We demonstrate the potential of birefringence-based, all-optical, ultrafastconversion between the transverse modes in integrated optical waveguides bymodelling the conversion process by numerically solving the multi-mode couplednonlinear Schroedinger equations. The observed conversion is induced by acontrol beam and due to the Kerr effect, resulting in a transient index gratingwhich coherently scatters probe light from one transverse waveguide mode intoanother. We introduce birefringent phase matching to enable efficientall-optically induced mode conversion at different wavelengths of the controland probe beam. It is shown that tailoring the waveguide geometry can beexploited to explicitly minimize intermodal group delay as well as to maximizethe nonlinear coefficient, under the constraint of a phase matching condition.The waveguide geometries investigated here, allow for mode conversion with overtwo orders of magnitude reduced control pulse energy compared to previousschemes and thereby promise nonlinear mode switching exceeding efficiencies of90% at switching energies below 1 nJ.
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