AIP Advances 8 , 085205 (2018); https://doi.org/10.1063/1.5038137 8 , 085205
© 2018 Author(s).
Enhanced photon-extraction efficiency
from InGaAs/GaAs quantum dots in
deterministic photonic structures at 1.3
μm fabricated by in-situ electron-beam
lithography
Cite as: AIP Advances 8 , 085205 (2018); https://doi.org/10.1063/1.5038137
Submitted: 02 May 2018 . Accepted: 25 July 2018 . Published Online: 07 August 2018
N. Srocka, A. Musiał , P.-I. Schneider, P. Mrowiński , P. Holewa, S. Burger , D. Quandt , A.
Strittmatter , S. Rodt, S. Reitzenstein , and G. Sęk
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AIP AD V ANCES 8 , 085205 (2018)
Enhanced phot on-e xtr action efficiency from InGaAs/GaAs
quantum dots in det erministic photonic structures
at 1.3 µ m fabricated b y in-situ electron-beam lithograph y
N. Srocka, 1 A. Musiał, 2, a P .-I. Schneider, 3 P . Mrowi ´
nski, 2 P . Holewa, 2
S. Burger, 3,4 D. Quandt, 1 A. Strittmatt er, 1, b S. Rodt, 1 S. Reitzenst ein, 1
and G. Se ęk 2
1 Institute of Solid State Physics, T echnical Univer sity of Berlin, Har denber gstraße 36,
D-10623 Berlin, Germany
2 Laboratory for Optical Spectr oscopy of Nanostructur es, Department of Experimental
Physics, F aculty of Fundamental Pr oblems of T echnology , Wr ocław University of Science
and T echnolo gy , W ybrze ˙
ze W yspia ´
nskie go 27, 50-370 Wr ocław , P oland
3 JCMwave GmbH, Bolivarallee 22, D-14050 Berlin, Germany
4 Zuse Institute Berlin, T akustraße 7, D-14195 Berlin, Germany
(Recei ved 2 May 2018; accepted 25 July 2018; published online 7 August 2018)
The main challenge in the de velopment of non-classical light sources remains their
brightness that limits the data transmission and processing rates as well as the
realization of practical de vices operating in the telecommunication range. T o o ver -
come this issue, we propose to utilize uni versal and flexible in-situ electron-beam
lithography and hereby , we demonstrate a successful technology transfer to tele-
com wa velengths. As an e xample, we fabricate and characterize especially designed
photonic structures with strain-engineered single InGaAs/GaAs quantum dots that
are deterministically integrated into disc-shaped mesas. Utilizing this approach, an
extraction ef ficiency into free-space (within a numerical aperture of 0.4) of (10 ± 2) %
has been experimentally obtained in the 1.3 µ m w av elength range in agreement
with finite-element method calculations. High-purity single-photon emission with
g (2) (0) < 0.01 from such deterministic structure has been demonstrated under quasi-
resonant excitation. © 2018 A uthor(s). All article content, except wher e other -
wise noted, is licensed under a Cr eative Commons Attrib ution (CC BY) license
( http://cr eativecommons.or g/licenses/by/4.0/ ). https://doi.org/10.1063/1.5038137
V ery important building blocks for the realization of practical quantum information technolo-
gies are quantum emitters operating at telecommunication wa velengths. Their compatibility with the
existing fiber netw orks is crucial for the implementation and future dev elopment and competitiv e-
ness of quantum technology schemes such as long-distance quantum communication via the quantum
repeater concept. The main challenge for semiconductor -based sources of non-classical light remains
still the brightness of the de vices limited mainly by the photon-extraction ef ficiency ( η ext ). Se veral
approaches ha ve been de veloped to o vercome this issue within the last fe w years. In general, in view
of the physical mechanism responsible for enhancing the brightness of the source, the y can be catego-
rized into engineering of the far field emission pattern of the quantum emitter to match collection optics
with broadband enhancement of η e xt , e.g., microlenses [ Hadden ( 2010 ), Gschrey ( 2015 )], microob-
jecti ves [ Fischbach ( 2017 ), Gissibl ( 2016 )], solid immersion lenses [ Sartison ( 2017 )] or photonic
wires [ Zhang ( 1995 ), Friedler ( 2009 ), Bleuse ( 2011 ), Claudon ( 2010 ), Reimer et al. ( 2012 )] as well
as wa ve guides [ Prtljaga , ( 2014 ), K oseki ( 2009 )] and embedding the emitter into a microcavity with
narro wband enhancement of η e xt to tailor its emission rate together with directionality of emission
a Electronic mail: anna.musial@pwr .edu.pl
b A. Strittmatter is currently at Institute of Experimental Physics, Otto v on Guericke Univ ersity Magdebur g, D-39106
Magdebur g, Germany .
2158-3226/2018/8(8)/085205/9 8 , 085205-1 © Author(s) 2018

085205-2 Srocka et al. AIP Adv ances 8 , 085205 (2018)
[ Y ablonovitch ( 1993 ), Gerard ( 1998 ), Haroche ( 1983 ), Gayral ( 2000 ), Kiraz ( 2001 ), Moreau ( 2001 ),
V aroutsis ( 2005 ), Laurent ( 2005 ), Heindel ( 2010 ), Kumano ( 2013 ), K ojima ( 2013 ), Dav anco ( 2011 ),
Strauf ( 2007 ), Ellis ( 2008 ), Ding ( 2013 ), Gazzano and Solomon ( 2016 ), Unsleber ( 2016 ), Ding
( 2016 )]. These scenarios can be realized via standard techniques or deterministic nanotechnology
concepts. The deterministic solutions are far more application-rele v ant due to a high yield for de vice
fabrication. W ithin one approach the positions of the emitters can be controlled on the le vel of
gro wth (e.g., by filled nanoholes [ Schneider ( 2012 )] or apertures in oxide layer [ Strittmatter ( 2012 ),
Kaganskiy ( 2018 )] as stressors, metal nanoparticles as catalysts for local nano wire gro wth [ Nguyen
( 2005 )] or via droplet etching of nanoholes [ K ¨
uster ( 2016 )]). The emitters’ positions can also be
random, b ut the nanophotonic structure is deterministically positioned with respect to the emitter
(combination of markers on the surf ace, cathodo- (CL) or photoluminescence (PL) spectroscopy for
the characterization and localization of the emitters, and optical or electron-beam lithography (EBL)
for structure fabrication [ K ojima ( 2013 ), Nogues ( 2013 ), Zadeh ( 2016 ), Sapienza ( 2015 )]) as well
as using microscopy techniques, e.g., atomic force (AFM) or scanning electron microscop y (SEM)
for position determination [ Pfeif fer ( 2012 ), Pfeiffer ( 2014 )]. Additionally , in-situ solutions based on
pre-selection of the emitter and taking into account its position together with the optical properties of
the emitter are the most adv anced and advantageous as the y of fer the opportunity to design structures
optimized for a tar get wa velength and specific applications, e.g., via numerical simulations. Examples
of such approaches include: in-situ 3D EBL [ Gschre y ( 2013 ), Gschrey ( 2015 )], in-situ laser lithogra-
phy combined with microphotoluminescence ( µ PL) spectroscopy [ Somaschi ( 2016 ), Dousse ( 2008 ),
Sartison ( 2017 ), Sawicki ( 2015 )], 3D laser printing [ Sartison ( 2017 ), Fischbach ( 2017 ), Gissibl
( 2016 )] or direct gluing of the emitter to a fibers’ facet [ Cadeddu ( 2016 )].
The abov ementioned approaches hav e been prov en very successful and enabled one to reach
record extraction ef ficiencies of (29-72) % for broadband enhancement approaches [ Claudon ( 2010 ),
Maier ( 2014 ), Schlehahn ( 2015 )] and (66-79) % for narro w-band cavity-based solutions [ Gazzano
( 2013 ), Ding ( 2016 ), Unsleber ( 2016 )]. Using in-situ lithography techniques 79% e xtraction efficienc y
was reported in [ Gazzano ( 2013 )] for the narro wband regime and 29% in [ Schlehahn ( 2015 )] for the
broadband regime. Ev en though most of the techniques claim to be flexible with respect to the emission
wa velength of the source as well as material system, only v ery few were applied to quantum emitters
operating in the application-rele vant range of telecommunication w a velengths and none of them was
a deterministic approach. For the narro wband enhancement utilizing microcavities in this spectral
range η e xt of 3.3% was reported for micropillar cavities [ Chen ( 2017 )], 10% for GaAs-based QDs
in a planar microca vity (N A=0.5) [ Zinoni ( 2006 )] and 36% for InP-based QDs in photonic crystal
ca vities (N A=0.7) [ Kim ( 2016 )]. Broadband approaches ha v e resulted so far in a maximum of 6%
extraction ef ficiency for a tapered-mesa design [ Usuki ( 2006 )].
In this work we demonstrate O-band emitting quantum dots (QDs) that are deterministically
integrated into a photonic mesa structure with e xperimentally obtained η e xt of at least (10 ± 2) %
exceeding the typical e xtraction ef ficiency of semiconductor QDs embedded in a planar sample by
an order of magnitude [ Barnes ( 2002 )] while maintaining single-photon character of the emission.
The QD-mesas were fabricated by lo w-temperature in-situ EBL.
In order to demonstrate the technology transfer of the proposed flexible approach for deter -
ministic de vice fabrication from sub- µ m wa velengths to telecom wa velengths, strain-engineered
self-assembled (Stranski-Krastano w) MOCVD-grown In 0.75 Ga 0.25 As/In 0.2 Ga 0.8 As/GaAs QDs emit-
ting in the 1.3 µ m range ha ve been chosen. Belo w the single QD layer a distributed Bragg reflector
(DBR) section (23 pairs of GaAs/Al 0.9 Ga 0.1 As layers) was introduced and the QDs were capped
with 634 nm of GaAs layer forming a 2 λ ca vity and providing material for nanophotonic structure
fabrication. Due to a relati vely high QD spatial density of a fe w times 10 9 /cm 2 (Fig. 1(a) ) resulting
from yet not fully optimized gro wth, mesas of diameters in the range of (500 – 2500) nm were
fabricated deterministically o ver the selected QDs with respect to the brightness and spectral range,
to maximize the probability that only a single QD is embedded within the mesa structure via the
lo w-temperature in-situ EBL approach [ Kaganskiy ( 2015 ), Gschrey ( 2015 ), Gschre y ( 2013 )] uti-
lizing CSAR62 [ Kaganskiy ( 2016 )] electron-beam sensiti ve resist. As it has recently been pro ven
theoretically , the main photon losses are related to the in-plane propag ation [ Schneider ( 2018 )]
which can be limited by forming e ven relati vely simple disc-shaped mesa structures. Its additional

085205-3 Srocka et al. AIP Adv ances 8 , 085205 (2018)
FIG. 1. (a) Lo w-temperature (T=5K) spatially-resolved cathodoluminescence (CL) map with emission from QDs in the range
of (1316-1326) nm from the planar sample (before mesa fabrication) with a tar get QD marked by the white circle. (b) Scanning
electron microscopy (SEM) image of part of the writing field corresponding to the CL map in (a). Lo w-temperature (T=5K)
CL spectrum (before mesa fabrication, monochromator slit width = 100 µ m for an increase of detected emission intensity) (c)
and microphotoluminescence ( µ PL) spectrum (after mesa fabrication) (d) of the tar get QD.
adv antage is that such photonic structures can be fabricated with high accuracy and an epitaxially
flat top surface.
The optical properties of the QDs in the mesa structures were in vestigated by means of high-
resolution µ PL. The QD structure was mounted in a liquid-helium continuous-flo w cryostat and kept at
a temperature of 5 K. The polarization-resolv ed and e xcitation-po wer dependent µ PL measurements
were carried out under non-resonant continuous-wa ve (cw) e xcitation with a semiconductor laser
diode emitting at 661 nm. A spatial resolution of a single micrometer was pro vided by a long-working-
distance microscope objecti ve with 0.4 numerical aperture. A spectral resolution of at least 25 µ eV has
been assured by using a 1-m focal length monochromator equipped with a LN 2 -cooled InGaAs linear
multichannel detector . For η ext measurements a non-resonant (805 nm) pulsed e xcitation with 80 MHz
repetition rate and 50 ps long pulses provided by a semiconductor laser diode w as used to excite
the tar get QD and the optical signal was detected emplo ying a fiber -coupled NbN superconducting
single-photon counting module with ∼ 20% quantum ef ficiency and 10 dark counts/s at 1.3 µ m. The
same modules were further used for emission autocorrelation e xperiment which was carried out in
Hanb ury-Brown and T wiss configuration with a single monochromator as a spectral filter (100 µ eV
resolution) follo wed by 50:50 fiber beam splitter . It was performed under quasi-resonant cw excitation
provided by e xternal-cavity tunable laser in Littman-Metcalf configuration at the temperature of
30 K to additionally test the possibility to realize the single-photon operation in a cryogenic-free
cryocoolers (e.g., Stirling cryocooler).
The numerical calculations of the photon-extraction ef ficiency from the QD-mesa structure were
performed utilizing a finite-element method (FEM) in the frequenc y domain [ Monk ( 2003 )] follo wing
the approach described in detail in [ Schneider ( 2018 )]. The QD emitter is modelled by a dipole
source. T ime-harmonic Maxwell equations for the exact layer design of the in v estigated structure
and according to measured mesa dimensions were solved by e xploiting non-uniform local mesh
refinement and the radial symmetry of the system as well as by applying a subtraction method for the
singularity in the electromagnetic field of the dipole emitter . The extraction ef ficiency is calculated as
the ratio of the po wer scattered upwards into a gi ven numerical aperture and the total po wer emitted
by the dipole.
The main challenges in the processing of deterministic mesas to o vercome the lo w extraction
ef ficiency for QDs operating at telecom wa velengths were: i) worse performance of photodetectors

085205-4 Srocka et al. AIP Adv ances 8 , 085205 (2018)
for the near infrared range abov e 1.1 µ m due to the necessity of using semiconductor compounds with
narro wer bandgap: ov er 1 order of magnitude higher dark counts for InGaAs chips in comparison
to silicon-based detection and the lack of char ged-coupled device technology for these materials
- both increase drastically the required integration time needed for resolving lo w emission signals
due to worse signal-to-noise ratio, ii) increased mechanical and thermal stability of the cryostat
required due to the longer (approx. 2 times) CL mapping times. At the same time, the inte gration
time for CL is limited to 30 ms by the resist’ s dependence on the introduced ener gy dose [ Gschrey
( 2015 ), Kaganskiy ( 2016 )]. A resist layer of 160 nm thickness was spin-coated on the sample surf ace
prior to the CL imaging step (Fig. 1(a) ) and further used to transfer the written pattern to the GaAs
capping layer via resist de velopment and inducti vely coupled-plasma reacti ve-ion dry etching. The
measured etching depth of 630 nm should assure that the QDs located outside the mesa are either
remov ed or made optically inacti ve and will not contrib ute to the emission. These challenges hav e
been tackled and the requirements were fulfilled to perform successful processing of a deterministic
QD-mesa structure, which was pro ven by in vestigating the resulting optical properties as presented
belo w .
Figure 1(a) presents an example of a CL map of the sample surface with a pre-selected QD with
emission around 1326 nm used further for spectroscopic study and marked by a white circle. Except
of brightness and spectral response, the QD was chosen due to its good spatial isolation in contrast
to the bright emission spots on the right-hand side which origin from a fe w close-by QDs whose
emission intensities adds up.
For this selected QD a lo w-temperature CL spectrum (before processing of the mesa) and a
µ PL spectrum from the mesa are presented in Figures 1(c) and 1(d) proving that emission of the
QD before and after mesa processing sho ws the same basic optical properties [compare further to:
Figs. 2(a) and 2(b) ]. The relati ve change in intensity between the lines as well as ener gy shifts for
some of them can be attrib uted to the dif ferent excitation mechanisms and excitation po wer densities
in CL and µ PL. More than 100 deterministic mesas were fabricated o ver pre-selected QDs and their
emission was studied in µ PL. A statistical comparison of both, total inte grated emission intensity
as well as maximum intensity of indi vidual emission lines at saturation, between QD-mesas and the
planar region of the sample sho ws an av erage intensity enhancement of approx. 6 times due to the
reduction of QD emission propagating in-plane (and therefore lost for collection). A detailed optical
study on an ex emplary QD embedded in a mesa with a diameter of about 1.32 µ m (determined by
SEM – compare Fig. 1(b) ) is presented in Fig. 2(a) and 2(b) .
Emission of v arious excitonic comple xes (neutral exciton – X and bie xciton – XX; charged
complex es (trions) - CX1 and CX2) was identified by means of polarization-resolv ed (Fig. 2(a) ) and
FIG. 2. (a) Lo w-temperature polarization-resolved (T=5K) microphotoluminescence ( µ PL) spectra under continuous-w av e
non-resonant excitation measured at an e xcitation power corresponding to the saturation of the neutral exciton emission.
V arious excitonic complex es from the same QD are observed: neutral exciton – X and bie xciton – XX as well as trions – CX1
and CX2. Linear scale is used to color -code the emission intensity . (b) Lo w-temperature (T=5K) µ PL spectrum under non-
resonant pulsed excitation (805 nm) at saturation po wer (P sat =1 µ W) measured using superconducting nano wire single-photon
counting detectors. Inset: second order correlation function g (2) (t) for CX1 emission line determined from autocorrelation
measurements under quasi-resonant excitation into the 1 st e xcited state in the QD at the temperature of 30 K (black dots) and
fit (red solid line) to the experimental data decon voluted with the o verall temporal resolution of the e xperimental setup.

085205-5 Srocka et al. AIP Adv ances 8 , 085205 (2018)
excitation po wer-dependent (not sho wn here) high-resolution measurements and their origin from
the same QD was pro ven via cross-correlation measurements (not sho wn here). The basic optical
properties of the in vestigated QD were determined, i.e., a bie xciton binding energy of 3.6 meV ,
and a fine structure splitting of the two bright e xcitonic states of 60 µ eV , which are typical v alues
for the in vestigated structures and reported pre viously for similar InGaAs/GaAs QDs [ Paul ( 2015 ),
Olbrich ( 2017 )]. The identification of excitonic comple xes is important for the proper e xperimental
determination of the photon extraction ef ficiency [follo wing the approach used in Gschrey ( 2015 )]
as one has to e valuate the number of photons emitted by a QD at saturation, and therefore has to
add all photons emitted by mutually exclusi ve single-e xcitonic complex es (like neutral exciton and
trions). In this procedure we assume that a QD emits one photon per excitation pulse from a single
excitonic comple x, and hence, the total number of photons emitted by the QD equals to the repetition
rate of the pulsed laser used to excite the QD (80 MHz in our case). The underlying assumption
is that the internal quantum ef ficiency (no contrib ution of non-radiativ e recombination) of the QD
and the excitation ef ficiency is 100%. These parameters are dif ficult to determine experimentally ,
and thus we use the worst-case approximation which o verestimates the total number of photons
emitted by the QD and therefore most probably underestimates the v alue of extraction ef ficiency
determined in this way and hence constituting its lo wer limit rather . W e excite the QD at saturating
po wer , i.e. corresponding to equal emission intensities of X and XX lines (Fig. 2(b) ) and detect the
emission by a single-photon-counting module. Carrying out the measurement in a calibrated setup of
kno wn efficienc y the ratio between the number of photons emitted into the first lens to the repetition
rate can be treated as a measure of η ext . Using this method and taking into account emission only
from neutral and char ged excitons we obtain an e xtraction ef ficiency of at least (10 ± 2) % from the
deterministically fabricated mesa with a single QD inside, which is one order of magnitude higher
than in the case of a QD embedded belo w a planar and non-structured surface [ Barnes ( 2002 )]. This
result nicely demonstrates the potential of the in-situ EBL nanofabrication concept, here applied for
QDs in the telecom range. T o further prov e the applicability of the realized fabrication approach
for quantum technologies we performed the emission autocorrelation measurements to demonstrate
generation of single photons from such a deterministic structure. Under non-resonant e xcitation quite
substantial emission background could still be observed (Fig. 2 ) which is a consequence of yet too
high spatial QD density , and hence hardly a voidable emission from other QDs. In these e xcitation
conditions the obtained v alue of g (2) (0) w as on the le vel 0.5 (not sho wn here), at the very limit of
the single-photon emission condition. T o ov ercome this problem a quasi-resonant excitation scheme
was utilized and as measured g (2) (0) v alue of 0.09 ( < 0.01 after decon volution with setup response
function) was obtained – the inset to Fig. 2(b) presents the result for a positi vely char ged trion line.
This prov es that high purity of the single-photon emission can be obtained from such deterministic
structures with improv ed extraction ef ficiency .
For a direct comparison to the e xperimentally determined photon-extraction ef ficiency it w as also
calculated by the numerical method as described abov e. The actual structural data of the in vestig ated
mesa structure was used as input for the calculations that were performed for a model structure
as sho wn in Fig. 3(a) . The resulting electric field distribution of the scattered dipole emission is
depicted in Fig. 3(b) – 3(d) display the extraction ef ficiency as a function of emission wa velength
and lateral dipole of fset, respectiv ely . The obtained e xtraction ef ficiency of 8.5% for a wa velength
around 1326 nm and a numerical aperture of 0.4 is in a very good agreement with the e xtraction
ef ficiency determined e xperimentally . This supports the assumption of 1 photon per pulse emitted
from the QD used while determining the measured extraction ef ficiency as also in the calculation no
non-radiati ve recombination is included and 100% internal quantum ef ficiency of the model QD is
assumed.
The obtained extraction ef ficiency is a fingerprint of a proper structural quality of the processed
mesa, the good optical quality of the QD, as both a reduced internal quantum ef ficiency of the QD
and shape irregularities of the mesa would result in a smaller photon-e xtraction ef ficienc y . Also,
there is a high accuracy in positioning the mesa with respect to the selected QD estimated to be
better than 50 nm as η ext depends strongly on the relati ve position of the QD and the mesa center
(Fig. 3(d) ). Additional numerical simulations (not sho wn here) demonstrate that in a fully opti-
mized de vice design (including a QD position in the growth direction and thicknesses of all layers)

085205-6 Srocka et al. AIP Adv ances 8 , 085205 (2018)
FIG. 3. (a) Model structure used for the calculations follo wing the actual structure’ s layer design and measured geometry of the
mesa. (b) Electric field distrib ution calculated for parameters corresponding to that of the selected QD-mesa. (c) Dependence of
the extraction ef ficiency on the emission wa velength of the dipole calculated for a numerical aperture N A of 0.4 (corresponding
to the N A of the microscope objectiv e used in the spectroscopic studies) for a dipole positioned in the center of the mesa. (d)
Calculated extraction ef ficiency dependence on a lateral dipole displacement (of fset) from the center of the mesa for a dipole
emission wa velength corresponding to the X emission from the selected QD.
an η e xt exceeding 50% can be achie ved for simple mesa structures on a DBR for QDs emitting
at 1300 nm.
In conclusion, we ha v e demonstrated the successful transfer of our in-situ EBL approach to
QDs emitting at telecommunication wa velengths. T echnologically less challenging and less sensi-
ti ve to processing imperfections, disc-shaped mesas were processed to enhance η ext of single QD
emission instead of more sophisticated photonic structures like curv ed lenses. A sixfold increase in
emission intensity in comparison to the QDs in the planar part of the sample was observ ed while
maintaining the spectral emission features and high optical quality of the integrated QD. Ev en with-
out full optimization of the mesa and QD structure design yet, η ext of at least (10 ± 2) % from a QD
embedded deterministically in such a mesa structure emitting at the telecom O-band together with
high single-photon purity with g (2) (0) < 0.01 under quasi-resonant e xcitation at 30 K were achie ved.
Experimentally determined extraction ef ficiency is in good agreement with numerical simulations.
The photon-extraction ef ficiency could be further impro ved by utilizing detection system with higher
N A or by realizing numerically-determined optimized mesa design, b ut for that, a lower spatial QD
density is required to assure that only a single QD is present in a nanophotonic structure to a void
the contrib ution of other quantum emitters to the spectrum. Extraction ef ficiencies exceeding 50%
are predicted to be achie vable within this approach. This constitutes an important step to wards the
fabrication of practical single-photon sources for quantum communication applications, which are
based on quantum emitters fulfilling the demands for brightness and fiber -compatible spectral range,
and operating at ele vated temperatures making them suitable for the use in compact, cryogenic-free
cryocoolers. This approach can be extended further for the f abrication of 3D structures as has already
been sho wn with microlenses [ Gschrey ( 2015 )].
W e would lik e to thank PicoQuant GmbH for pro viding pulsed e xcitation source for the e xtraction
ef ficiency measurements as well as Artem Bercha and W itold A. T rzeciako wski from Institute of High
Pressure Physics of Polish Academy of Sciences (W arsaw , Poland) for pro viding tunable cw external-
ca vity laser utilized to e xcite the QD quasi-resonantly for e mission autocorrelation measurements.
W e also ackno wledge financial support via the FI-SEQUR project jointly financed by the European
Regional De velopment Fund (EFRE) of the European Union in the frame work of the programme to

085205-7 Srocka et al. AIP Adv ances 8 , 085205 (2018)
promote research, innov ation and technologies (Pro FIT) in Germany , and by the National Centre for
Research and De velopment in Poland within the 2nd Poland-Berlin Photonics Programme, grant No.
2/POLBER-2/2016 (project v alue 2 089 498 PLN). In addition, we ackno wledge financial support
by the German Research Foundation via CRC 787.
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