Chaotic polarization dynamics and chaos
synchronization in VCSELs(Invited Paper)
Marc Sciamanna∗, Krassimir Panajotov †, Ignace Gatare †, Hugo Thienpont †,
Angel Valle ‡, Mikel Arizaleta §, Atsushi Uchida ¶
∗Supelec, LMOPS CNRS UMR-7132, 2 rue Edouard Belin, F-57070 Metz (France)†Vrije Universiteit Brussel, TONA Department, Pleinlaan 2, B-1050 Brussels (Belgium)
‡Instituto de Fisica de Cantabria, CSIC-Universidad de Cantabria, Avda. Los Castros s/n, E-39005 Santander (Spain)§Universidad Publica de Navarra, Department of Electrical and Electronic Engineering, E-31006 Pamplona (Spain)
¶Saitama University, Department of Information and Computer Sciences, 255 Shimo-Okubo, Sakura-ku, 338-8570 Saitama (Japan)
Abstract—We review our recent results related to nonlinearpolarization dynamics and chaos in VCSELs. The possibilityto generate multimode chaos motivates the study of chaossynchronization in coupled VCSELs and its application for securecommunications.
I. INTRODUCTION
Vertical-cavity surface-emitting lasers (VCSELs) exhibit
interesting polarization properties: they typically emit a lin-
early polarized along one of two preferential and orthogonal
directions (x and y) but light polarization can easily switch
between the x and y linearly polarized (LP) modes when
modifying the injection current and/or device temperature [1].
The interplay between VCSEL peculiar polarization properties
and the nonlinear dynamics resulting from optical feedback,
optical injection or large current modulation induces new, pos-
sibly chaotic polarization dynamics and polarization switching
mechanisms that we review here.
II. OPTICAL FEEDBACK: SWITCHING AND RESONANCE
When VCSEL is subject to a relatively strong optical feed-
back, its dynamics may exhibit severe instabilities resulting
in chaos in its two orthogonal polarization modes. A typical
example is the low-frequency fluctuation (LFF) regime where
the chaotic fluctuations of the LP mode dynamics may either
be in phase and then lead to similar dynamics in the VCSEL
total power, or rather be anticorrelated and lead to a laser
output power almost constant in time [2], [3]. Recently, we
have shown that another dynamics resulting from optical
feedback consists of slow hopping between the two LP modes
complemented by fast anticorrelated pulses at the external
cavity frequency [4]; see Fig. 1. Interestingly, the VCSEL
can exhibit a resonant behavior at the time-scale of the time-
delayed optical feedback when adding an optimal amount
of noise in the laser injection current, a situation typically
referred as coherence resonance for nonlinear systems [5].
III. OPTICAL INJECTION: ROUTE TO CHAOS
We have investigated another configuration where a VCSEL
is subject to optical injection with an orthogonal polarization.
0 0.5 1 1.5 20
0.01
0.02
0.03
0.04
Time (s)I x
(ar
b.un
its)
20 30 40 500.01
0.02
0.03
0.04
0.05
Time (ns)
I x, Iy (
arb.
units
)
0 10 20 300
0.02
0.04
0.06
Time (ns)
I x , I to
t (ar
b.un
its)
(a)
(b) (c)
Fig. 1. (a) Typical time-trace of mode hopping in the LP mode intensityof a VCSEL induced by weak optical feedback. (b) is an enlargement of (a)showing the two LP mode intensities when the light polarization hops betweenthe two orthogonal directions. (c) shows a time-trace of the LP mode intensity(solid curve) together with the one of the total intensity (dotted curve).
For a large enough injection, the VCSEL polarization switches
to the one of the injected light and its frequency locks to
that of the so-called master laser [6]. However this injection
locking steady state dynamics may easily destabilize and lead
to complex polarization dynamics [7]; see Fig. 2. The VCSEL
initially is locked to the master laser (a) but when increasing
the injection strength it exhibits a Hopf bifurcation to a self-
pulsating dynamics (b)-(c), which in turn may exhibit a period
doubling bifurcation (d) to chaos (e). We have analyzed in
detail the bifurcation scenarios as a function of the frequency
detuning between VCSEL and master laser and as a function
of the injection strength [8], [9].
IV. LARGE CURRENT MODULATION: CHAOTIC PULSING
When VCSEL is subject to current modulation with large
modulation amplitude and frequency above the relaxation
oscillation frequency, theoretical works have predicted the
existence of chaotic dynamics in the VCSEL higher order
transverse modes [10] or in its two LP modes [11]. We have
recently shown theoretically that the transverse mode and
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Fig. 2. Samples of polarization-resolved optical spectra showing a perioddoubling cascade of bifurcations to chaos (e), following by a reverse perioddoubling cascade, as the injection strength increases for a fixed detuning.
polarization mode competitions in VCSELs may interplay and
lead to new dynamical scenarios: transverse mode competition
may suppress chaos or, by contrast, lead to chaos in parameter
regions where otherwise the VCSEL polarization competition
leads to regular pulsing [12]. We have moreover confirmed
experimentally two theoretical predictions. First, nonlinear
dynamics can be observed in VCSELs with large current
modulation as a result of polarization mode competition [13];
see Fig. 3 where the polarization modes exhibit an irregular
pulsing at half the modulation frequency (period doubling)
while the total power exhibits a regular period-two dynamics.
Second, we have shown that transverse mode competition only
can lead to nonlinear dynamics [14].
Fig. 3. Experimental time traces of the intensities of the total, x-polarizedand y-polarized powers, showing nonlinear dynamics in VCSEL with largecurrent modulation. Results plotted in (d)-(f) correspond to zooms of (a)-(c),respectively, where the latter result from three independent experimental runs.
V. VCSEL CHAOS SYNCHRONIZATION
Apart from optical feedback, injection or large current
modulation, coupling between VCSELs may also significantly
modify their polarization properties and dynamics. We have
shown for example that mutual coupling between VCSELs
may induce successive polarization switchings with increasing
coupling strength in otherwise polarization stable VCSELs
[15]. Mutually coupled VCSELs may also exhibit chaotic
dynamics in almost perfect synchronism; see Fig. 4. The anti-
correlated dynamics between orthogonal polarization modes of
each VCSEL yields moreover to anti-synchronization between
coupled orthogonal polarization modes.
-400
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0
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0 5 10 15 20 25 30
Inte
nsit
y[a
rb.
un
its]
Time [ns]
VCSEL1 (y-mode)
VCSEL2 (y-mode)
-150
-100
-50
0
50
100
150
200
-150 -100 -50 0 50 100 150 200
VC
SE
L2
y-m
ode
[arb
.un
its]
VCSEL1 y-mode [arb. units]
C = 0.943
-200
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-50
0
50
100
150
200
-150 -100 -50 0 50 100 150 200
VC
SE
L2
x-m
od
e[a
rb.u
nit
s]
VCSEL1 y-mode [arb. units]
C = -0.942
-400
-300
-200
-100
0
100
200
0 5 10 15 20 25 30
Inte
nsit
y[a
rb.u
nit
s]
Time [ns]
VCSEL1 (y-mode)
VCSEL2 (x-mode)
Fig. 4. Experimental observation of synchronization of chaos in the twopolarization modes of mutually coupled VCSELs. Temporal waveforms andcorrelation plots for (a),(b) y-mode of VCSEL 1 and y-mode of VCSEL2,and (c),(d) y-mode of VCSEL 1 and x-mode of VCSEL 2.
VI. CONCLUSION
We have shown several configurations leading to bistable
polarization switching and rich nonlinear dynamics in VC-
SELs. The possibility to synchronize VCSEL chaos opens the
way towards high speed, multiplexed secure communication
schemes that are currently in progress.
Acknowledgment- We acknowledge the support of Conseil
Regional de Lorraine, VUB-OZR, GOA, FWO and IAP.
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