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\begin{document}

\title{Existence of Coupled Optical Vortex Solitons Propagating in a Quadratic
Nonlinear Medium}



\author[1]{Luciano Medina}%
\affil[1]{New York University}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\begin{abstract}
We consider the coupled propagation of an optical field and its second
harmonic in a quadratic nonlinear medium governed by a coupled system of
Schrodinger equations. We prove the existence of ring-profiled optical
vortex solitons appearing as solutions to a constrained minimization
problem and as solutions to a min-max problem. In the case of the
constrained minimization problem solutions are shown to be positive but
the wave propagation constants undetermined, but in the min-max approach
the wave propagation constants can be prescribed. The quadratic
nonlinearity introduces some interesting properties not commonly
observed in other coupled systems in the context of nonlinear optics,
such as the system not accepting any semi-trivial solutions, meaning,
that optical solitons cannot be observed when, say, one of the beams are
off. Additionally, the second harmonic always remains positive.%
\end{abstract}%



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