Observation of fractional evolution in nonlinear optics

TL;DR

This paper reports the experimental observation of a new class of optical solitons governed by a fractional nonlinear wave equation, revealing unique properties like non-exponential tails and minimal time-bandwidth product.

Contribution

First experimental realization and full characterization of fractional Laplacian governed optical solitons in nonlinear optics.

Findings

Observation of fractional optical solitons with non-exponential tails

Characterization of solitons with very small time-bandwidth product

Validation of fractional nonlinear wave equation in optical systems

Abstract

The idea of fractional derivatives has a long history that dates back centuries. Apart from their intriguing mathematical properties, fractional derivatives have been studied widely in physics, for example in quantum mechanics and generally in systems with nonlocal temporal or spatial interactions. However, systematic experiments have been rare due to challenges associated with the physical implementation. Here we report the observation and full characterization of a family of temporal optical solitons that are governed by a nonlinear wave equation with a fractional Laplacian. This equation has solutions with unique properties such as non-exponential tails and a very small time-bandwidth product.