Generation of solitons in media with arbitrary degree of nonlocality using an optimization procedure

Duque, Erick I.; López-Aguayo, Servando

doi:10.1103/physreva.99.013831

Cited by 8 publications

(3 citation statements)

References 34 publications

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“…Hence, they have been often replaced by a simpler function, usually a Gaussian, with the hope that the resulting predictions based on a simplified kernel are accurate enough. Extreme caution should be exercised though, as predictions with Gaussian functions in the director kernel can be inaccurate when compared with solutions with the actual Green's function [138,139,140], so that any solutions obtained using simplified kernels need to be compared with numerical solutions of the actual model. Care must also be taken in the choice of trial function, which should have the correct asymptotic behaviour as r → ∞.…”

Section: Approximate Nematicon Solutionsmentioning

confidence: 99%

Self-confined light waves in nematic liquid crystals

Assanto

Smyth

2020

Physica D: Nonlinear Phenomena

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The study of light beams propagating in the nonlinear, dispersive, birefringent and nonlocal medium of nematic liquid crystals has attracted widespread interest in the last twenty years or so. We review hereby the underlying physics, theoretical modelling and numerical approximations for nonlinear beam propagation in planar cells filled with nematic liquid crystals, including bright and dark solitary waves, as well as optical vortices. The pertinent governing equations consist of a nonlinear Schrödinger-type equation for the light beam and an elliptic equation for the medium response. Since the nonlinear and coupled nature of this system presents difficulties in terms of finding exact solutions, we outline the various approaches used to resolve them, pinpointing the good agreement obtained with numerical solutions and experimental results. Measurement and material details complement the theoretical narration to underline the power of the modelling.

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Section: Approximate Nematicon Solutionsmentioning

confidence: 99%

Self-confined light waves in nematic liquid crystals

Assanto

Smyth

2020

Physica D: Nonlinear Phenomena

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“…where w is a real waist parameter and ( ) ( ) * ^Ĝ H r r is the 2 dimensional convolution of the functions G and H [57]. Using the convolution theorem…”

Section: Vortex Solitons In Nonlocal Mediamentioning

confidence: 99%

Fast Petviashvili–Hankel method for vortex solitons in the generalized nonlinear Schrödinger equation

Ramesh

López-Aguayo

2020

J. Opt.

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We present a robust numerical procedure for obtaining ring-type spatial optical beams with phase singularities in nonlinear media. This numerical algorithm can be used for fast computing stationary solutions with high topological charge for the case of a generalized nonlinear Schrödinger equation. Remarkably, we find that the method converges to the ring-type solution starting virtually from any initial condition. The method is based in the use of Chebyshev spectral methods for the calculation of a required Hankel transform. We provide the codes for the straightforward use of this algorithm in Matlab.

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“…[21][22][23][24][25][26][27][28] In recent years, the nonlinear media with nonlocal response has become the focus of interest due to the potential applications, such as soliton or self-trapped beams generation. 29,30) Thus, it is necessary to investigate the characteristics of the optical pulses when propagated in nonlinear media. In previous studies, researchers have introduced the dynamics of optical pulses in highly noninstantaneous Kerr media.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Pearcey pulses in highly noninstantaneous Kerr media

Yi¹,

Chen²,

Hong³

2020

Jpn. J. Appl. Phys.

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We investigate the dynamics of Pearcey pulses in the highly noninstantaneous Kerr media. Setting appropriate pulse power and relaxation time of the media, an interesting phenomenon is found that the Pearcey pulse will exhibit an energy transfer property during propagation. We further investigate the evolution characteristics by changing the pulse power and relaxation time of the media, while keeping a constant ratio in the simulation. It is shown that the transversal motion of Pearcey pulses is proportional to the ratio between the pulse power and relaxation time of the media in the highly noninstantaneous limit.

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Generation of solitons in media with arbitrary degree of nonlocality using an optimization procedure

Cited by 8 publications

References 34 publications

Self-confined light waves in nematic liquid crystals

Self-confined light waves in nematic liquid crystals

Fast Petviashvili–Hankel method for vortex solitons in the generalized nonlinear Schrödinger equation

Dynamics of Pearcey pulses in highly noninstantaneous Kerr media

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