Observation of Optical Solitons Governed by Fractional Dispersion

Solitons are pulses that propagate while maintaining their shape by balancing nonlinear and dispersive effects [1]. Optical solitons have been used in numerous applications, such as telecommunications and ultrafast lasers [1], [2]. Typical studies considered even order dispersion because it provides the monotonic increase in group velocity with increasing frequency, required for soliton formation [3]. Here, we report the generation and study of a novel type of optical soliton governed by a dispersion relation of the form <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\beta(\omega)=-\vert \beta_{1}\Vert \omega-\omega_0)\vert$</tex> (see Fig. 1(a)) [4]. This dispersion profile has a discontinuous derivative at the central frequency <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\omega_{0}$</tex> and decreases linearly away from the frequency. It can be mathematically described by a fractional Laplacian [5].