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Complex Dynamics Induced by Optical Feedback in Semiconductor Lasers

Friday, 9 September, 2005 - 17:00
Campus: Brussels Humanities, Sciences & Engineering campus
Andrzej Tabaka
phd defence

Semiconductor lasers are the most widely used type of lasers. The very broad area of
applications makes them almost indispensable in our every day life. We find them in CD
and DVD players, in laser printers or in supermarkets. Semiconductor lasers can be very
easy integrated in the optical systems and they have found numerous applications in
science, technology, industry and medicine. We should also mention the enormous
development of lasers in the telecommunication technology where they are used for data
transmission in optical fibers.

Semiconductor lasers are also sensitive to external perturbations. These perturbations
may cause pulsations of the laser output and induce complex dynamics. This makes the
semiconductor laser systems to be of great relevance from the nonlinear dynamics point
of view: the ease of control and their common availability constitutes them as a perfect
tool to study different bifurcation scenarios and routes to chaos.

The thesis is concerned with the dynamical properties of the semiconductor laser system
subject to external optical feedback, i.e., external reflection of light which re-enters the
laser cavity after a certain delay time. Such time-delayed optical feedback might
significantly affect the stable laser operation and induce complex dynamics, such as selfpulsations,
multistability and chaos. Feedback in semiconductor lasers is quite a general
issue because it inevitably appears when lasers are inserted in any optical system. It is
therefore not only to satisfy people's curiosity, but it is also a challenging problem for
many scientists and engineers.

Nowadays, for most applications in which a stable laser operation is indispensable, i.e. in
data transmission, the instabilities induced by optical feedback are still avoided by means
of expensive optical isolators. However, it has been realized that a deep understanding of
this problem, rather then simply avoiding it, can not only save a lot of money, but can
also give rise to many interesting new applications. Optical feedback can, for example,
narrow the linewidth of the emitted light. Moreover, it can be used for optical data
readout systems and frequency tuning. The feedback-induced chaotic output of the laser
intensity is nowadays potentially considered for other applications, such as for example,
chaotic encryption for secure communication. Moreover, semiconductor lasers with optical feedback are interesting theoretical problem of a system with time-delay. It is
much more convenient to study the time-delay effects in the semiconductor laser system,
as it is easy accessible experimentally and well described theoretically. Moreover, it is
easy to control not only the feedback parameters, but also the object of study itself.
Therefore, our study of nonlinear laser system with feedback is of particular importance
not only in the field of semiconductor lasers and their applications, but can also be
applied, and help to understand, other dynamical systems with time delay.

Even though the long cavity regime has extensively been studied, the short cavity regime
still awaits considerable interest. Therefore, in the thesis we focus on the case of short
external cavity feedback. It was recently shown that when the edge-emitting
semiconductor laser is subject to optical feedback for external cavity lengths of a few cm
the laser output exhibits fast intensity pulsations at the external cavity frequency grouped
in regular packages underlying a low frequency envelope, the so-called regular pulse
packages or RPP dynamics. We study the bifurcation scenario of this new dynamical
regime. Using a time-delayed rate-equation model for semiconductor laser we show the
sequence of bifurcations from external-cavity mode steady states, time-periodic
oscillations, and finally the RPP dynamics, when treating the feedback rate and the
injection current as bifurcation parameters. We identify regions of feedback parameters
for which RPP occurs. Detailed mapping shows that with increasing the delay time the
windows of RPP broaden, merge and finally shrink when approaching the relaxation
oscillation period.

In the second part of the thesis we address the question whether similar dynamical effects
can also be observed in the case of new type of semiconductor lasers i.e., vertical-cavity
surface emitting lasers (VCSELs). Our results demonstrate the emergence of pulse
packages (PP) in the total intensity dynamics of VCSELs. We identify characteristic
differences to the PP dynamics in edge emitters originating from the interplay between
time-delay induced dynamics and polarization mode competition. For clarification, we
provide detailed analysis of the polarization dynamics applying complementary crosscorrelation
and spectral analysis techniques. The analysis reveals interplay of the
dynamics linked to the hierarchy of time-scales present in the laser system: the fast timescale
of the delay, the slower time-scale of the PP, and the slow time-scale of the
polarization mode competition. In order to get insight into this behavior, we provide a
toolbox of methods adapted to the different relevant time scales and temporal variations
of the dynamics, namely, correlation and spectral analysis and sliding time-resolved
cross-correlation analysis. These complementary methods reveal distinct changes in the
phase relation between the dynamics of the two polarization modes when changing the
injection current, both, on the fast as well as on the slow time scales. Furthermore, our
results emphasize the significance of polarization mode competition for PP dynamics in
VCSELs, contrasting the observed behavior to that reported for edge emitters.

In the next part of the thesis we study both theoretically and experimentally, the
polarization mode hopping in VCSELs induced by feedback. The existence of two nearly
degenerated polarization modes in VCSELs gives rise to polarization bistability. By
applying external optical feedback we observe stochastic hops between this two well-defined polarization states. Besides the low frequency random jumps such system shows
fast oscillations at the external cavity frequency, which are related to the feedback. We
experimentally measure the residence-time distributions of the polarization state of the
VCSEL, compare them with the numerically calculated ones, and demonstrate a very
good correspondence between them.

Finally, we study also the case of feedback from an extremely short external cavity. We
present different theoretical models combining butt-coupling of the semiconductor laser
and fibre (waveguide) model and time delayed models. We experimentally study the
influence of the feedback phase on the output power of the edge-emitting semiconductor
lasers. We show that the output power exhibits an oscillatory behaviour with changing
the external cavity length. The period of these oscillations corresponds to the half of the
wavelength of the emitted light and the amplitude depends on the feedback strength.