Supp o rting Info rmation
T w o-Photon based Pulse A uto co rrelation with CdSe Nanoplatelets
Michael T. Quick, † Nina Owschimik o w, † Ali Hossain Khan, ‡ , ¶ Anatolii
P olovitsyn, ‡ , ¶ Iw an Mo reels, ‡ , ¶ Ulrik e W oggon, † and Alexander W. A chtstein ∗ , †
†
Institute of Optics and Atomic Physics, T echnical University of Berlin, Strasse des 17. Juni 135,
10623 Berlin, Germany
‡ Instituto Italiano di T ecnologia, via mor ego 30, 16163 Genova, Italy
¶ Department of Chemistry , Ghent University , krijgslaan 281-S3, 9000 Gent, Belgium
E-mail: achtstein@tu- b erlin.de
Fax: +49(0)30 31421079
Linear Absorbance and V olume Fraction
CdSe nanoplatelets (NPLs) of 4.5 monolayers thickness (a single monolayer is
∼
0.305 nm)
and 24x12 nm
2
and 29x6 nm
2
lateral size wer e dispersed in a polystyr ene matrix. Their
synthesis is described in Ref.
1
. Size and shape of the NPLs wer e determined by TEM-
images, see figs. 1 and 2, respectively . W e r emark that TEM was done with the platelet
dispersion, dried on TEM grids. Stacking does not occur in the polystyrene embedded
samples.
Figur e 3 shows the linear absorption of the used CdSe nanoplatelets (NPLs). Follow-
ing Hens et al. 2 the volume fraction can be estimated by
1
Electronic Supplementary Material (ESI) for Nanoscale.
This journal is © The Royal Society of Chemistry 2019

Figur e 1: TEM of 24x12 nm 2 NPLs.
Figur e 2: TEM of 29x6 nm 2 NPLs.
2

3 0 0 3 5 0 4 0 0 4 5 0 5 0 0 5 5 0
0 . 0
0 . 5
1 . 0
1 . 5
29x 6 nm
2
A b so r b a n ce
W a v e l e n g t h ( n m )
2 4 x 1 2 n m
2

Figur e 3: Absorption spectra of both NPLs (dispersed in PS) under consideration.
f V = ln ( 10 ) A ( λ )
L µ i ( λ ) , (1)
wher e
A
,
L
and
µ i
r epr esent the absorbance, sample’s thickness and the intrinsic absorption
coef ficient of a specific NPL, r espectively . V olume fractions in the or der of 7
·
10
− 5
(see
main text) ar e estimated for both platelets, r eferring to r eported µ i from Achtstein et. al. 3
The thicknesses of both colloidal samples (entir ety of NPL dispersion in solid polystyr ene
matrix) ar e 0.95 mm (24x12 nm 2 ) and 0.90 mm (29x6 nm 2 ).
Excitation Beam Diameter Determination
Figur e 4 displays the excitation power dependent emission of the NPLs and CdS bulk.
The observed linear dependence in the logarithmic pr esentation corr esponds to a near
quadratic power dependence. Beam A and B wer e switched on independently to acquir e
the two data sets. Since the beam pr ofiles of beam A and B dif fer slightly , the same
input power delivers dif fer ent signals, due to the changing excitation density . However ,
dif fer ences in the signal can ultimately be related to the distinct beam diameters (of Beam
3

A and B) at a given position of the sample on the optical axis. This means, once the
beam pr ofiles (as functions of the optical axis z) are known, the ef fective beam diameter
exciting a sample can be determined. T o r etrieve the beam diameters accor ding to eq. 2,
the mismatch parameter
K
(see figur e 4) is evaluated. In logarithmic depiction a r elative
shift (her e: of the data points of Beam B) of
log ( K )
along the or dinate is done to overlay
the data of Beam A and B. In the linear r egime this is equivalent to a scaling factor applied
to the signal generated by Beam B. Since both signals exhibit inher ent dependence on the
squar e of input intensity (see main text), the ratio of both signals can be reduced to the
ratio of beam diameters and thus be linked to K .
B e a m A
B e a m B
S c a l e d B
1 0
1
1 0
2
1 0
- 1
1 0
0
1 0
1
1 0
2

B e a m A

B e a m B

S c a l e d B
1 0
2
1 0
2
1 0
- 1
1 0
0
1 0
1
1 0
2
1 0
3
1 0
- 1
1 0
0
1 0
1
1 0
2
1 0
3
l o g ( K )
P L E m i ssi o n ( a r b . u n i t s)
A v e r a g e P o w e r ( m W )
C d S e N P L

4 . 5 M L C d S b u l k
2 8 8 n m
2
1 7 4 n m
2

Figur e 4: Collected fluor escence signal over average input power for CdSe NPLs of 174 nm
2
and 288 nm 2 ar ea, r espectively , as well as CdS bulk.
K = S ( P A )
S ( P B ) =  w B ( z ) 2
w A ( z ) 2  2
(2)
Assuming gaussian beams, of which the functions of the beam radii
w ( z )
ar e known, the
equation can be solved to give the position
z
. In turn, knowledge about the (effective)
beam diameters (for A and B) can be used to plot the signal over excitation intensity (see
main text, Fig. 3).
4

Measured pulse width vs. input power
0
1 x 1 0
4
2 x 1 0
4
3 x 1 0
4
100
125
150
175
200
225
250
288 nm
2
N P L
175 nm
2
N P L
P u l se d u r a t i o n
p , 1
( f s)
I n p u t p o w e r t o se co n d o r d e r
P
A

·
P
B
( m W
2
)
B B O R e f e r e n ce

Figur e 5: Measured pulse duration vs. second order input power for two nanoplatelets
(NPL) dif fering in size. The obtained pulse durations agree with the r eference value of 171
fs given by a BBO-SHG autocorr elation measur ement (depicted in gr een).
In or der to asses the r eliability of the two dif fer ent NPL-autocorr elators (174 nm
2
and
288 nm
2
) at dif fr ent input powers, we plot the results of autocorr elation measurements
against the input power to second or der . Since the TP A autocorr elation signal, our figur e
of merit, r elies on the pr oduct of input powers (
P i
) deliver ed by both beams (A and B), the
pulse duration is depicted against the pr oduct of
P A
and
P B
. The r esults agr ee r easonably
within their standar d deviation among each other as well as with the BBO r eference (Fig.
5). Hence the TP A autocorr elation is shown to be independent on the input power .
Fluorescence Quantum Y ield of CdS Bulk
The absolute fluor escence quantum yield of CdS bulk (wurtzite) is gained by a comparative
measur ement with r espect to Coumarin 307 (C307) in chlor oform. Starting fr om the
most general definition of fluor escence quantum yield, we ar e looking at the number of
5

4 0 0 4 5 0 5 0 0 5 5 0 6 0 0
0
2 0 0
4 0 0
6 0 0
8 0 0
P L E m i ssi o n ( a r b . u n i t s)
W a v e l e n g t h ( n m )
T P I F C d S
T P I F C 3 0 7
x 1 0 0

Figur e 6: PL signal of CdS bulk sample and Coumarin 307 over wavelength.
fluor escence photons
N E m
with r espect to the number of initially absorbed photons
N Abs
r elated via the quantum yield.
η = N F l s
N Abs
(3)
This equation can be formulated for two dif fer ent materials, allowing for determination
of η (sample) by comparison between a sample (s) and a r efer ence (r).
η s = η r
N F l s , s N Abs , r
N F l s , r N Abs , s
(4)
At first we r elate the number of fluor escence photons to the integral over the luminescence
spectrum
F
. The detected luminescence is r educed by r eflection of the excitation beam
(800nm) upon entering and r eflection of the leaving fluor escence (see main text).
N F l s ∝ 1
( 1 − R i n ) 2 ( 1 − R o u t ) Z ∞
0 F ( λ ) d λ (5)
T o find the number of absorbed photons we start with the two photon absorption rate
Γ Abs
.
Considering only the ratio of absorbed photons as in eq. 4, it is equally valid to look at the
6

ratio of absorption rates.
Γ Abs = β I 2
e x c
h ν V (6)
wher e
β
is the TP A coef ficient,
I e x c
the excitation intensity ,
V
the corr esponding volume of
inter est and
h ν
r epr esents the ener gy per photon of fr equency
ν
. The excitation intensity
is linked to the average input power
¯
P
and the ar ea of the excitation spot, and thus to the
spot radius
w
. As befor e, the experimental initial excitation intensity is to be corr ected by
r eflection upon meeting the sample’s surface.
I e x c ∝ ( 1 − R i n ) ¯
P
w 2 (7)
Combining eqns. 4 to 6, assuming that
V
for any measur ement is lar ger than the sampling
volume of the 0.2 NA micr oscope objective, yields
η s = η r
β r
β s
Z ∞
0 F s ( λ ) d λ
Z ∞
0 F r ( λ ) d λ  ¯
P r w 2
s
¯
P s w 2
r  2 ( 1 − R i n , r ) 4 ( 1 − R o u t , r )
( 1 − R i n , s ) 4 ( 1 − R o u t , s ) (8)
with the average Power
¯
P
and ef fective excitation spot radius
w
for both sample s and
r efer ence r . Performing the calculation a fluor escence quantum yield for the CdS bulk of
0.062
±
0.026 (
∼
40 % deviation) is obtained. Here we r eferred to Xu and W ebb (Ref.
4
)
r eporting an action cr oss section
η · σ ( 2 )
of 19
±
5.5 GM. For the quantum yield of C307 in
chlor oform we use a value of
η =
0.724.
5
T o calculate an ef fective two photon absorption
coef ficient β in solution, we applied the following formula
β = σ ( 2 ) C p ar t
h ν , (9)
wher e the particle concentration
C p ar t
(m
− 3
) in the sample cuvette is determined by a
7

linear absorption experiment at 400 nm excitation.
C p ar t = C mo l · N A = A
ε L · N A (10)
Her e
C m o l
,
N A
,
A
,
ε
and
L
denote the molar concentration, A vogadro’s number , the ab-
sorbance (0.85), the molar decadic extinction coefficient after Ref.
6
(1.85
·
10
4
mol L
− 1
cm
− 1
)
and the sample’s thickness (1 mm).
References
(1)
Bertrand, G. H. V .; Polovitsyn, A.; Christodoulou, S.; Khan, A. H.; Moreels, I. Chem.
Commun. 2016 , 52 , 11975–11978.
(2) Hens, Z.; Moreels, I. J. Mater . Chem. 2012 , 22 , 10406–10415.
(3)
Achtstein, A. W .; Antanovich, A.; Pr udnikau, A.; Scott, R.; W oggon, U.; Artemyev , M. J.
Phys. Chem. C 2015 , 119 , 20156–20161.
(4) Xu, C.; W ebb, W . J. Opt. Soc. Am. B 1996 , 13 , 481–491.
(5)
Choi, K.; Lee, C.; Lee, K. H.; Park, S. J.; Son, S. U.; Chung, Y . K.; Hong, J.-I. Bull. Korean
Chem. Soc. 2006 , 27 , 1549–1552.
(6) Brackmann, U. Lambdachrome laser dyes. 1986.
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