JSTQE-CON-SL-04090-2010.R1
1
Abstract— We report a first experimental study of the
polarization-resolved nonlinear dynamics of a 1550 nm single-
mode VCSEL subject to orthogonal optical injection. Stability
maps identifying the boundaries between regions of different
nonlinear dynamics are reported for two different values of the
bias current. A rich variety of nonlinear behaviours including
periodic, period doubling, and irregular dynamics are observed
for both polarizations. Polarization switching and injection
locking induced by the optical injection are also included in the
mapping. Analysis is given also in terms of the frequency
detuning between the injected light and the orthogonal linear
polarization of the VCSEL. When the frequency detuning is
positive polarization switching can be observed in a periodic
dynamical regime, including both period one and period two
behaviors. For positive frequency detuning, the only polarization
that contributes to the dynamics of the total power is the
orthogonal polarization. For negative frequency detunings both
linear polarizations contribute to the dynamics of the total power.
Index Terms—Polarization switching, optical injection,
injection locking, nonlinear dynamics, vertical-cavity surface-
emitting lasers (VCSELs).
I. INTRODUCTION
O
ptical injection in semiconductor lasers is a technique that
is commonly employed to improve the performance of these
lasers without modifying their design [1-3]. It can be used for
reduction of the laser linewidth, of the mode partition noise or
for modulation bandwidth enhancement. Interest in optical
injection in vertical-cavity surface-emitting lasers (VCSELs)
has recently increased [4-8] due to the inherent advantages of
this type of semiconductor lasers. These include single-
longitudinal mode operation, circular beam profile, low
threshold current, reduced fabrication costs, ease of fabrication
of 2D arrays, compactness, etc. [4]. Besides the interest from
Manuscript received November, 2010. This work has been funded in part
by the Ministerio de Ciencia e Innovación, Spain, under project TEC2009-
14581-C02-02, and by EC Project PHOCUS (FP7-ICT-2009-C-240763).
P.Pérez, A.Quirce, L. Pesquera and A.Valle are with the Instituto de Física
de Cantabria, Consejo Superior de Investigaciones Científicas (CSIC)-
Universidad de Cantabria, E-39005 Santander, Spain. P. Pérez and A. Quirce
are also with the Departamento de Física Moderna, Univ. de Cantabria,
Facultad de Ciencias, E-39005, Santander, Spain (Phone: (34) 942 201465.
Fax: (34) 942 200935. E-mail: perezg@ifca.unican.es;
quirce@ifca.unican.es; pesquerl@ifca.unican.es); valle@ifca.unican.es
the applications point of view, optical injection in
semiconductor lasers is interesting for obtaining a wealth of
complex nonlinear dynamics and bifurcations [9]. Period
doubling, quasiperiodicity, chaos and injection locking have
been demonstrated [9]. These studies have also been extended
to VCSELs [10-17] since they offer additional degrees of
freedom, like the direction of the emitted polarization and the
presence of multiple transverse modes, when compared with
their edge-emitting counterparts. Extensive research efforts
have been undertaken to explain the polarization switching
(PS) in free-running VCSELs [18-22]. Different physical
mechanisms can lead to PS, such as the relative modification
of the net modal gain and losses with the injection current [18-
19], spatial hole burning [20], or microscopic spin-flip
processes in the presence of birefringence and linewidth
enhancement factor [21]. In all the previous mechanisms the
role played by birefringence and dichroism [22] is essential.
Most of the studies about the nonlinear dynamics of optically
injected VCSELs have been performed for devices emitting
near 850 nm wavelength. The behaviour of these systems not
only includes high-frequency periodic dynamics, chaotic
dynamics and injection locking, but also PS and Optical
Bistability (OB). The extension of these results to the telecom
wavelength of 1550 nm is of interest in present and future
optical telecommunication networks. For instance, applications
of these phenomena for all-optical signal processing using
VCSELs has recently appeared [3-4],[8].
Although pionering experiments considered parallel
polarization directions for injected and VCSEL laser beams
[10], most of the studies on dynamics have been performed
under orthogonally polarized optical injection conditions.
Orthogonal optical injection (OOI) was first proposed by Pan
et al. to obtain PS and OB between the two linear polarizations
of a short-wavelength VCSEL [23]. In this configuration
linearly polarized light from an external laser is injected
orthogonally to the linear polarization of a free-running
VCSEL. PS and OB induced by OOI have been also recently
obtained in 1550-nm wavelength VCSELs [24-28].
Most of the nonlinear dynamics analysis have been done in
short-wavelength VCSELs with small values of the
birefringence and showing PS in absence of optical injection.
Rich nonlinear dynamics have been found including period
doubling, quasi-periodicity, injection locking, bistability and
chaos [13-16]. A mapping of the dynamics identifying
boundaries between those behaviors was presented in [13]. A
Hopf bifurcation, not reported for edge-emitting lasers, on a
Polarization-resolved nonlinear dynamics
induced by orthogonal optical injection
in long-wavelength VCSELs
P. Pérez, A.Quirce, L. Pesquera, and A.Valle
JSTQE-CON-SL-04090-2010.R1
2
two-polarization-mode solution delimits the injection locking
region [14]. A torus bifurcation, that corresponds to the
excitation of two-polarization mode dynamics in the route to
PS and injection locking, has been described theoretically and
experimentally [14].
Only recently the nonlinear dynamics of a 1550-nm
wavelength single transverse mode VCSEL subject to OOI has
been experimentally analyzed [17]. This VCSEL was
characterized by very large values of the birefringence
parameter and by emission in a single linear polarization over
the whole bias current range in absence of optical injection. A
stability map was reported for the total power identifying the
boundaries between regions of different behavior, including
periodic dynamics, PS and irregular and possibly chaotic
behaviour [17]. However that work only reported the analysis
of the dynamics of the total power because only measurements
of their RF spectra and temporal traces were performed.
In this work we report for the first time to our knowledge an
experimental study of the polarization-resolved nonlinear
dynamics of a 1550 nm-VCSEL subject to OOI. Our VCSEL
is characterized by very large values of the frequency splitting
between both linear polarizations. The device emits in a
linearly polarized fundamental transverse mode over the whole
bias current range. Measured stability maps identifying the
boundaries between regions of different nonlinear dynamics
are reported for several values of the bias current. A rich
variety of nonlinear behaviours including periodic, period
doubling, and irregular dynamics are observed for both
polarizations. More diverse dynamics is observed as the bias
current is increased. Polarization switching and injection
locking induced by the optical injection are also discussed. We
also make an analysis for different frequency detunings
between the injected light and the orthogonal linear
polarization of the VCSEL. We show that the contribution of
the linear polarizations to the dynamics of the total power
depends on the sign of the frequency detuning.
The paper is organized as follows. Section II describes the
experimental setup. Nonlinear dynamics for small and large
values of the bias current are analyzed in sections III and IV,
respectively. Finally, in section V, a summary and conclusions
are presented.
II. EXPERIMENTAL SETUP
The orthogonal optical injection from a tunable laser
(Tunics Plus-CL) into a quantum-well 1550 nm VCSEL is
achieved by using the all-fibre setup shown in Fig. 1. A
commercially available VCSEL (Raycan) was used in the
experiments. The same device was also analyzed in [17]. The
VCSEL bias current and temperature are controlled,
respectively, by a laser driver (Thorlabs LDC200) and a
temperature controller (Thorlabs TED200). The temperature
was held constant at 298
o
K during the experiments. A
variable optical attenuator is included after the tunable laser to
control the level of optical power of the externally injected
signal. The output of the tunable laser is then injected into the
VCSEL using a three-port optical circulator. The polarization
of the external signal is controlled using a fibre polarization
controller. A 90/10 fibre directional coupler divides the optical
path in two branches; the 10% branch is used to monitor the
optical input power with a power meter whereas the 90%
output is directly connected to the SL. The reflected output of
the VCSEL is analyzed by connecting different measurement
equipment to the third port of the circulator. One half of the
power is used to obtain optical spectra with an Optical
Spectrum Analyzer (OSA) or with a Fabry-Perot (FP) analyzer
with resolutions of 70 and 4 pm, respectively. The other half of
the power is directed to a polarization beam splitter that selects
the polarization direction in which the RF spectra are
measured. A fast-photodiode (9 GHz bandwidth) and an
electrical spectrum analyzer (Anritsu MS2719B) were used to
obtain the RF spectra.
Fig. 1. (a) Experimental setup for orthogonal optical injection in a VCSEL.
Fig. 2(a) plots the L-I curve of the free-running device. The
VCSEL emits in the fundamental transverse mode with a
threshold current of I
th
=1.64 mA. The VCSEL emits in a linear
polarization which we will call the “parallel” polarization.
Emission in the parallel polarized fundamental mode is
obtained along the whole current range. Fig. 2(b) shows the
optical spectrum of the VCSEL biased at 8 mA (4.88 I
th
). The
lasing mode of the device with parallel polarization is located
at the wavelength
λ
= 1536.6 nm. The subsidiary mode
corresponds to the fundamental transverse mode with
“orthogonal” polarization and its wavelength (
λ
⊥
) is shifted
0.49 nm to the long-wavelength side of the lasing mode. This
value for the frequency splitting between the two orthogonal
polarizations is very large in comparison to those reported in
short-wavelength devices [13]. A Side Mode Suppression
Ratio (SMSR) of 43 dB is measured for the orthogonal
polarization. Spectra of this form are measured for all biases
and no polarization switching is observed for bias current
above the threshold value. This is probably due to a large
value of the dichroism parameter for our VCSEL.
JSTQE-CON-SL-04090-2010.R1
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0 2 4 6 8 10
0
100
200
300
400
500
1535.5 1536.0 1536.5 1537.0 1537.5
-80
-70
-60
-50
-40
-30
-20
-10
0
P (µW)
I (mA)
a)
P (dBm)
λ (nm)
b)
Fig. 2. (a) L-I curve and (b) spectrum of the free- running VCSEL (applied
bias current of 8 mA) [17].
III. NONLINEAR DYNAMICS AT SMALL BIAS CURRENT
Fig. 3 shows the mapping of the dynamics of the total power of
the VCSEL when it is subject to orthogonal optical injection.
Measurements are performed with the VCSEL biased with an
applied current of 4 mA (2.44 I
th
). The relaxation oscillation
frequency of the free-running VCSEL,
ν
R
, is 2.95 GHz. The
optical injection is characterized by its strength, given by the
value of the optical power arriving at the VCSEL, P
inj
, and by
its frequency,
ν
inj
. We consider values of
ν
inj
, that are close to
the frequency of the perpendicular polarization,
ν
⊥
, the
frequency detuning being
∆ν
=
ν
inj
-
ν
⊥
. The experimental
mapping is obtained by fixing a value of
∆ν
and increasing P
inj
from low values. The different dynamical regimes of the total
power are then identified by using its RF spectrum, recorded at
the output of the 50/50 coupler. In Fig. 3 the region P1 shows
periodic (period 1) behaviour, region IR corresponds to
irregular and possibly chaotic dynamics, and region SL
represents the stable locking range. We have considered P1
dynamics when the peak in the RF spectrum measured in the
RF analyzer is 10 dB above the noise floor. The shape of the
SL region is rather symmetric around
∆ν
=0, in contrast to the
asymmetric shape observed in short-wavelength VCSELs [13].
In fact stable locking associated to the fundamental transverse
mode was only obtained at negative values of
∆ν
[13]. Also in
contrast with the results reported in [13], the irregular behavior
observed in Fig. 3 is only obtained for negative values of
∆ν
and is not the result of a period doubling route to chaos. All
these differences are possibly due to the very large value of the
birefringence parameter and to the single polarization mode
characteristics of our free-running long-wavelength VCSEL.
10 100
1000
-12
-10
-8
-6
-4
-2
0
2
4
6
8
PS
Frecuency Detuning (GHz)
P
inj
(µW)
SL
P1
P1
IR
P1
IR
SL
PS
Fig. 3. (color online) Stability map of the VCSEL subject to orthogonal
optical injection [17]. Different regions are observed: SL (stable injection
locking), P1 (period 1), IR (irregular dynamics), and PS (polarization
switching). The stars mark the situations analyzed in Figs 4 and 5. Applied
bias current of 4 mA
Fig. 3 also shows the injected power required for PS to the
orthogonal polarization of the VCSEL. It is found that PS is
always accompanied with stable locking for negative
∆ν
.
However, PS can be also observed in a periodic (P1)
dynamical regime for positive values of
∆ν
. RF spectra for the
two polarizations and for the total power are shown in the left
column of Fig. 4 for different dynamical regimes. They
correspond to a fixed frequency detuning of 6 GHz and
different values of the injected power. The cases considered in
Fig. 4 are identified in Fig. 3 with white stars. The
corresponding optical spectra of the total emitted light
obtained with the FP analyzer are shown in the right column of
Fig. 4. Showing these results is enough to describe the optical
spectra of both linear polarizations. We have checked that
optical spectra of the orthogonal (parallel) polarization
correspond to the optical spectra of the total emitted light for
frequencies below (above) 30 GHz. The zero value of the
frequency has been chosen to coincide with the frequency of
the orthogonal polarization without optical injection. The
values of the frequency of the optical injection are marked
with arrows in the plots corresponding to optical spectra.
Fig. 4(a) show the dynamics just before reaching the P1
region. The RF spectra shown in this work have been obtained
by subtracting the RF spectra in the absence of light to the RF
spectra with optical injection. We have done it in order to
subtract the noise in the photodetector and RF analyzer. A
peak in the RF spectrum of the total power appears near the
frequency detuning. A similar peak appears in the RF spectrum
of the orthogonal polarization power. The optical spectrum of
Fig. 4(b) shows that two peaks are excited. The highest one
corresponds to the injected light that is reflected at the VCSEL
cavity while the smallest one corresponds to the parallel
polarization mode of the VCSEL. The parallel polarization is
excited with a constant value because its spectrum is flat as it
JSTQE-CON-SL-04090-2010.R1
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is shown in Fig. 4(a).
0 2 4 6 8 10
-100
-90
-80
-70
-60
-50
0 10 20 30 40 50 60 70
0.0
0.5
1.0
1.5
2.0
2.5
0 2 4 6 8 10
-100
-90
-80
-70
-60
-50
0 10 20 30 40 50 60 70
0.0
0.5
1.0
1.5
2.0
2.5
0 2 4 6 8 10
-100
-90
-80
-70
-60
-50
0 10 20 30 40 50 60 70
0
1
2
3
4
5
0 2 4 6 8 10
-100
-90
-80
-70
-60
-50
0 10 20 30 40 50 60 70
0
1
2
3
4
5
0 2 4 6 8 10
-100
-90
-80
-70
-60
-50
0 10 20 30 40 50 60 70
0
1
2
3
4
5
a)
P (dBm)
Total
Orthogonal
Parallel
b)
P (a. u.)
c)
P (dBm)
d)
P (a. u.) P (a. u.)
P (a. u.)
P (a. u.)
e)
f)
g)
h)
f (GHz)
f (GHz)
P (dBm)
P (dBm)
P (dBm)
i)
j)
Fig. 4. (color on line) (Left column) RF spectra of the total and polarized
powers. (Right column) Optical spectra of the total emitted light. Several
values of injected power are considered: (a,b) P
inj
= 168.9 µW, (c,d) P
inj
=
202.7 µW, (e-f) P
inj
=355.1 µW, (g,h) P
inj
= 496.8 µW, and (i,j) P
inj
= 1083.5
µW. The frequency detuning is
∆ν
= 6 GHz and the bias current is 4 mA.
A clear P1 dynamics in the total and orthogonal polarized
powers is obtained when increasing P
inj
as it is shown in Fig.
4(c). Fig. 4(d) shows that the orthogonal polarization is
excited. The frequency difference between the orthogonal
polarization and injection frequencies is 6.1 GHz that
corresponds to the frequency of the peak in the RF spectrum.
This is an indication of a P1 dynamics caused by beating
between the optical injection and the orthogonal mode of the
VCSEL. The parallel polarization can not be appreciated in the
FP spectrum. However the VCSEL has not reached the PS
region yet because the parallel polarization is appreciable in
the OSA spectrum. We have used the optical spectra obtained
with the OSA to depict the PS region in Fig. 3. Our criterion
has been the following: PS is achieved when the ratio between
the power of the orthogonal and parallel polarizations is higher
than 30 dB. The situation in which PS and P1 dynamics is
obtained is illustrated in Figs. 4(e-f). The peaks appearing at
the RF spectrum have shifted to larger frequency values. An
increase of P
inj
produces a larger amount of stimulated
recombination of carriers and hence a smaller carrier density.
In this way the refractive index and the wavelength of the
orthogonal polarization increase producing a larger detuning in
Fig. 4(f), that is a “frequency pushing” effect. Peaks in the RF
spectrum appear at a frequency (7.1 GHz) that approximately
correspond to the frequency detuning in the optical spectrum
(6.3 GHz), the discrepancy being caused by the resolution of
our FP analyzer (0.6 GHz). The frequency pushing effect will
be made clearer in the results presented in the next section.
Further increase of P
inj
produces a decrease of the amplitude
of the peaks in the RF spectrum (see Fig. 4(g)) and also of the
peak corresponding to the orthogonal polarization in the
optical spectrum (see Fig. 4(h)). Operation in the SL regime is
illustrated in Figs. 4(i-j). The orthogonal polarization mode of
the VCSEL is stably locked to the optical injection and the RF
spectra become flat. This is in fact the criterion that we have
used to depict the SL region in Fig. 3. We note that stable
injection locking is observed for larger injected powers than
those required for PS. This is in contrast with results reported
in [13] in which no locking of the fundamental mode was
observed for
∆ν
>0. This is an indication of the different role
played by the much larger values of our birefringence
parameter when compared to those considered in [13].
Fig. 5 shows the RF and optical spectra for a negative value
of the frequency detuning,
∆ν
= -2 GHz. The positions in the
mapping of the cases analyzed in Fig. 5 are indicated in Fig. 3
with red stars. Figs. 5(a-b) illustrate the behavior obtained for
small values of P
inj,
in such a way that the system is in the P1
regime. RF spectra of both polarizations and total power have
peaks at 1.9 GHz frequency and their harmonics. This
frequency corresponds to the frequency detuning that is also
visible in the left peak in Fig. 5(b): the small shoulder
appearing near zero frequency corresponds to the orthogonal
polarization mode that is not clearly separated from the
injection peak due to the 0.6 GHz resolution of our FP
analyzer. Fig. 5(b) also shows that the parallel polarization has
appreciable power. In contrast with Fig. 4 both polarization
modes have periodic dynamics, as it can be seen in Fig. 5(a).
Periodic behavior in both polarizations was also obtained for
850-nm wavelength VCSELs [14]. A torus bifurcation before
reaching the locking region was characterized by a limit cycle
dynamics of the parallel polarization at the relaxation
oscillation frequency and by a wave mixing dynamics between
the orthogonal polarization and the optical injection [14]. Figs.
5(b),(d) do not give clear indications of such a dynamics. The
very different values of birefringence parameter and the single
polarization mode characteristics of our free-running VCSEL
could explain this discrepancy. Increasing P
inj
produces an
increase of the wavelength of the orthogonal polarization
mode in such a way that it approaches the optical injection
wavelength. This is shown in Fig. 5(c-d): RF spectra of both
polarizations and total power have a major peak located at 1.5
GHz and the shoulder in the optical spectrum tends to merge
with the optical injection peak.
The peaks in the RF spectra tend to disappear as P
inj
is
further increased as it can be seen in Fig. 5(e). Broad spectra
are obtained that are the signature of irregular and possibly
chaotic dynamics. This is the behavior characteristic of the IR
region in Fig. 3. The better defined peak appears near 1 GHz
frequency. This is possibly the value of the frequency detuning
that would appear in Fig. 5(f) if our FP analyzer had a better
resolution. The amplitude of the peak near zero frequency in
Fig. 5(f) has increased due to the merger of the orthogonal
JSTQE-CON-SL-04090-2010.R1
5
polarization and the injection peaks. The peak corresponding
to the parallel polarization is much weaker and broader than
that corresponding to the orthogonal polarization (the inset in
Fig. 5(f) is a zoom of that peak). This means that the parallel
polarized mode dynamics is more irregular than the dynamics
of the orthogonal mode. In fact Fig. 5(e) shows that the RF
spectrum corresponding to the parallel polarized power is
much broader than that of the orthogonal polarized power.
This corresponds to irregular and periodic dynamics for the
parallel and orthogonal polarizations, respectively.
0 2 4 6 8 10
-100
-90
-80
-70
-60
-50
-20 0 20 40 60 80
0.00
0.25
0.50
0.75
1.00
1.25
0 2 4 6 8 10
-100
-90
-80
-70
-60
-50
-20 0 20 40 60 80
0.00
0.25
0.50
0.75
1.00
1.25
0 2 4 6 8 10
-100
-90
-80
-70
-60
-50
-20 0 20 40 60 80
0.00
0.25
0.50
0.75
1.00
1.25
0 2 4 6 8 10
-100
-90
-80
-70
-60
-50
-20 0 20 40 60 80
0.0
0.5
1.0
1.5
2.0
2.5
0 2 4 6 8 10
-100
-90
-80
-70
-60
-50
-20 0 20 40 60 80
0.0
0.5
1.0
1.5
2.0
2.5
P (dBm)
Total
Orthogonal
Parallel
a)
P (a. u.)
b)
c)
P (dBm)
P (a. u.)
d)
P (dBm)
e)
50 55 60 65 70
0.00
0.05
0.10
P (a. u.)
f (GHz)
P (a. u.)
f)
P (dBm)
g)
P (a. u.)
h)
P (dBm)
f (GHz)
i)
P (a. u.)
f (GHz)
j)
Fig. 5. (color on line) (Left column) RF spectra of the total and polarized
powers. (Right column) Optical spectra of the total emitted light. Several
values of injected power are considered: (a,b) P
inj
= 26.9 µW, (c,d) P
inj
= 35.5
µW, (e-f) P
inj
=42.4 µW, (g,h) P
inj
= 53.6 µW, and (i,j) P
inj
= 79.1 µW. The
frequency detuning is
∆ν
= -2 GHz and the applied bias current is 4 mA.
Figs. 5(g-h) show the spectra when P
inj
is increased such that
the system is near the border of the IR region in Fig. 3. Peaks
in the broad RF spectra are less defined than those in Fig. 5(e).
Fig. 5(h) shows that the amplitude of the peak corresponding
to the parallel polarization is very small. In fact the PS is
obtained by increasing slightly P
inj
to 65 µW. A sudden
decrease of the RF spectra to the flat shape characteristic of
SL is also obtained at that injected power value. Spectra
corresponding to the SL regime are illustrated in Figs. 5(i-j)
when P
inj
= 79.1 µW.
One of the main differences between results for positive and
negative
∆ν
is the following. When
∆ν
is positive the only
polarization that contributes to the dynamics of the total power
is the orthogonal one, as it is shown in the RF spectra of Fig. 4.
The parallel polarization is characterized by flat and much
weaker RF spectra. When
∆ν
is negative, both polarizations
contribute to the dynamics of the total power as it is illustrated
in the RF spectra of Fig. 5.
IV. NONLINEAR DYNAMICS AT LARGE BIAS CURRENT
Fig. 6 shows the mapping of the dynamics of the total power
when the bias current of the VCSEL subject to orthogonal
optical injection is increased to 8 mA (4.88 I
th
). There are
several differences with respect to the mapping discussed in
the previous section. First, period doubling (P2) dynamics is
obtained for positive and negative
∆ν
values. Second, PS can
be observed in a periodic dynamical regime including P2
behavior. Third, the PS and the SL regions become more
asymmetric as the current is increased, as it was obtained in
[27] and [28], respectively. As in Fig. 3, PS is always
accompanied with SL for negative
∆ν
. Also the irregular
behavior is only obtained for negative values of
∆ν
.
100 1000
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
PS
IR
Frecuency Detuning (GHz)
P
inj
(µW)
P1
P2
SL
P2
P1
P1
P2
SL
PS
IR
Fig. 6. (color online) Stability map of the VCSEL subject to orthogonal
optical injection. Different regions are observed: SL (stable injection locking),
P1 (period 1), P2 (period 2), IR (irregular dynamics), and PS (polarization
switching). The stars mark the situations analyzed in Figs 7 and 8. Applied
bias current of 8 mA.
RF and optical spectra are shown in Fig. 7 for different
dynamical regimes. They correspond to a fixed frequency
detuning of 6 GHz and different values of P
inj
. The cases
considered in Fig. 7 are identified in Fig. 6 with stars. Fig. 7(a)
show the dynamics near the border of the P1 region. A peak in
the RF spectra of the total power and of both linear
polarizations appear near 6.4 GHz, that is near the difference
(6.1 GHz) between the orthogonal polarization and injection
frequencies in Fig. 7(b). A smaller symmetric peak is also
observed at -6.1 GHz. A period doubling dynamics is
illustrated in Fig. 7(c). Two well defined peaks appear at 3.5
and 6.9 GHz. These frequencies correspond to the relaxation
oscillation frequency of the free-running VCSEL,
ν
R
, and to
2
ν
R
(
ν
R
measured at 8mA is 3.5 GHz). This is probably due to
a subharmonic resonance. Four peaks appear in the left part of
Fig. 7(d). The separation between consecutive peaks is 7.1
GHz. This figure also shows that the parallel polarization is
![Fig. 3. (color online) Stability map of the VCSEL subject to orthogonal optical injection [17]. Different regions are observed: SL (stable injection locking), P1 (period 1), IR (irregular dynamics), and PS (polarization switching). The stars mark the situations analyzed in Figs 4 and 5. Applied bias current of 4 mA](/figures/fig-3-color-online-stability-map-of-the-vcsel-subject-to-34ay8lk6.webp)
![Fig. 2. (a) L-I curve and (b) spectrum of the free- running VCSEL (applied bias current of 8 mA) [17].](/figures/fig-2-a-l-i-curve-and-b-spectrum-of-the-free-running-vcsel-3s82kqyw.webp)