Optical solitons in nematic liquid crystals: arbitrary deviation angle model

BORGNA, JUAN PABLO; PANAYOTAROS, PANAYOTIS; RIAL, DIEGO FERNANDO; CONSTANZA S. F. DE LA VEGA

PHYSICA D - NONLINEAR PHENOMENA

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2020 vol. 408

0167-2789

We study a coupled Schrödinger-elliptic evolution system that de-scribes the propagation of a laser beam in nematic liquid crystals. Theelliptic equation describes the effects of the beam electric field on thelocal orientation (director field) of the nematic liquid crystal and hasan important regularizing effect, seen experimentally and understoodtheoretically in related models. In the present work we propose a newnonlinear elliptic equation for the director field that makes no assump-tion on the size of the director field angle. The analysis of this ellipticequation leads to an upper bound for the size of the director anglethat we believe is optimal and physically relevant, and that impliesthat the elastic response of the medium prevents a complete alignmentbetween the electric field and the orientation of the liquid crystal. Theresults on the elliptic problem are combined with arguments from dis-persive wave theory to show the local and global well-posedness ofthe evolution problem and the decay of small initial conditions. Wealso show the existence of constrained minimizers of the Hamiltonian,assuming sufficiently large optical power.These minimizers are solitons with radial, monotonically decreasingprofiles.