26th Australian Institute of Physics Congress and the Australian and New Zealand Conference on Optics and Photonics

Cubic Fractional Solitons in a Mode-Locked Fiber Laser

Not scheduled

20m

Belinda Hutchinson Building (The University of Sydney )

Contributed Oral ANZOS | Photonics and Optics (ANZCOP)

Description

Fractional derivatives, and particularly fractional Laplacian operators, have been studied intensively in physics, mathematics and engineering [1]. In optics, such operators offer a route to generalize the conventional nonlinear Schrödinger equation by replacing the usual quadratic dispersion with a fractional dispersion law. The fractional Laplacian operator is written as {(-\nabla^2)}^{\alpha/2}. While most studies of fractional optical systems have focused on Lévy indices in the range (1<α<2), higher-order fractional regimes remain unexplored experimentally [2].
In this study, we report the observation of optical solitons formed in the presence of Kerr nonlinearity and a piecewise cubic dispersion relation. This dispersion profile is chosen such that the corresponding group velocity varies monotonically with frequency, a necessary condition for stable soliton formation. Unlike conventional quadratic dispersion (α=2) or pure-quartic dispersion (α=4), the cubic dispersion considered here has a discontinuity in its third derivative. In the time domain, this non-analytic spectral response is equivalent to a nonlocal fractional Laplacian operator with Lévy index (α=3).
The cubic solitons are generated in a passively mode-locked fibre laser incorporating an intracavity spectral pulse shaper, which imposes the desired cubic dispersion while compensating quadratic and third order dispersion [3]. The measured optical spectra and retrieved temporal pulse profiles are in good agreement with numerical stationary solutions of the governing fractional nonlinear wave equation. The retrieved pulses exhibit properties distinct from quadratic and pure-quartic solitons. In particular, the energy scaling E\propto\tau^{-2} is intermediate between conventional solitons (E\propto\tau^{-1}), and pure-quartic solitons (E\propto\tau^{-3}), providing strong evidence for the distinctive scaling properties of the cubic solitons emitted by our laser [4]. This confirms that the observed pulses constitute a distinct family of cubic fractional solitons.

1. B. A. Malomed, 022102429.
2. T. Hoang, et al, Nature Communications.
3. A. F. Runge, et al, Nature Photonics.
4. T.T. Ha, et al, APL Photonics.