Mapping of two-polarization-mode dynamics in vertical-cavity surface-emitting lasers
with optical injection
I. Gatare,
1
M. Sciamanna,
2
M. Nizette,
3
H. Thienpont,
1
and K. Panajotov
1
1
Department of Applied Physics and Photonics, Vrije Universiteit Brussel, 2 Pleinlaan, B-1050 Brussels, Belgium
2
Supélec, LMOPS, CNRS UMR-7132, 2 Rue Edouard Belin, F-57070 Metz, France
3
Optique Non Linéaire Théorique, Université Libre de Bruxelles (U.L.B.), CP 231 Boulevard du Triomphe, 1050 Bruxelles, Belgium
Received 6 November 2008; revised manuscript received 16 February 2009; published 28 August 2009
We report theoretically on the interplay between polarization switching and bifurcations to nonlinear dy-
namics in a vertical-cavity surface-emitting laser VCSEL subject to orthogonal optical injection. Qualita-
tively different bifurcation scenarios leading to polarization switching are found and mapped out in the plane
of the injection parameters, i.e., the frequency detuning vs injection strength plane. A Hopf bifurcation mecha-
nism on the two-polarization-mode solution determines the injection-locking boundaries and influences polar-
ization switching induced by optical injection. We furthermore report on a torus bifurcation emerging from a
two-linearly polarized LP mode time-periodic dynamics before polarization switching and injection locking
appear. It corresponds to an interesting combination of relaxation oscillation dynamics in the x-LP mode
together with wave mixing dynamics in the injected y-LP mode. In agreement with recent experiments, we
unveil a period-doubling route to chaos that involves both VCSEL orthogonal LP modes. The corresponding
region of chaotic dynamics coincides with abrupt changes in the polarization switching boundaries in the plane
of the injection parameters.
DOI: 10.1103/PhysRevE.80.026218 PACS numbers: 05.45.-a, 42.65.Sf
I. INTRODUCTION
Semiconductor lasers subject to external optical injection
can exhibit nonlinear dynamics which are attractive in a
range of applications dealing with optical communications.
Under injection-locking conditions, improvement of lasing
operation properties has been demonstrated in edge-emitting
lasers EEL: reduction in frequency chirp under modulation
1, laser spectral narrowing 2, suppression of mode parti-
tion noise 3, and modulation bandwidth enhancement 4.
Optical injection in semiconductor lasers can also be used to
address a number of applications including all-optical signal
processing 5, microwave generation 6, and wavelength
add-drop functionalities for optical communication systems
7. From the fundamental viewpoint, rich and complex non-
linear dynamics such as period-one oscillations 8, period-
three limit cycles 9, subharmonic resonance 10, wave
mixing, and deterministic chaos 11,12 have been exten-
sively investigated in optically injected EEL. Detailed bifur-
cation studies have yielded a unified view which reveals how
qualitatively different dynamical regimes may interconnect
in a very intricate way when changing the injection param-
eters 13–15, i.e, the injection power and the frequency de-
tuning between the master and the slave laser.
The study of optical injection in semiconductor lasers has
recently been extended to vertical-cavity surface-emitting la-
sers VCSELs. The growing interest in VCSELs is due to
their competitive performances in the following areas: circu-
lar output beam with narrow divergence, low threshold cur-
rent, and the possibility to fabricate dense two-dimensional
VCSEL arrays for optical network interconnects 16.
Single-mode VCSELs typically emit a linearly polarized
LP light aligned along one of two preferential orthogonal
crystallographic axes x and y. However, a change in their
operating conditions, such as bias current or temperature,
may induce polarization switching PS between the orthogo-
nal LP states 17. PS may also be induced by external per-
turbations such as current modulation, delayed optical feed-
back 18, or optical injection 19. In spite of the fact that
VCSEL polarization instabilities are major drawbacks for
polarization-sensitive applications, they can also turn out to
be useful in areas such as all-optical switching 20 or optical
signal processing 21.
In their pioneering experimental work, Pan et al. have
investigated in particular the polarization switching proper-
ties of a VCSEL subject to orthogonal optical injection 19.
In this configuration, the external light has polarization
which is linear and orthogonal to that of the free-running
VCSEL. They have demonstrated that PS induced by optical
injection is achieved with bistability. In agreement with the
experiments carried out by Pan. et al., theoretical studies
22,23, based on the so-called spin-flip model SFM
24,25, have successfully reproduced the bistable PS behav-
ior and its dependence on the injection parameters. Further-
more, the same studies 22,23 reported on the existence of
two qualitatively different injection-locked solutions and also
predicted complex nonlinear polarization dynamics induced
by orthogonal optical injection. Recent experiments have
confirmed the existence of nonlinear dynamics accompany-
ing polarization switching in a VCSEL subject to orthogonal
optical injection 26,27. In particular, they showed that PS
may be accompanied by a period-doubling PD route to
chaos and that the onset of these nonlinear dynamics appears
in the detuning conditions for which PS is achieved with
minimum injected power. Recently, a two-polarization-mode
time-periodic dynamics accompanying PS with injection
locking has been found in 28.
In this paper we extend the theoretical results reported in
Ref. 28 and provide comprehensive investigations of the
interplay between polarization switching and nonlinear dy-
PHYSICAL REVIEW E 80, 026218 2009
1539-3755/2009/802/02621813 ©2009 The American Physical Society 026218-1