J. Opt. B: Quantum Semiclass. Opt. 1 (1999) 128–132. Printed in the UK
PII: S1464-4266(99)96009-3
Polarization and transverse mode
dynamics of VCSELs
Francesco Marin† and Giovanni Giacomelli‡§
† Laboratorio Europeo di Spettroscopie Nonlineari, Firenze, Italy and INFM, sezione di
Firenze, Italy
‡ Istituto Nazionale di Ottica, Firenze, Italy and INFM, sezione di Firenze, Italy
Received 9 July 1998, in final form 9 November 1998
Abstract. The investigation of the dynamics of transverse modes in vertical cavity surface
emitting lasers is reported. Their intensity fluctuations are anticorrelated, originating a less
noisy total intensity. The role of these modes in the polarization competition is analysed.
Keywords: VCSEL, polarization, transverse modes, noise
1. Introduction
The vertical cavity surface emitting lasers (VCSELs) show
dynamics and noise features which are peculiar of their
symmetric structure. In fact, due to the small length of
the laser cavity, one single longitudinal mode is supported.
On the other hand, the output window is large enough to
support several tranverse modes (a typical Fresnel number
can be as high as 102 in a standard VCSEL). Moreover,
the rotational symmetry is broken by the laser birefringence;
as a consequence, two linear polarization directions for the
emitted field can be selected. For these reasons, the dynamics
of the mode competition and of the polarization fluctuations
is rather complex.
What is observed in general is that higher-order
transverse modes appear with a polarization direction
perpendicular to that of the main lasing mode [1, 2]. This
phenomenon can be followed by polarization switchings that
have been explained as thermal effects [3], or as transitions
between different stability regions of the laser equations [4,5].
In our case, we show that the higher-order modes
are first observed in the main polarization. The rise of
a transverse mode in the orthogonal polarization leads to
strong anticorrelated polarization fluctuations, eventually
with non-Gaussian statistics, that we have experimentally
characterized in previous works [6, 7].
In this work, we analyse the role of the different
transverse modes involved in this dynamics.
2. Experimental set-up
The laser we have studied is a sample provided by the Paul
Scherrer Institute (Switzerland) [8]. The device is an airpost VCSEL, fabricated by selective lateral etching, with
distributed Bragg reflectors. The active medium is composed
§ Author to whom correspondence should be addressed. E-mail address:
gianni@ino.it
1464-4266/99/010128+05$19.50
© 1999 IOP Publishing Ltd
P (mW)
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Figure 1. Laser intensity versus pump current. (a) x-polarization;
(b) TEM00 -x mode; (c) full triangle-up: TEM10 -x mode; empty
circle: TEM01 -x; full triangle-down: TEM01 -y. In (b) and (c) the
transmission peaks of a Fabry–Perot are measured with the same
arbitrary units.
of three 8 nm wide quantum wells in the centre of a onewavelength thick layer. The output window has a diameter
of 8 µm. Two perpendicular linear polarizations are defined,
parallel and perpendicular to the h110i crystal direction [1].
The threshold current is about 5 mA and the differential
efficiency is 0.1 W A−1 near threshold.
We analysed the intensity fluctuations by means of
an avalanche photodiode (2 GHz bandwidth) and a PIN
photodiode, which has a narrower bandwidth (about 20 MHz)
but an higher quantum efficiency and a larger area (2.5 mm
diameter). The analysis of the transverse modes was
performed by means of two confocal Fabry–Perot spectrum
analysers (free spectral range of 2.5 GHz and 3 GHz), a
monochromator and a CCD camera. A translating 0.2 mm
wide slit allowed the spatial analysis of the beam profile.
Polarization and transverse mode dynamics of VCSELs
(a)
(b)
Figure 2. Intensity profile of the field in the transverse plane at I = 10.7 mA. In (a) (x-polarization), different modes are superposed; the
resulting profile is mainly determined by the (more intense) TEM00 -x mode. In (b) (y-polarization) the TEM01 -y mode is present alone.
A more detailed description of the experimental set-up
is given in [6].
3. Analysis of the lasing modes
For low injection current, the laser emission is well-polarized.
By increasing the current, there is a threshold for the emission
in the secondary polarization. We have observed in a
previous work [6] that, in this situation, the gain is somehow
subtracted from the main polarization, whose growth is
inhibited. For larger currents, the secondary polarization
is again depressed and the power is recovered by the main
polarization. Detecting the unpolarized intensity (without
selecting the polarization direction), we do not observe any
effect of this power partition: the laser intensity increases
regularly with the pump current (see figure 1 of [7]).
A similar behaviour can be observed by looking at the
different transverse modes. Just above threshold, the laser
is in a TEM00 mode, well polarized. We will refer to this
polarization axis as ‘x’. Increasing the pump current, above
8 mA two other modes appear (still x polarized). The
assignment of these modes as TEM01 -x and TEM10 -x has
been done by observing the intensity transmitted through a
Fabry–Perot, while a slit is translated across the beam, in the
two directions. We stress that the axes for the description
of the transverse pattern and of the polarization are the same
within the experimental error.
We will refer throughout the text to the laser intensity,
integrated over the tranverse plane, as ‘total’ intensity.
The intensity of the different modes, measured from the
height of the transmission peaks of a Fabry–Perot, is reported
in figures 1(b) and (c). The first-order modes clearly grow
with the current, while the power in the mode TEM00 is
unchanged. Again, observing the total intensity (figure 1(a)),
there is no noticeable effect of this behaviour.
Figure 3. Optical spectra for the x- (a) and y-polarization (b) at
I = 10.7 mA. The free spectral range is 3 GHz, corresponding to
the entire horizontal axis. The vertical scale of (b) is magnified by
a factor of ten with respect to that in (a). The numbers refer to the
order of the corresponding TEM modes.
By further increasing the pump current, as already
noticed, the laser emission also starts in the secondary
polarization, in a TEM01 -y mode. It is now mainly the
intensity of this new mode which increases with the current,
while the intensity of all the -x modes is stable. The lasing
threshold current for the modes TEM01 -x and TEM10 -x is
about I = 8.5 mA, while for the mode TEM01 -y it is about
I = 9 mA.
We point out that the evaluation of the near-threshold
mode power from the height of the Fabry–Perot peak (as in
figure 1) is understimated, due to the broadened linewidth.
The situation at I = 10.7 mA is described in figures 2(a) and
(b) and figure 3. In figure 2(b) the structure of the TEM01 -y
mode is very clear, while in figure 2(a) different -x modes
are superposed.
The frequency of the TEM00 -x mode is about 100 GHz
lower than that of first-order modes. The TEM10 -x mode
and the TEM01 -y mode are at the same frequency, while the
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F Marin and G Giacomelli
frequency of the TEM01 -x mode is about 9 GHz higher; this
splitting increases at the rate of about 1 GHz mA−1 . The
frequency separations of the different modes are important
parameters for the theoretical models, since they give
information on the anisotropy and the birefringence of the
laser [9].
Above I ' 11 mA, the intensity in the -y polarization
rapidly decreases. We notice that, due to the noise-induced
broadening of the Fabry–Perot peaks in this region (see
next paragraph), the measurment of the mode intensities is
affected by large errors. In fact, the slight decrease of the
mode intensities visible in figure 1 at I ' 11.5 mA for the
different modes is an artifact: observing the total intensity,
no such effect is noticed, and the power regularly increases.
Above I ' 12 mA, it is mainly the TEM10 -x mode who
contributes to the increasing laser power.
We remark that above I ' 16 mA, other modes can be
observed from the optical spectrum in the -x polarization .
As we will show, they are higher-order transverse modes.
(a)
(b)
(c)
4. Intensity noise
In [6] we reported the analysis of the amplitude noise
integrated over the whole beam, without spatial selectivity,
i.e. without separating the different transverse modes. We
observed that the fluctuations are much stronger in each
polarization, with respect to the total intensity (without
polarization selectivity). This behaviour is characterized
by a strong anticorrelation between the polarized intensity
fluctuations; the two phenomena (anticorrelation and excess
noise) are in fact related to each other. This property also
extends to the quantum regime [10].
The noise in the -y polarization and the unpolarized
intensity noise are reported as a function of the pump current
in figures 4(a) and (b), respectively. Besides the already
discussed lower noise of trace (b), we point out that there is
no signature of the emergence of the first-order modes.
However, if we select with the slit a portion of the laser
beam, the situation is different. Figures 4(c) and (d) report the
intensity noise measured with a slit, respectively horizontal
and vertical, situated in the centre of the beam waist. We can
clearly recognize the noise peaks at the threshold of modes
TEM01 -x in (c) and TEM10 -x in (d).
These features are clarified in figure 5, where we plot
the unpolarized intensity noise while scanning the beam
along x with a vertical slit (figure 5(a)) and along y with
an horizontal slit (figure 5(b)). The arrows (1) evidence
the noise at the threshold of the main TEM00 -x laser
mode. In correspondence with the arrows (2), indicating
the rise of the first-order -x modes, a noise increase can
be seen both at the centre of the beam (mode TEM00 )
and in the wings (modes TEM01 and TEM10 ). Since the
total intensity noise is insensitive to this effect, we can
deduce that the fluctuations of the TEM00 and of the firstorder modes are anticorrelated. Evidence of anticorrelated
fluctuations among a strong lasing mode and several nearthreshold modes (in that case, longitudinal modes) have
already been reported in the quantum regime for edgeemitting semiconductor lasers [11].
130
(d)
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Figure 4. Laser amplitude noise, measured on the spectrum
analyser at 10 MHz with a resolution bandwidth of 1 MHz. (a)
total, y-polarized intensity; (b) total, unpolarized intensity; (c)
unpolarized intensity, but with a horizontal slit in the centre of the
beam; (d) as in (c), but with a vertical slit.
The same effect is found at higher pump current (arrows
(3)), where the -y polarization switches off: the excess noise
can be noticed either in the spatially integrated intensity, by
selecting the polarization (figure 4(a)), or in the unpolarized
intensity, by selecting a portion of the laser beam (or a
transverse mode).
By further increasing the pump current, the noise due to
the emergence of higher-order modes is evident (arrows (4))
in figure 5. Again, this phenomenon is not visible in the total
intensity noise; as already said, these modes can be detected
using the Fabry–Perot, but at a higher current level.
5. Polarization and modes dynamics
The dynamics of the polarization fluctuations during the
switch-off of the -y polarization (here around I ' 11.5–
12 mA) presents some peculiar characteristics. As described
in [6], these fluctuations are strongly non-Gaussian, resulting
from rapid intensity jumps between two levels. This
dynamics has been described in [7] using a Langevin
model with a phenomenological quasi-potential. We have
suggested that this behaviour can be physically reconduced to
polarization flips of laser modes, and is thus somehow related
to the transverse modes structure. The only current region
where this kind of dynamics can be observed is indeed that
mentioned above (indicated by arrows (3) in figure 5). In the
Polarization and transverse mode dynamics of VCSELs
(a)
(b)
Figure 5. Unpolarized intensity noise, measured as in figure 4. On the horizontal axis, we report in (a) the position of a 0.2 mm wide
vertical slit scanning along the x direction. In (b), the position of a 0.2 mm wide horizontal slit scanning along the y direction. The profiles
are then shown increasing the pump current from bottom to top.
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Figure 6. (a) Laser beam shape, in the y-polarization (along the
vertical direction). The profile is obtained by scanning a 0.2 mm
wide slit. The vertical units are normalized to the total power in
the y-polarization. (b) Intensity noise, for the same conditions as
(a), measured as in figure 4. In the inset, the histogram of the
intensity fluctuations is shown on a logarithmic scale of six
decades. The pump current is I ' 12 mA.
other situations, even in the presence of strong excess noise
(the rise of the first-order transverse modes), the fluctuations
are Gaussian.
A more realistic model of the laser, suitable to
completely describe the reported behaviours, must take into
account the higher-order transverse modes. However, our
previous works do not enter into details about the role of the
different modes, being focused on the polarization dynamics.
Here, we give instead a characterization of the spatial features
of the phenomenon.
A scan of the slit along the -y axis (figure 6) shows that
the noise in the -y polarization follows the shape of the TEM01
mode. It can be deduced that, concerning the -y polarization,
it is indeed the TEM01 that, switching on and off, gives rise to
the observed intensity jumps. For the current value of figure 6
(I = 12 mA) the TEM01 -y mode is most of the time off, as
shown by the shape of the histogram in the inset.
We notice that the fluctuations are recorded using the PIN
photodiode and the hoppings are smoothed due to the low cutoff frequency. A faster photodiode would have given a two
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Figure 7. Unpolarized intensity noise measured as in figure 4 at
I ' 12 mA, with a vertical slit scanning along the horizontal
direction (the position of the slit is reported on the abscissa). The
insets show the histograms of the intensity fluctuations, with the
slit on the wings ((a) and (c)) and in the centre (b) of the beam.
The histograms are shown on a log scale as in figure 6.
peaks histogram, with the lower peak on the right (higher
level; see figure 6 of [6]).
An important point is to determine whether the
jumps in the polarized intensity are due to flips of the
TEM01 mode only, or whether other modes are involved.
Our measurements indeed provide evidence of multimode
behaviour: in fact, as a part of the beam is selected, the
intensity jumps are still observed even without polarization
selectivity.
In particular, scanning the vertical slit along x (figure 7),
we can observe that on the wings (mode TEM10 -x) the
intensity signal is in the upper level most of the time, while in
the centre (all other modes) it is on the lower level; here the
fluctuations of the TEM01 -y, not completely compensated,
predominate (see insets). A scanning of the horizontal slit
along y gives the opposite result.
The TEM00 could be separated from the first-order
modes by means of a monochromator, exploiting the large
frequency separation. The observation of the amplitude
noise changing the current shows that the main mode does
not participate either in the dynamics of the polarization
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F Marin and G Giacomelli
switchings or, in general, in the large polarization noise. In
fact, after the birth of the first-order modes, the amplitude
fluctuations of the TEM00 remain constant like its dc power,
while the large noise increase is observed on the polarized
first-order modes.
no 96.00267.CT02 and no 98.00444.PF48 (MADESS), by
EEC contract no ERBFMRXCT960010 and by the PAIS
project ‘Quantum noise reduction in semiconductor optical
systems’ of INFM. We also acknowledge A Bialetti for
providing us with useful equipment.
6. Conclusions
References
We have analysed the amplitude noise of VCSELs, in
particular for that which concerns the transverse mode
structure.
The fluctuations of the different mode intensities are in
general correlated, leading to a less noisy total emission.
As a consequence, both polarization selectivity and spatial
filtering lead to increased laser amplitude noise.
The dynamics of the intensity fluctuations is generally
Gaussian, except in the case analysed in [6,7] of polarization
hoppings. We have observed that, in this situation, the
competition is between the TEM01 -y on one side, and both
TEM01 -x and TEM10 -x on the other.
These results can stimulate the development of
theoretical models and the investigation of the range of
system parameters suitable to completely describe the laser
behaviour.
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Acknowledgments
We thank K Gulden of the Paul Scherrer Institute (Zurich,
Switzerland) and M Gabrysch for providing the lasers and
I Ciofa for technical support.
This work was partially supported by CNR contracts
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