Conical soliton escape into a third dimension of a surface vortex

TL;DR

This paper derives an exact 3D solitonic solution describing a surface vortex in nematic liquid crystals, revealing how it extends into the third dimension and relates to known point defects.

Contribution

It provides a novel exact solution to a sine-Gordon-type equation modeling surface vortices with third-dimensional escape in nematic films.

Findings

Solution describes a surface vortex escaping into the third dimension.

Identifies the solution as a section of a known point defect.

Applicable to nematic liquid-crystal textures with tangential alignment.

Abstract

We present an exact three-dimensional solitonic solution to a sine-Gordon-type Euler-Lagrange equation, that describes a configuration of a three-dimensional vector field n constrained to a surface p-vortex, with a prescribed polar tilt angle on a planar substrate and escaping into the third dimension in the bulk. The solution is relevant to characterization of a schlieren texture in nematic liquid-crystal films with tangential (in-plane) substrate alignment. The solution is identical to a section of a point defect discovered many years ago by Saupe [Mol. Cryst. Liq. Cryst. 21, 211 (1973)], when latter is restricted to a surface.