Controllable Raman-like nonlinearities from nonstationary, cascaded quadratic processes

We show that useful noninstantaneous, nonlinear phase shifts can be obtained from cascaded quadratic processes in the presence of group-velocity mismatch. The two-field nature of the process permits responses that can be effectively advanced or retarded in time with respect to one of the fields. There is an analogy to a generalized Raman-scattering effect, permitting both red and blueshifts of short pulses. We expect this capability to have many applications in short-pulse generation and propagation, such as the compensation of Raman-induced effects and high-quality pulse compression, which we discuss.