Alternative nonlinear-optical expansion and diagrammatic approach:Nth-order dephasing-induced effects

Abstract

We show that dephasing-induced nonlinear-optical effects whose amplitudes are proportional to trinomials of dephasing rates, ${\Gamma }_{\mathrm{ij}}$+${\Gamma }_{\mathrm{jk}}$-${\Gamma }_{\mathrm{ik}}$, exist in all nonlinear orders of perturbation theory. To do this, we derive a new form for the perturbation expansion of the susceptibility, equivalent to the currently used expansion, but which writes each order as a sum of (1) terms due to single-sided diagrams, and (2) correction terms, all of which are proportional to trinomials of dephasing rates. The proof of this result utilizes a diagrammatic approach involving a new type of double-sided diagram for the latter terms. These diagrams immediately yield the terms proportional to trinomials of dephasing rates in all orders without the need for algebraic manipulation. This approach also reveals some general properties of the Nth-order susceptibility.