Optimization of nonlinear enhancement through linear dispersion engineering

Abstract

We consider nonlinear pulse propagation in media with a dispersion relation exhibiting $J$ periodically spaced identical maxima in a co-moving frame. The nonlinear interactions lead to $J$ pulses centered at each of these frequencies. These pulses propagate at the same group velocity and interfere, leading to a highly non-uniform signal in time. This results in the enhancement of effective nonlinear effects, as we recently demonstrated experimentally [Nat. Phys. {\bf 18}, 59 (2022)]. Here we present a detailed theoretical and numerical study of this nonlinear enhancement. We show that the amplitudes of the frequency components approximately follow a simple relation, which allows us to derive that the nonlinear enhancement factor increases as $0.687J$. Hence, enhancements of order $10$ can be achieved with $15$ frequency components.