Next: About this document
REGULAR AND CHAOTIC BEHAVIOR IN THE VECTOR COMPLEX
Antoni Amengual, Emilio Hernández-García,
Raúl Montagne, Maxi San Miguel, and Daniel Walgraef
Departament de Física, Universitat de les Illes Balears
E-07071 Palma de Mallorca, Spain
E.H-G e-mail address: email@example.com
On leave from
Université Libre de Bruxelles.
The complex Ginzburg-Landau equation describes generically the amplitude
unstable modes near a homogeneous Hopf bifurcation in spatially extended
It has been recently shown that a vector generalization of this equation
adequate for describing the dynamics of light polarization in some
optical systems . An exploratory analysis of the behavior of this
complex Ginzburg-Landau equation in the one-dimensional case will be
here. Travelling and standing wave patterns, localized
pulses, regimes of spatio-temporal intermitency and the consequences of
breaking of rotational symmetry will be described.
San Miguel M., Phys. Rev. Lett 75, 425 (1995); Gil L.,
Phys. Rev. Lett, 70, 162-165, (1993).
- The VCGL Equation and its Physical Origin
Dynamics of Polarization-Phase Instabilities
- The phase of the TW solutions is linearly
unstable for .
- The phases and of SW solutions are simultaneously
linearly unstable for .
- The depolarized solutions have also a region of the -plane centered in
beyond which they are phase-unstable. Our numerical analysis shows that TW
and SW unstable solutions evolves to other solutions of the same class and
smaller wavenumber through transient
depolarized states (FIGURE 2a) .
Unstable depolarized solutions evolve
in time to other states, which generically are also depolarized, through a
mechanism in which the circularly polarized
component of larger wavenumber reduces its wavenumber while the other component
remains stable (FIGURE 2b) .
Spatio-Temporal Intermittency Regimes
- As for the scalar equation, there are parameter regimes in which the
solutions of the VCGL consist of regions close to the "simple" solutions above,
separated by turbulent regions in which localized objects can be identified
- For close to 1, the main localized objects are circulary
polarized spots in a linearly polarized background.
- Increasing the coupling
the chaotic dynamics of the two components
becomes strongly correlated (syncronized) (FIGURE 4)
Breaking of the internal rotational symmetry
- The introduction of terms breaking the -phase symmetry
(birrefringence, imperfections,...) leads to new phenomenology.
- The anisotropy fixes the direction of polarization of the TW, and
modifies the SW:
- For (
if ) these solutions destabilize, giving rise to TW with oscillating
propagation direction (FIGURE 5) .
- Spatio-temporal intermittency regimes are also present in
(FIGURE 6) .
Next: About this document
Tue Jul 11 11:05:19 MET DST 1995