2D optical rogue waves in self-focusing Kerr-type media with spatially modulated coefficients

Zheng Ping Yang; Wei Ping Zhong; Milivoj Belić

doi:10.1088/1054-660X/25/8/085402

2D optical rogue waves in self-focusing Kerr-type media with spatially modulated coefficients

Zheng Ping Yang
, Wei Ping Zhong
, Milivoj Belić

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

A similarity transformation is introduced to reduce the generalized two-dimensional (2D) nonlinear Schrödinger (NLS) equation with modulated spatial coefficients and a special external potential to the standard NLS equation with constant coefficients. The 2D rogue wave solutions are constructed with the help of Whittaker functions in polar coordinates. We present some typical examples of the obtained solutions by selecting the two free parameters: the azimuthal number (the topological charge) and the radial node. With the help of two free parameters, the unique properties of solutions are discussed. Furthermore, we find that the rogue waves display different intensity patterns, such as the circular-pyramid, annular-ring and vortex-ring patterns.

Original language	English
Article number	085402
Journal	Laser Physics
Volume	25
Issue number	8
DOIs	https://doi.org/10.1088/1054-660X/25/8/085402
Publication status	Published - 1 Aug 2015
Externally published	Yes

Keywords

nonlinear Schrödinger equation
nonlinear optics
optical rogue waves

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10.1088/1054-660X/25/8/085402

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title = "2D optical rogue waves in self-focusing Kerr-type media with spatially modulated coefficients",

abstract = "A similarity transformation is introduced to reduce the generalized two-dimensional (2D) nonlinear Schr{\"o}dinger (NLS) equation with modulated spatial coefficients and a special external potential to the standard NLS equation with constant coefficients. The 2D rogue wave solutions are constructed with the help of Whittaker functions in polar coordinates. We present some typical examples of the obtained solutions by selecting the two free parameters: the azimuthal number (the topological charge) and the radial node. With the help of two free parameters, the unique properties of solutions are discussed. Furthermore, we find that the rogue waves display different intensity patterns, such as the circular-pyramid, annular-ring and vortex-ring patterns.",

keywords = "nonlinear Schr{\"o}dinger equation, nonlinear optics, optical rogue waves",

author = "Yang, \{Zheng Ping\} and Zhong, \{Wei Ping\} and Milivoj Beli{\'c}",

note = "Publisher Copyright: {\textcopyright} 2015 Astro Ltd.",

year = "2015",

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doi = "10.1088/1054-660X/25/8/085402",

language = "English",

volume = "25",

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T1 - 2D optical rogue waves in self-focusing Kerr-type media with spatially modulated coefficients

AU - Yang, Zheng Ping

AU - Zhong, Wei Ping

AU - Belić, Milivoj

PY - 2015/8/1

Y1 - 2015/8/1

N2 - A similarity transformation is introduced to reduce the generalized two-dimensional (2D) nonlinear Schrödinger (NLS) equation with modulated spatial coefficients and a special external potential to the standard NLS equation with constant coefficients. The 2D rogue wave solutions are constructed with the help of Whittaker functions in polar coordinates. We present some typical examples of the obtained solutions by selecting the two free parameters: the azimuthal number (the topological charge) and the radial node. With the help of two free parameters, the unique properties of solutions are discussed. Furthermore, we find that the rogue waves display different intensity patterns, such as the circular-pyramid, annular-ring and vortex-ring patterns.

AB - A similarity transformation is introduced to reduce the generalized two-dimensional (2D) nonlinear Schrödinger (NLS) equation with modulated spatial coefficients and a special external potential to the standard NLS equation with constant coefficients. The 2D rogue wave solutions are constructed with the help of Whittaker functions in polar coordinates. We present some typical examples of the obtained solutions by selecting the two free parameters: the azimuthal number (the topological charge) and the radial node. With the help of two free parameters, the unique properties of solutions are discussed. Furthermore, we find that the rogue waves display different intensity patterns, such as the circular-pyramid, annular-ring and vortex-ring patterns.

KW - nonlinear Schrödinger equation

KW - nonlinear optics

KW - optical rogue waves

UR - https://www.scopus.com/pages/publications/84938359635

U2 - 10.1088/1054-660X/25/8/085402

DO - 10.1088/1054-660X/25/8/085402

M3 - Article

AN - SCOPUS:84938359635

SN - 1054-660X

VL - 25

JO - Laser Physics

JF - Laser Physics

IS - 8

M1 - 085402

ER -

2D optical rogue waves in self-focusing Kerr-type media with spatially modulated coefficients

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Keywords

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