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Evidence of 1+1D photorefractive stripe solitons deep in the Kerr limit

Ludovica Falsi, Alberto Villois, Francesco Coppini, Aharon J. Agranat, Eugenio DelRe, Stefano Trillo

Abstract

The Kerr nonlinearity allows for exact analytic soliton solutions in 1+1D. While nothing excludes that these solitons form in naturally-occurring real-world 3D settings as solitary walls or stripes, their observation has previously been considered unfeasible because of the strong transverse instability intrinsic to the extended nonlinear perturbation. We report the observation of solitons that are fully compatible with the 1+1D Kerr paradigm limit hosted in a 2+1D system. The waves are stripe spatial solitons in bulk copper doped potassium-lithium-tantalate-niobate (KLTN) supported by the unsaturated photorefractive screening nonlinearity. The parameters of the stripe solitons fit well, in the whole existence domain, with the 1+1D existence curve that we derive for the first time in closed form starting from the saturable model of propagation. Transverse instability, that accompanies the solitons embedded in the 3D system, is found to have a gain length much longer than the crystal. Findings establish our system as a versatile platform for investigating exact soliton solutions in bulk settings and in exploring the role of dimensionality at the transition from integrable to non-integrable regimes of propagation.

Evidence of 1+1D photorefractive stripe solitons deep in the Kerr limit

Abstract

The Kerr nonlinearity allows for exact analytic soliton solutions in 1+1D. While nothing excludes that these solitons form in naturally-occurring real-world 3D settings as solitary walls or stripes, their observation has previously been considered unfeasible because of the strong transverse instability intrinsic to the extended nonlinear perturbation. We report the observation of solitons that are fully compatible with the 1+1D Kerr paradigm limit hosted in a 2+1D system. The waves are stripe spatial solitons in bulk copper doped potassium-lithium-tantalate-niobate (KLTN) supported by the unsaturated photorefractive screening nonlinearity. The parameters of the stripe solitons fit well, in the whole existence domain, with the 1+1D existence curve that we derive for the first time in closed form starting from the saturable model of propagation. Transverse instability, that accompanies the solitons embedded in the 3D system, is found to have a gain length much longer than the crystal. Findings establish our system as a versatile platform for investigating exact soliton solutions in bulk settings and in exploring the role of dimensionality at the transition from integrable to non-integrable regimes of propagation.
Paper Structure (1 section, 8 equations, 3 figures)

This paper contains 1 section, 8 equations, 3 figures.

Table of Contents

  1. Acknowledgments

Figures (3)

  • Figure 1: (a) Existence curves, FWHM $\Delta x$ vs. $u_0$ of the soliton family, comparing exact result from Eq. \ref{['existence']} (solid black curve), with Kerr limit (dashed red curve). Insets: soliton profiles (exact, black solid; Kerr limit, dashed red) sampled at (b) $\gamma=0.95$, Kerr region; (c) $\gamma=0.7$, near the minimum where the Kerr limit starts to exhibit significant deviations; (d) $\gamma=0.02$, fully saturated regime.
  • Figure 2: (a) Profiles of the input beam (left) and the diffracted output beam (middle) when nonlinearity is deactivated, and the soliton output (right) in the Kerr limit, with a peak amplitude $u_0$ = 0.43. (b) Soliton existence curve: experimentally measured points (diamonds) compared to the analytical curve from Eq. \ref{['existence']} (solid curve).
  • Figure 3: Pseudo-color map of TI gain $g_{TI}=g_{TI}(u_0,k_y)$ vs. soliton peak amplitude $u_0$ and transverse wavenumber $k_y$. Insets: (a) Peak gain (blue curve) vs. $u_0$ compared with the existence curve (red curve); (b,c) Output beams in $(x,y)$ plane for $u_0=0.21$, when the input FWHM is reduced to 10 $\mu$m, for two different bias showing dominant diffraction (b, $V=405$ V) and break-up due to TI (c, $V=705$ V).