequency domain) or response function (time domain) of wth-order. Nonlinear Raman effects appear at third order in this expansion. Second, the perturbation theory derivation of the third-order nonlinear susceptibility in terms of molecular eigenstates and transition moments will be outlined, leading to a connection with the spontaneous Raman scattering tensor components. Last, the interaction of the initial field distribution with the created polarization will be evaluated and the signal expression obtained for the relevant techniques of Table 1. 

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