Nonlinear dynamics of self-diffraction
at leaky wave resonances
R. Petruskevicius and Z. Kuprionis
Institute of Physics,
A.Gostauto 12, Vilnius 2600, Lithuania
Conventionally, for degenerate two-wave mixing in a thin nonlinear film it is applied Raman-Nath self-diffraction approach. There are no instabilities in the behavior of induced dynamic grating. A new situation occurs when two-wave induced dynamic grating overlaps with leaky wave resonances in a thin periodically modulated film and Woods anomalies appear. Leaky wave resonances are related to excitation of surface polaritons or guided waves in the thin slab. These resonances give rise to enhancement of local field and all nonlinear processes at the surface. The self-diffraction of laser radiation on the dynamic grating at these resonances exhibits instabilities which are not considered previously. The goal of this report is to present results of study of these new phenomena.
We have developed a theory of self-diffraction at leaky wave resonances
using coupled-mode approach. The steady state solutions of this problem are
multistable. In particular, very interesting steady state bifurcations were
obtained at double leaky wave resonances. It is possible to achieve an
overlap of several bistability loops of different nature and to obtain a
pitchfork bifurcation for symmetric wave illumination conditions. The
dynamical solutions of this problem have shown variety of temporal behavior:
relaxation to stacionars, self-pulsing, Ruelle-Takens-Newhousen route to
chaos. Some initial experimental observations of self-diffraction at leaky
wave resonances also are presented. The experiments were carried out with
the 
cw and pulsed lasers on liquid crystal films and atmospheric ice
films on cooled metal mirror.