Nonlinear phase shift as a result of cascaded third-order processes

In centrosymmetric media, in addition to the third-and fifth-order nonlinearity, a cascaded chi((3)):chi((3)) nonlinearity contributes to the nonlinear refraction. The described effect takes place when the input beam is involved in nearly phase-matched third-harmonic generation. The nonlinear phase shift produced by this new cascaded nonlinearity is comparable to the nonlinear phase shift caused by the direct third-order nonlinearity chi((3)). A new analytical approach, low depletion approximation, was developed and used to study the cascaded third-order processes in the conditions of not very high third-harmonic conversion coefficients. At higher conversion coefficients the effect was studied by numerical simulations. The presence of a seeded third-harmonic wave gives another possibility of controlling the additional phase shift of the fundamental wave. The conditions for stationary copropagation of the fundamental and the generated wave an presented.