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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