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. 18, 59 (2022)NPAHAX1745-247310.1038/s41567-021-01400-2]. 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 0.687 J . Hence, enhancements of order 10 can be achieved with 15 frequency components.