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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978-1-4244-2611-9/09/$25.00 IEEE

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

-150

-100

-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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