Nonlinear susceptibilities integral time

In summary, in this section (Section III.B) we give a consistent procedure yielding the integral relaxation time and initial nonlinear susceptibilities for an... 

Explicit formulas for the nonlinear susceptibilities xljL Xuu derived by working out the coefficients c (t), c (r),..., respectively, in the time-ordered expansion (1.96). Straightforward evaluation of the integrals in the time-ordered expansions rapidly becomes unwieldy, and an efficient diagrammatic technique is developed in Section 11.1 for writing down the contributions to cj r) that are pertinent to any multiphoton process of interest. In Sections 11.2 and 11.3, we apply this technique to obtaining the nonlinear susceptibilities for two important nonlinear optical processes, SHG and CARS. Experimental considerations that are unique to such coherent optical phenomena are also discussed. 

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