Optical vortex solitary wave in a bounded nematic-liquid-crystal cell

Modulation theory, based on a Lagrangian formulation of the governing equations, is used to investigate
the propagation of a nonlinear, nonlocal optical vortex solitary wave in a finite nematic-liquid-crystal cell. The
nematic response to the vortex is calculated using the approach of the method of images (MOI). It is demonstrated
that the MOI is a reliable alternative to the usual Fourier series solution as it requires an order of magnitude
fewer terms to obtain excellent agreement with numerical solutions. It is found that the cell walls, in addition
to repelling the optical vortex solitary wave, as for an optical solitary wave, can destabilize it due to the fixed
director orientation at the walls. A linearized stability analysis is used to explain and analyze this instability.
In particular, the minimum distance of approach of a stable vortex to the wall is determined from the stability analysis. Good agreement is found with numerical minimum approach distances.