Two-dimensional matrix parabolic cylinder beams

Zhengping Yang; Wei Ping Zhong; Milivoj Belić; Wen Ye Zhong

doi:10.1016/j.physleta.2021.127557

Two-dimensional matrix parabolic cylinder beams

Zhengping Yang, Wei Ping Zhong^*, Milivoj Belić, Wen Ye Zhong

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

We investigate the two-dimensional normalized linear Schrödinger equation describing the propagation of diffraction-free beams in free space using the traditional variable separation method. We discover that each beam component satisfies the standard Weber differential equation. From this fact, we construct exact solutions utilizing two parabolic cylinder functions, which are denoted as the two-dimensional (2D) parabolic cylinder beams with diffraction-free characteristics that can be described by two mode numbers. By using numerical simulation and choosing appropriate mode numbers, we exhibit intensity profiles of the 2D parabolic cylinder beams, which display a matrix structure. It is demonstrated that the beams can be completely controlled by the choice of two mode numbers.

Original language	English
Article number	127557
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	412
DOIs	https://doi.org/10.1016/j.physleta.2021.127557
Publication status	Published - 7 Oct 2021
Externally published	Yes

Keywords

Diffraction-free parabolic cylinder beams
Parabolic cylinder functions
Two-dimensional linear Schrödinger equation

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10.1016/j.physleta.2021.127557

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title = "Two-dimensional matrix parabolic cylinder beams",

abstract = "We investigate the two-dimensional normalized linear Schr{\"o}dinger equation describing the propagation of diffraction-free beams in free space using the traditional variable separation method. We discover that each beam component satisfies the standard Weber differential equation. From this fact, we construct exact solutions utilizing two parabolic cylinder functions, which are denoted as the two-dimensional (2D) parabolic cylinder beams with diffraction-free characteristics that can be described by two mode numbers. By using numerical simulation and choosing appropriate mode numbers, we exhibit intensity profiles of the 2D parabolic cylinder beams, which display a matrix structure. It is demonstrated that the beams can be completely controlled by the choice of two mode numbers.",

keywords = "Diffraction-free parabolic cylinder beams, Parabolic cylinder functions, Two-dimensional linear Schr{\"o}dinger equation",

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

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2021",

month = oct,

day = "7",

doi = "10.1016/j.physleta.2021.127557",

language = "English",

volume = "412",

journal = "Physics Letters, Section A: General, Atomic and Solid State Physics",

issn = "0375-9601",

publisher = "Elsevier B.V.",

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TY - JOUR

T1 - Two-dimensional matrix parabolic cylinder beams

AU - Yang, Zhengping

AU - Zhong, Wei Ping

AU - Belić, Milivoj

AU - Zhong, Wen Ye

PY - 2021/10/7

Y1 - 2021/10/7

N2 - We investigate the two-dimensional normalized linear Schrödinger equation describing the propagation of diffraction-free beams in free space using the traditional variable separation method. We discover that each beam component satisfies the standard Weber differential equation. From this fact, we construct exact solutions utilizing two parabolic cylinder functions, which are denoted as the two-dimensional (2D) parabolic cylinder beams with diffraction-free characteristics that can be described by two mode numbers. By using numerical simulation and choosing appropriate mode numbers, we exhibit intensity profiles of the 2D parabolic cylinder beams, which display a matrix structure. It is demonstrated that the beams can be completely controlled by the choice of two mode numbers.

AB - We investigate the two-dimensional normalized linear Schrödinger equation describing the propagation of diffraction-free beams in free space using the traditional variable separation method. We discover that each beam component satisfies the standard Weber differential equation. From this fact, we construct exact solutions utilizing two parabolic cylinder functions, which are denoted as the two-dimensional (2D) parabolic cylinder beams with diffraction-free characteristics that can be described by two mode numbers. By using numerical simulation and choosing appropriate mode numbers, we exhibit intensity profiles of the 2D parabolic cylinder beams, which display a matrix structure. It is demonstrated that the beams can be completely controlled by the choice of two mode numbers.

KW - Diffraction-free parabolic cylinder beams

KW - Parabolic cylinder functions

KW - Two-dimensional linear Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=85111054751&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2021.127557

DO - 10.1016/j.physleta.2021.127557

M3 - Article

AN - SCOPUS:85111054751

SN - 0375-9601

VL - 412

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

M1 - 127557

ER -

Two-dimensional matrix parabolic cylinder beams

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Keywords

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