Polarization properties of small-area VCSELs
Polarization dynamics in free running mode
Due to the isotropy in the plane of the active zone the direction of polarization
is not or only weakly pinned so that VCSELs are very sensitive to polarization
instabilities. In real device there are some preferred directions due to
the crystal symmetry and/or due to strain left from the growth process.
Therefore typically a state with a defined linear polarization emerges
at threshold, which is however not stable but gives way to the orthogonal
one as the current is increased
[1,2,4,5]
.
Furthermore, it was noted that the primary polarization can be recovered
after a second polarization switching.
Many aspects of this switching behaviour can be understood by considering
linear (i.e. unsaturated), but temperature dependent gain or loss anisotropies for the two
polarization modes which are frequency split by birefringence
[1,2].
Other aspects require the inclusion of nonlinear effects like saturable
dispersion
[3,4,5],
which is very
pronounced in semiconductor lasers due to the strong coupling between amplitude
and phase. The interplay between the different effects is still not fully
clarified, although first generalized model have been worked out recently
[6].
The aim of the project is extract the relevant mechanism from systematic
measurements of the bifurcation diagram in dependence of current and temperature
and to provide a quantitative base for a theoretical modelling. Therefore
the work is at present limited to a parameter region where spatial degrees
of freedom are of no or minor importance.
 Basic experimental setup
Our experiments yielded the
emergence of elliptically polarized states ("phase instability"),
spontaneous self-oscillation of polarization state with a frequency of a few GHz,
polarization switching with a drop in total output power, i.e.\ to a mode with a lower unsaturated net gain,
no selection of well defined polarization state even at threshold ("two-frequency emission").
These observations indicate the need for a model that allows for a description of the phase of the optical field (i.e. a model which goes beyond intensity rate equations) and for the selection of a polarization mode which is not the one favoured by the unsaturated gain-loss balance.
These prerequisites are fulfilled in the so-called spin-flip model (SFM)
[3,4,6], which takes into account explicitly the spin degrees of freedom of a semiconductor quantum well. The experimental results are found to be consistent with the model, if a low spin-flip rate is assumed. These investigations are performed in collaboration with S. Balle and J. Mulet (IMEDEA, Palma de Mallorca, Spain).
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Polarization dynamics with optical feedback
Another important aspect of our work is the characterization of the polarization dynamics of VCSELs with feedback from a distant reflector. This situation is very interesting from a nonlinear dynamics point of view and its understanding is crucial for applications, since feedback arises nearly inevitably in typical operating conditions of semiconductor lasers and usually results in instabilities and increased noise.
[8]
In the special case of VCSELs, a thorough understanding of the polarization properties with optical feedback might also open the possibility of new - polarization based - sensors.
A particularly intriguing phenomenon are the so-called "low-frequency fluctuations" (LFF). They consist of sudden drops in the output power followed by a slow recovery. The time scale is of the order of some tens or hundreds of nanoseconds and thus much longer than the feedback time and the intrinsic time scales of a semiconductor laser, which explains the name "low-frequency". They were observed first more than 25 years ago
[9],
but their properties and origin are still a matter of intensive discussion
[10].
Our experiments yielded the
demonstration of the existence of LFF in VCSELs,
the amount of participation of both polarization mode depends on the dichroism of the free running device,
different synchronization behaviour between polarization modes on different time scales and in dependency on parameters.
Many aspects of the observed dynamics can be reproduced qualitatively by considering the SFM-model with feedback terms. These investigations are carried out in collaboration with N. A. Loiko and A. Naumenko (Academy of Sciences of Belarus, Minsk, Belarus).
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