Parametric oscillation in a vertical microcavity: A polariton condensate or micro-optical
parametric oscillation
J. J. Baumberg,
1
P. G. Savvidis,
1
R. M. Stevenson,
2
A. I. Tartakovskii,
2
M. S. Skolnick,
2
D. M. Whittaker,
3
and J. S. Roberts
4
1
Department of Physics & Astronomy, University of Southampton, SO17 1BJ, United Kingdom
2
Department of Physics, University of Sheffield, Sheffield S3 7RH, United Kingdom
3
Toshiba Research Europe Ltd, Cambridge, CB4 4WE, United Kingdom
4
Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield, S1 3JD, United Kingdom
共Received 3 August 2000兲
Semiconductor microcavities can support quasiparticles which are half-light and half-matter with interac-
tions possessed by neither component alone. We show that their distorted dispersion relation forms the basis of
a quasiparticle ‘‘trap’’ and elicits extreme enhancements of their nonlinear optical properties. When driven by
a continuous wave laser at a critical angle, the quasiparticles are sucked into the trap, condensing into a
macroscopic quantum state which efficiently emits light. This device is thus an optical parametric oscillator
based on quasiparticle engineering. In contrast to a laser, macroscopic coherence is established in the electronic
excitations as well as the light field. This paves the way to new techniques analogous to those established in
atomic and superconducting condensates, such as ultrasensitive solid-state interferometers.
Parametric oscillators are nonlinear resonators in which a
coherent pump wave is converted into coherent ‘‘signal’’
and ‘‘idler’’ waves of different frequency, thus forming the
basis for broadband tunable sources and mixers.
1
They have
found widespread application in both microwave and optical
frequency regions, as well as providing a ‘‘quantum testbed’’
for some of the most profound demonstrations of nonclassi-
cal photon states.
2
The major stumbling block for optical
parametric oscillators 共OPO’s兲 has been their inefficient op-
tical nonlinearities, only recently improved with the intro-
duction of periodically patterned media which modify the
photon modes. In a similar fashion, the ability to control the
wave functions of electrons by tightly confining them inside
semiconductor heterostructures has revolutionized the sci-
ence and technology of light emitters, modulators, and lasers.
By combining these approaches a new generation of light-
matter interactions can be built which yield novel science
and useful applications. This is most apparent in the vertical
cavity surface emitting laser 共VCSEL兲 which uses mono-
lithic integration of a semiconductor quantum well 共QW兲
emitter surrounded by highly reflecting semiconductor Bragg
mirror stacks.
3
By manipulating both the optical and elec-
tronic degrees of freedom, low-threshold highly efficient las-
ing is possible. This planar microcavity design has also
shown bistability and amplification.
4
However, such devices
operate in a regime with a large density of excited electron-
hole pairs whose effect is to broaden the transitions and re-
duce their coupling to light. In the opposite limit, when high-
quality microcavities contain sufficient oscillator strength
they can enter a new regime due to the strong coupling of
light and matter, producing mixed ‘‘exciton-polariton’’
modes split in energy.
5,6
Much controversy in recent years
has centered on whether strongly excited polaritons can
show a new type of laser action known as a ‘‘boser.’’
7–10
This confusion exists because the mixed exciton-photon
states appear to possess properties inaccessible to their com-
ponent particles.
Here we report an optical parametric oscillation of a mi-
crocavity 共termed a
OPO) which crucially depends on this
exciton-photon physics. Successful shrinking of the shortest
previous OPO device by a factor of 10 000 results from the
formation of a trap for polaritons in the microcavity which
efficiently channels energy from the pump. Resonant wave
interactions are simultaneously possible for the pump, signal,
and idler photons due to the Coulomb interaction between
electrons and holes in the semiconductor layers. By looking
at light emitted in different directions we directly prove the
scattering processes postulated. The threshold power density
is to our knowledge lower than any VCSEL emitter. The
quantum properties of the microcavity inhibit spontaneous
emission into nonoscillating modes, enhance the stimulated
gain and produce ultralow threshold operation. The physics
in this class of solid-state coherent oscillators is akin to co-
operative phenomena such as Bose-Einstein condensation,
ferromagnetism, and superfluidity.
11
Devising an
OPO depends crucially on two distinct fea-
tures: a strong optical parametric interaction, and the effi-
cient photon dynamics of microcavities. Conventionally
centimeter-long inorganic crystals are used for nonresonant
second-order parametric processes in which a pump photon
at 2
is split into a signal photon at
⫹
⑀
and idler photon at
⫺
⑀
. However current materials are insufficiently nonlinear
to allow for submicron interaction lengths. Here another ex-
treme is adopted, using instead a material resonance, in this
case the exciton-polariton in a semiconductor heterostruc-
ture, for resonant third-order parametric interaction of two
pump photons at
to produce the signal and idler emission
(
⫾
⑀
) 关Fig. 1共a兲兴. The free-particle-like dispersion relations
of bound electron-hole pairs 共excitons兲 and the dispersion of
the confined photon cavity mode are both quadratic 关Fig.
1共b兲兴. Very little scattering can occur between such particles,
since energy-momentum conservation is highly restrictive.
By strongly coupling together the excitons and photons in a
microcavity, two new dispersion branches are produced
which have radically different shapes and allow extra scat-
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terings to take place, in particular the process shown in Fig.
1共c兲. Recent pulsed excitation experiments
12
have transiently
revealed the presence of these scattering processes, which
can occur when pump polaritons are injected at a critical
angle to the microcavity normal, near the turning point of the
dispersion. This process has been shown to provide ex-
tremely strong gain, building up substantial polariton popu-
lations in the lowest states which emit directly out of the
sample. A crucial step is the suppression of the normal non-
linear excitonic properties that are inevitably observed at
higher excitation densities, in which filling up of the indi-
vidual electron states prevents their occupation by other elec-
trons, i.e., a fermionic blocking. This is typically seen in the
bleaching of the exciton state when strongly exciting a semi-
conductor. Since lasing requires a large exciton population
this would normally prevent any coherence from building up.
However, dressing the excitons with photons in a strongly
bound ‘‘polariton’’ with a large coherence area, allows them
to overlap with bosonic quantum statistics at low densities
below those at which the fermionic aspects of electron and
hole are manifested. This can be easily identified from the
increase of the scattering rate into a polariton state when it is
occupied.
12
The bosonic stimulated scattering of semicon-
ductor polaritons 共as opposed to stimulated scattering of pho-
tons in a conventional laser兲 transiently identified in time-
resolved measurements leads us to ask whether a polariton
condensation process
13
is possible under CW excitation.
The semiconductor microcavity 关Fig. 1共a兲兴 consists of two
pairs of three 10 nm In
0.06
Ga
0.94
As QW’s in 10 nm GaAs
barriers of refractive index
, sandwiched between 17 共20兲
pairs of GaAs/Al
0.18
Ga
0.82
As distributed Bragg reflectors
共DBRs兲 on top 共bottom兲. The sample is held in a cold-finger,
wide field-of-view cryostat at a temperature of 4 K, allowing
access to the dispersion relation of coupled polariton modes
where different angles of incidence,
, correspond to differ-
ent in-plane photon momenta. The effective optical cavity
length
d⬃3
ex
/2, where the QW emission wavelength is
ex
⫽ 850 nm, producing a cavity mode at
c
⫽
ex
冑
1⫺ sin
2
(
)/
2
with a finesse f ⬃1300. The linewidths
of the bare exciton 共0.8 meV兲 and cavity 共1.2 meV兲 modes
are much smaller than the polariton splitting of ប⍀⫽ 7 meV.
Polaritons are injected resonantly at differently angles using
a tunable CW Ti:sapphire laser focused to a spot diameter
␦
⫽ 100
m, and the central part of the emission is collected
in a fiber-coupled goniometer, dispersed in a 0.5 m mono-
chromator and spectra recorded over 8 decades of intensity
using a cooled CCD.
When the lower polariton branch is excited at the exciton
energy at large angles (⬎ 25°), photoluminescence spectra
measured at intervals along the dispersion clearly resolve the
two strongly coupled polaritons 关Figs. 2共a兲 and 2共c兲兴. Light is
emitted by the sample within a broad cone concentrated
FIG. 1. 共a兲 Geometry of
OPO: pump (16.5°), signal (0°) and
idler (35°) beams defined by the planar microcavity. Beams emerge
in both the forwards and backwards directions with the same in-
plane momentum. 共b兲 In-plane dispersion relation showing energy
of photon and exciton modes vs their in-plane momentum 共or inci-
dent angle兲. 共c兲 Modified dispersion of polaritons in the strong-
coupling regime. The parametric scattering process shown is only
possible for polaritons on the lower branch.
FIG. 2. 共a兲, 共b兲 Photoluminescence spectra at 0° 共signal direc-
tion, solid兲 and 35° 共idler direction, dashed兲 for a 100 mW CW
pump incident at 共a兲 27.6° and 共b兲 16.8° tuned to the lower polar-
iton branch. The elastic pump scatter (
p
), lower polariton (
LP
),
signal (
s
) and idler (
i
) energies are marked. 共c兲, 共d兲 Contour
plots of the emission in energy momentum on a logarithmic scale of
eight decades, from a different sample excited at 共c兲 35° and 共d兲
16.5° with 40 mW, clearly identifying the well-formed polaritons
within the
OPO regime. The dispersion curves on the right show
the dominant processes.
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R16 248 PRB 62J. J. BAUMBERG et al.
within ⫾ 20° due to the effect of the ‘‘polariton energy trap’’
formed by the dispersion relation. This is in complete con-
trast to the microcavity emission when the pump excites the
lower polariton branch at the critical angle
c
⯝ sin
⫺1
兵
冑
3⍀/2
ex
其
⯝ 16.5°. Even at low absorbed pump
powers (2W/cm
2
), stronger emission emerges at near normal
incidence. At still higher powers 共40 W/cm
2
), the
⫽ 0°
‘‘signal’’ emission increases rapidly and the
OPO oscil-
lates 关Fig. 2共b兲 and 2共d兲兴. Also clearly apparent in the spectra
is the ‘‘idler’’ mode at
⫽ 35°, which is more than an order
of magnitude weaker than the signal. Despite the stringent
constraints, we observe oscillation at many locations on a
sample and show data from two different samples in Fig. 2.
The polariton dispersion allows all three polariton modes to
be simultaneously resonant in the optical cavity, drastically
reducing the threshold of the process by a factor
f
signal
f
pump
⬃10
6
. Although pairwise polariton creation
would imply that equal signal and idler powers are expected,
slower photon escape and faster scattering of polaritons at
large angles into high momentum states means that far fewer
photons are eventually emitted. The spectra in Fig. 2 show
that the polariton dispersion is shifted 1 meV to higher en-
ergies in the parametric process
12,14
but the polariton still
remains well defined and is not screened out by the large
polariton population. This relies on the reduction of the OPO
threshold density below the saturation density of excitons.
14
Key evidence for parametric oscillation is provided by the
spectra of this signal beam 关Fig. 3共a兲兴, which shows the dra-
matic superlinear increase of its emission 共normalized to the
pump power兲, and the corresponding reduction in linewidth.
The spectrally integrated power dependence 关Fig. 3共b兲, filled
circles兴 shows the onset of oscillation, with a threshold
which is much less sharp than a conventional OPO, and
which has the expected low-power linear behavior of lumi-
nescence 共dotted兲, switching to exponential amplification
around threshold. The open circles show the almost linear
increase of the lower polariton emission when pumping in-
stead the upper polariton. The solid line is a fit to a simple
model,
15
I
out
⬀r⫺ 1⫹
冑
(r⫺ 1)
2
⫹ 4r/p, which takes into ac-
count the number of modes into which polaritons can spon-
taneously decay (p) and the normalized pump rate, r
⫽ I
pump
/I
th
. For optimum conditions, we find the best fit
with a threshold pump power absorbed in the microcavity of
1.25 mW producing an output of 250
W 共a 20% maximum
conversion efficiency of absorbed power兲 with the number of
spontaneous modes available, p⬃40. Thus the polariton
stimulated parametric scattering forces a significant fraction
of the pump polaritons into the normal incidence mode 共at
the bottom of the trap in the polariton energy dispersion兲,
and hence the need for restricting lateral modes as in a
VCSEL no longer exists. In fact, the current planar device
has a very similar number of spontaneous modes to high
quality laterally defined VCSEL devices.
16,17
The threshold pump density in the semiconductor hetero-
structure ⬃15 W/cm
2
is considerably smaller than that found
in the active region of high-quality oxide-apertured
VCSEL’s 共typically several 100 W/cm
2
),
17
due to the highly
efficient pumping scheme in which the active signal mode
‘‘sucks’’ down carriers from the pump energy through
stimulated parametric scattering. We verify this by pumping
the microcavity at photon energies above the mirror stop
band so that all the light is absorbed and the microcavity
lases as a VCSEL. In this regime, the polariton collapses,
8
the lasing emission is at the exciton energy, and the threshold
is 5 times higher than the
OPO in good agreement with
optimized VCSEL’s. Parametric oscillation also occurs at
other pump angles, though less efficiently, due to multiple
parametric scattering. However when resonantly exciting the
excitons at large angles, no
OPO behavior is found, which
accounts for the failure to observe this mechanism with non-
resonant excitation. With a large thermalized population of
excitons present, many competing Coulomb-mediated para-
metric scatterings occur which prevent a sufficient buildup of
the lower polariton population. The restricted range of pump
angles also shows that in the present case the lasing mecha-
nism is driven by Coulomb scattering between polariton con-
stituents along the dispersion curve, rather than by phonon
interactions. Because the coherent emission is clearly at the
polariton rather than the exciton energy, the device is not
FIG. 3. 共a兲 Power-dependent emission spectra of the signal
beam at 0° normalized to the pump power 共incident at 16.5°). At
high and low powers the emission is linear, while nonlinear at in-
termediate powers. The energies of lower polariton (
LP
), pump
(
p
), signal (
s
) and bare exciton (
ex
) are marked. Inset: FWHM
emission linewidth vs absorbed pump power. 共b兲 Extracted inte-
grated power output vs incident and absorbed power for excitation
at 16.5° at energies on the lower polariton 共solid兲 and upper polar-
iton 共open兲. The line is a fit described in the text. Inset: Signal beam
output.
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simply an exciton laser, but a polariton condensate, with co-
herence in both exciton and photon components.
The advantage of a microcavity comes from the reduction
in the number of cavity modes available for polaritons to
emit into, and from the increase in the stimulated scattering
rate produced by the resonant mode structure.
18–20
From
measurements of the scattering rates under pulsed excitation
conditions, we calculate the threshold incident pump power
for the doubly resonant signal and idler
OPO, I
th
⬃35 mW,
in reasonable agreement with our observations. The localiza-
tion in both energy and angle of the signal beam in disper-
sion space 关Fig. 2共d兲兴 is characteristic for all the conditions
we have investigated, with an angular divergence of the sig-
nal beam ⌬
⬃4° 共a fivefold increase over the pump angular
width兲. Microcavity-OPO theory
19
can account for this angu-
lar divergence, which arises from the lateral coherence
length of the polaritons in the Airy cavity mode of the Fabry-
Perot cavity,
20
l
coh
⫽ 2
冑
fp, producing an estimated diver-
gence ⌬
p
⫽ 2/
冑
fp⬇3°, in good agreement with our experi-
ment. The lateral coherence length describes the diameter of
each polariton, hence macroscopic electronic coherence ex-
ists over this length scale. The spontaneous symmetry break-
ing of the incoherent polariton reservoir when pumped above
threshold indicates a well-defined condensate phase whose
linewidth is currently not interferometrically resolvable
共⬍500 MHz兲. This implies a coherence time ⬎1 ns, far ex-
ceeding the polariton lifetime and unknown for a semicon-
ductor phase coherence. Finally, the quantum statistics of the
emitted photons are expected to be highly nonclassical, with
a high degree of correlation between the signal and idler
photon streams. Future exploitation of the macroscopic elec-
tronic coherence is underway to produce high-sensitivity
solid-state interferometers.
We conclude that strong coupling between photons and
excitons produces judicious quasiparticle dispersions that fa-
vor highly efficient
OPO devices containing a macroscopic
condensate of polaritons. Similar manipulation of atomic dis-
persions can also enhance nonlinear interactions.
21
To further
develop room-temperature devices, materials such as GaN
and organic light emitters are promising since they couple
more strongly to light and would give larger energy shifts
from the pump.
Note added in proof: We have recently observed the po-
lariton angular redistribution accompanying the condensation
process.
22
This work was partly supported by EPSRC GR/M43890,
GR/L32187, HEFCE JR98SOBA, and EC CLERMONT
HPRN-CT-1999-00132. We would like to acknowledge
helpful discussions with C. Ciuti, B. Deveaud, S. Savasta, D.
Hanna, and A.C. Tropper.
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