Existence of optical vortices

Yisong Yang, Ruifeng Zhang

Research output: Contribution to journalArticle

Abstract

Optical vortices arise as phase singularities of the light fields and are of central interest in modern optical physics. In this paper, some existence theorems are established for stationary vortex wave solutions of a general class of nonlinear Schrödinger equations. There are two types of results. The first type concerns the existence of positive-radial-profile solutions, which are obtained through a constrained minimization approach. The second type addresses the existence of saddlepoint solutions through a mountain-pass theorem or min-max method so that the wave propagation constant may be arbitrarily prescribed in an open interval. Furthermore, some explicit estimates for the lower bound and sign of the wave propagation constant with respect to the light beam power and vortex winding number are also derived for the first type of solution.

Original languageEnglish (US)
Pages (from-to)484-498
Number of pages15
JournalSIAM Journal on Mathematical Analysis
Volume46
Issue number1
DOIs
StatePublished - 2014

Fingerprint

Optical Vortex
Wave Propagation
Vortex
Vortex flow
Mountain Pass Theorem
Open interval
Winding number
Wave propagation
Constrained Minimization
Saddlepoint
Min-max
Existence Theorem
Nonlinear Equations
Physics
Singularity
Lower bound
Nonlinear equations
Estimate
Profile
Class

Keywords

  • Minimization
  • Mountain-pass theorem
  • Optical vortices
  • Palais-Smale condition
  • Schrödinger equations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics

Cite this

Existence of optical vortices. / Yang, Yisong; Zhang, Ruifeng.

In: SIAM Journal on Mathematical Analysis, Vol. 46, No. 1, 2014, p. 484-498.

Research output: Contribution to journalArticle

Yang, Yisong ; Zhang, Ruifeng. / Existence of optical vortices. In: SIAM Journal on Mathematical Analysis. 2014 ; Vol. 46, No. 1. pp. 484-498.
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