We show that useful non-instantaneous 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 blue shifts 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.
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