Management of solitons in medium with competing cubic and quadratic nonlinearities

TL;DR

This paper explores how to control solitons in media with both quadratic and cubic nonlinearities by using rapid parameter modulations, deriving averaged equations, and confirming results through numerical simulations.

Contribution

It introduces two modulation schemes for managing solitons and derives averaged wave equations, providing new insights into stabilization regions and effective nonlinearities.

Findings

Stabilization regions identified for mismatch management.

Effective $$ nonlinearity depends on harmonic intensity imbalance.

Numerical simulations confirm predictions from averaged equations.

Abstract

Management of solitons in media with competing quadratic and cubic nonlinearities is investigated. Two schemes, using rapid modulations of a mismatch parameter, and of the Kerr nonlinearity parameter are studied. For both cases, the averaged in time wave equations are derived. In the case of mismatch management, the region of the parameters where stabilization is possible is found. In the case of Kerr nonlinearity management, it is shown that the effective $\chi^{(2)}$ nonlinearity depends on the intensity imbalance between fundamental (FH) and second (SH) harmonics. Predictions obtained from the averaged equations are confirmed by numerical simulations of the full PDE's.