Analytical model for transverse mode conversion at all-optically induced, transient long-period gratings: from continuous-wave to ultrafast

Hellwig T, Sparenberg K, Fallnich C

Abstract

Transverse mode conversion at an index grating, all-optically induced by multi-mode interference and the optical Kerr effect, is commonly studied by numerical simulations relying on either multi-mode implementations of the generalized nonlinear Schrödinger equation or beam propagation methods. Here, we present and discuss an analytical model describing the directed energy exchange between two probe modes moderated by two control modes. The analytical model can be derived in a four-wave mixing representation as well as in a material representation in analogy to the different numerical approaches demonstrating their equivalence. The analytical nature of the model is used to provide general insight into the conversion process in dependence on phase mismatch as well as induced coupling strength. While being a continuous-wave model, the applicability of the model for mode conversion using ultrashort pulses is discussed and guidelines for using the model as a first estimate for experiments or for more precise but time-consuming numerical simulations are given.