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Modulational instability in nonlinear saturable media with competing nonlocal nonlinearity.
Conrad Bertrand Tabi1, Hippolyte Tagwo2, Timoléon Crépin Kofané1,2,3
1Department of Physics and Astronomy, Botswana International University of Science and Technology, Private Mail Bag 16 Palapye, Botswana.
Physical Review. E
|December 23, 2022
Summary
Modulational instability (MI) in nonlocal media is controlled by saturation effects. Saturation parameters, especially the index, can amplify MI, leading to robust rogue waves and nonlinear localized light patterns.
Area of Science:
- Nonlinear optics
- Wave propagation in optical media
Background:
- Modulational instability (MI) is a key phenomenon in nonlinear optics.
- Nonlocal nonlinear media exhibit unique wave propagation characteristics.
- Controllable saturation offers a mechanism to manage nonlinear effects.
Purpose of the Study:
- To investigate the modulational instability (MI) phenomenon in a nonlocal medium with controllable saturation.
- To analyze the influence of nonlocal and saturation parameters on MI.
- To explore the generation of nonlinear localized light patterns and rogue waves.
Main Methods:
- Linear stability analysis of plane-wave solutions to derive the MI growth rate.
- Parametric analysis of nonlocal and saturation parameters (nonlocal parameter, saturation coefficient, saturation index).
- Direct numerical simulations to confirm analytical predictions and observe pattern formation.
Main Results:
- The instability spectrum is generally quenched by high nonlocality but can be amplified by specific saturation parameters, particularly the saturation index.
- Competing nonlocal and saturable nonlinearities facilitate the emergence of pattern trains due to MI.
- Robust rogue waves, identified as Akhmediev breathers, are generated and confirmed as a signature of MI.
Conclusions:
- The saturation index is a crucial parameter for manipulating nonlinear waves in nonlocal media.
- MI can be controlled and utilized to generate stable localized light patterns and rogue waves.
- Direct numerical simulations validate the analytical predictions regarding MI in saturable nonlocal nonlinear media.
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