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Soliton self-frequency shift: Self-similar solutions and their stability
M Facão1, M I Carvalho, D F Parker
1Departamento de Física, Universidade de Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal. mfacao@ua.pt
Summary
Intrapulse Raman scattering (IRS) in optical fibers causes pulse shifts. New solutions reveal self-similar pulses with Airy tails, approximating simulations and explaining radiation loss.
Area of Science:
- Nonlinear optics
- Fiber optics
- Quantum optics
Background:
- Intrapulse Raman scattering (IRS) is a key effect influencing ultrashort pulse propagation in optical fibers.
- IRS causes frequency downshift and peak pulse displacement, typically analyzed using perturbation methods on the nonlinear Schrödinger equation.
- Previous research focused on soliton propagation dynamics under IRS effects.
Purpose of the Study:
- To find and analyze novel solutions for the nonlinear Schrödinger equation with IRS using an accelerating self-similarity variable.
- To investigate the stability and characteristics of these self-similar solutions, particularly their Airy function asymptotics.
- To compare these theoretical solutions with numerical simulations of full equation models.
Main Methods:
- Solving the model equation using an accelerating self-similarity variable.
- Analyzing the stability of the derived solutions.
- Comparing theoretical solutions with full equation simulations for varying strengths of IRS.
- Investigating the behavior of truncated self-similar solutions as initial conditions.
Main Results:
- Identified self-similar solutions with Airy function asymptotics, implying infinite energy.
- Demonstrated that these solutions closely approximate simulated pulse profiles for small IRS.
- Observed Airy oscillations in the left tails of self-similar pulses for strong IRS.
- Confirmed that truncated solutions lead to amplitude decay and radiation escape, consistent with continuum radiation.
Conclusions:
- The derived self-similar solutions offer a new perspective on pulse dynamics under IRS.
- The observed Airy oscillations and radiation escape are linked to the continuum nature of the pulse tail.
- These findings provide insights into the fundamental physics of ultrashort pulse propagation in nonlinear media.
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