IIMAS - FENOMEC
UNAM
The propagation of nonlinear optical beams in finite liquid crystal cells
Resumen:
A nonlinear medium that displays promise in all-optical communications is
a nematic liquid crystal. A nematic liquid crystal exhibits a “huge” nonlinearity,
so that nonlinear effects can be observed over millimetre distances
for relative low powered input beams (milliwatt power). Spatial optical solitons,
termed nematicons, are supported in nematic liquid crystals. A further
property of nematic liquid crystals is that there optical response is nonlocal,
in that the elastic response of the nematic extends beyond the optical perturbing
beam. This nonlocal response allows two dimensional beams, such
as nematicons and optical vortices, to be stable.
The equations governing nonlinear optical beam propagation in nematic
liquid crystals form a non-integrable, coupled system of an nonlinear Schrödinger type
equation for the beam and a Poisson’s equation for the medium response.
This system has no known, general solutions. In this talk, an
approximate variational technique, termed modulation theory, and numerical
solutions will be used to analyse the evolution and propagation of nematicons,
both circular and elliptical in cross section, and optical vortices
in a finite liquid crystal cell. Particular attention is paid to the effect of
boundaries on the beam trajectory and stability. Modulation theory has
the advantage that the coupled partial differential equations governing the
beam are reduced to a finite dimensional dynamical system, which yields
insights into the underlying physical mechanisms. In addition, modulation
theory can be easily extended to account for the effect of the diffractive
radiation shed as a beam evolves.
Two methods are used to solve the equation for the medium response,
Fourier series and the method of images, with the latter found to give a much
more efficient solution. It is found that the cell boundaries act as a repulsive
force on a beam, so that a beam has a spiral path down a cell. It is also found
that interaction with cell walls can destabilise an optical vortex. A linearised
stability analysis is used to determine the minimum distance of approach to
a cell boundary before instability sets in. This minimum distance is found to
be in excellent agreement with numerical solutions. Finally, the propagation
of an elliptic nematicon with orbital angular momentum in a finite-sized cell
is analysed. It is found that the inclusion of angular momentum loss to
radiation is vital for the accurate description of this beam. This loss is
included for the first time.
Informes: coloquiomym@gmail.com, o al 5622-3564.