Observation of the spectral bifurcation in the Fractional Nonlinear Schr\"{o}dinger Equation

• URL: http://arxiv.org/abs/2311.15150v1
• Date: Sun, 26 Nov 2023 00:34:15 GMT
• Title: Observation of the spectral bifurcation in the Fractional Nonlinear Schr\"{o}dinger Equation
• Authors: Shilong Liu, Yingwen Zhang, St\'ephane Virally, Ebrahim Karimi, Boris A. Malomed, Denis V. Seletskiy
• Abstract summary: We report a comprehensive investigation and experimental realization of spectral bifurcations of ultrafast soliton pulses. We propose an effective force' model based on the frequency chirp, which characterizes their interactions as either repulsion', attraction', or equilibration. The proposal for engineering spectral bifurcation patterns holds significant potential for ultrafast signal processing applications.
• Score: 6.4477590105028
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We report a comprehensive investigation and experimental realization of spectral bifurcations of ultrafast soliton pulses. These bifurcations are induced by the interplay between fractional group-velocity dispersion and Kerr nonlinearity (self-phase modulation) within the framework of the fractional nonlinear Schr\"{o}dinger equation. To capture the dynamics of the pulses under the action of the fractional dispersion and nonlinearity, we propose an effective `force' model based on the frequency chirp, which characterizes their interactions as either `repulsion', `attraction', or `equilibration'. By leveraging the `force' model, we design segmented fractional dispersion profiles that directly generate spectral bifurcations \{1\}$\rightarrow$ \{N\} at relevant nonlinearity levels. These results extend beyond the traditional sequence of bifurcations \{1\}$\rightarrow$ \{2\}$\rightarrow$ \{3\} ... $\rightarrow$ \{N\} associated with the growth of the nonlinearity. The experimental validation involves a precisely tailored hologram within a pulse shaper setup, coupled to an alterable nonlinear medium. Notably, we achieve up to N=5 in \{1\}$\rightarrow$ \{N\} bifurcations at a significantly lower strength of nonlinearity than otherwise would be required in a sequential cascade. The proposal for engineering spectral bifurcation patterns holds significant potential for ultrafast signal processing applications. As a practical illustration, we employ these bifurcation modes to optical data squeezing and transmitting it across a 100-km-long single-mode fiber.

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