Lecturer: Dr. Stanislav Derevyanko
Affiliation: Weizmann Institute of Science
Abstract:
The interplay between the nonlinearity
and disorder both in stationary and dynamical
systems has attracted a great deal
of attention over the past decade and a half.
In the context of the nonlinear optics
the key questions here are: (i) how initially
disordered pulses propagate in perfect
optical structures and (ii) how the imperfections
of the waveguide (or a waveguide system)
affect the transmission properties of light.
These sets of problems complement each
other and lead to different physical phenomena.
In this talk I will illustrate this complex
interconnection by considering three
representative problems: i) propagation
of soliton pulses in optical fiber in the presence
of inline noise sources ii) disordered beam
propagation in focusing nonlinear media with
applications to the nonlinear Hanbury Brown
and Twiss interferometry and iii) "thermalization"’
of polarized light in a system of coupled
nonlinear waveguides.
The theoretical analysis of all three problems
relies on continuous and discrete versions
of the nonlinear Schrodinger equation in the
presence of disorder (either in the initial
conditions or as a dynamical perturbation).
I will use the differences between discrete
and continuous systems to illustrate how
the methods and general ideology used in
(almost) integrable systems are different
from their non-integrable counterparts.