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Reorientational versus Kerr dark and gray solitary waves using modulation theory
Gaetano Assanto1, T R Marchant, Antonmaria A Minzoni
1NooEL, Nonlinear Optics and OptoElectronics Lab, University of Rome Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2012
Summary
We developed a modulation theory model to study dark and gray optical solitary waves in nonlinear optics. The study reveals that diffractive radiation drives the evolution of these waves, offering new insights into nonlinear beam propagation.
Area of Science:
- Nonlinear Optics
- Theoretical Physics
- Liquid Crystal Physics
Background:
- Optical spatial solitary waves are crucial in nonlinear optics, with applications in optical communications and information processing.
- The nonlinear Schrödinger (NLS) equation and nematicon equations model the propagation of such waves in various media, including nematic liquid crystals.
- Understanding the dynamics of dark and gray solitary waves, particularly in self-defocusing scenarios, is essential for controlling and utilizing these optical phenomena.
Purpose of the Study:
- To develop and apply a modulation theory model, based on a Lagrangian formulation, for investigating the evolution of dark and gray optical spatial solitary waves.
- To analyze these solitary waves in both the defocusing nonlinear Schrödinger (NLS) equation and the nematicon equations relevant to nonlinear beams in nematic liquid crystals.
- To compare the behavior of dark and gray solitary waves with bright solitary waves and to validate the theoretical model against numerical solutions.
Main Methods:
- Development of a modulation theory model using a Lagrangian formulation.
- Application of the model to the defocusing nonlinear Schrödinger (NLS) equation, serving as a test bed due to its exact soliton solutions.
- Extension and application of the modulation theory to nematicon equations, which lack exact solitary wave solutions, in self-defocusing nematic liquid crystals.
Main Results:
- The evolution of dark and gray NLS solitons and nematicons is primarily driven by the emission of diffractive radiation.
- This contrasts with the evolution of bright NLS solitons and bright nematicons, which exhibit different dynamics.
- The steady nematicon profile is nonmonotonic due to long-range nonlocality stemming from optic axis perturbation, and excellent agreement was found with numerical solutions.
Conclusions:
- The modulation theory provides an accurate framework for understanding the dynamics of dark and gray solitary waves in both NLS and nematicon systems.
- The findings highlight the critical role of diffractive radiation in the evolution of dark and gray solitary waves, differentiating them from bright counterparts.
- The study identifies subtle issues concerning the definition and measurement of dark or gray nematicon widths, necessitating further investigation.
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