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Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics
Theodoros P Horikis1, Dimitrios J Frantzeskakis2
1Department of Mathematics, University of Ioannina, Ioannina 45110, Greece.
Physical Review Letters
|July 1, 2017
Summary
Optical surface tension analogues in nonlocal nonlinear Schrödinger models create robust antidark solitons. These optical wave patterns resemble those seen in shallow water waves, demonstrating a fascinating cross-disciplinary parallel.
Area of Science:
- Optics
- Fluid Dynamics
- Nonlinear Physics
Background:
- Shallow water wave phenomena exhibit complex behaviors analogous to those in optics.
- Nonlocal nonlinear Schrödinger (NLS) models in 2+1 dimensions provide a framework for studying these optical analogues.
- Surface tension in shallow water waves significantly influences wave dynamics and dispersion.
Purpose of the Study:
- To identify and characterize an optical analogue of surface tension within a nonlocal NLS model.
- To investigate the impact of this optical surface tension analogue on wave dispersion and soliton formation.
- To explore the emergence of complex optical wave patterns and their relation to shallow water wave phenomena.
Main Methods:
- Utilized multiscale expansions to reduce the 2+1 dimensional nonlocal NLS model.
- Derived the Kadomtsev-Petviashvili (KP) equation, specifying KPII type for strong nonlocality and KPI type for weak nonlocality.
- Analyzed the formation and stability of optical antidark solitons under varying degrees of nonlocality.
Main Results:
- Identified a nonlocal parameter in optics analogous to surface tension, which alters the sign of dispersion.
- Demonstrated the formation of robust optical antidark solitons exhibiting Y-, X-, and H-shaped patterns.
- Showed that these optical patterns are well-approximated by colliding KPII line solitons, mirroring shallow water wave behavior.
Conclusions:
- The nonlocal parameter in optics acts similarly to surface tension in shallow water waves, controlling dispersion.
- Robust optical antidark solitons with complex shapes emerge from the nonlocal NLS model.
- The study highlights a strong analogy between optical wave phenomena in nonlocal NLS models and shallow water waves.
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