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Observation of fractional evolution in nonlinear optics
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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.
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Quiescent and traveling solitons in the fractional parametrically driven damped nonlinear Schr\"{o}dinger equation
In the fractional parametrically driven damped NLS equation, quiescent ψ+ solitons are stable below a Lévy-index-dependent threshold, while lossless moving solitons are stable only in intermediate or high velocity windows.
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