Modeling-shortcomings due to dismissing the multifrequency character of nonlinearities

The striking behavior of optical pulses propagating under dispersive nonlinearities reported theoretically in recent years is fueling the interest in these new phenomena to enhance the state-of-the-art control of light. To explore these effects properly, the full frequency dependence of nonlinearities should be incorporated into the pulse propagation equation so that accurate guidelines for engineering nonlinear dispersion could be derived. Nevertheless, this goal comes at the expense of some approximation about the truly multifrequency nature of nonlinearities, and hence of additional uncertainty in the theoretical predictions. Using the cancellation of instabilities during the spectral broadening of long pulses-one major practical consequence of a suitable design of nonlinear dispersion-as a test bed, in this Letter, we demonstrate analytically and numerically how an incomplete description of multifrequency nonlinearities may translate into substantial deviations compared to more rigorous treatments.