Anisotropic Photoluminescence from Isotropic Optical Transition

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Anisotropic Photoluminescence from Isotropic Optical Transition Dipoles in Semiconductor Nanoplatelets Xuedan Ma, Benjamin T. Diroll, Wooje Cho, Igor Fedin, Richard D. Schaller, Dmitri V. Talapin, and Gary P. Wiederrecht Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b00347 • Publication Date (Web): 09 Jul 2018 Downloaded from http://pubs.acs.org on July 13, 2018

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Anisotropic Photoluminescence from Isotropic Optical Transition Dipoles in Semiconductor Nanoplatelets ∗,†

Xuedan Ma,

Benjamin T. Diroll,

Schaller,

†Center

†,¶

†

‡

Wooje Cho,

Dmitri V. Talapin,

‡

‡

Igor Fedin,

Richard D.

†

and Gary P. Wiederrecht

for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439, United States

‡Department

of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, United States

¶Department

of Chemistry, Northwestern University, Evanston, Illinois 60208, United States

E-mail: [email protected]

Abstract Many important light-matter coupling and energy-transfer processes depend critically on the dimensionality and orientation of optical transition dipoles in emitters. We investigate individual quasi-two-dimensional nanoplatelets (NPLs) using higher-order laser scanning microscopy and nd that absorption dipoles in NPLs are isotropic in three dimensions at the excitation wavelength. Correlated polarization studies of the NPLs reveal that their emission polarization is strongly dependent on the aspect ratio of the lateral dimensions. Our simulations reveal that this emission anisotropy can be readily explained by the electric eld renormalization eect caused by the dielectric 1

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contrast between the NPLs and the surrounding medium, and we conclude that emission dipoles in NPLs are isotropic in the plane of the NPLs. Our study presents an approach for disentangling the eects of dipole degeneracy and electric eld renormalization on emission anisotropy and can be adapted for studying the intrinsic optical transition dipoles of various nanostructures.

Keywords CdSe/CdS core/shell nanoplatelets, optical transition dipole, higher-order Bessel-Gauss beam, emission anisotropy, electric eld renormalization eect Quasi-two-dimensional nanoplatelets (NPLs) possess extremely narrow spectral features due to their near-perfect monodispersity in the quantum-conned thickness dimension.

1,2

Their extended plate geometry leads to large exciton coherence size and giant oscillator strength,

24

making NPL-based optoelectronic devices promising for highly ecient dipole

coupling and energy transfer processes.

5,6

NPLs are also potentially interesting candidates

for single photon sources in quantum information processing due to their lifetime-limited spectral line width stration

9

3,7

and lateral size-dependent biexciton quantum yield.

4,8

A recent demon-

of strong light-matter interaction between NPLs and planar microcavities at room

temperature advocates the promising application of NPLs in integrated quantum photonic devices. To leverage these exceptional properties of NPLs for high-performance optoelectronic and quantum photonic applications, knowledge of their transition dipole moment is essential for ecient dipole-dipole and dipole-cavity mode coupling. Optical transition dipoles of materials can vary signicantly depending on their band structures and compositions. Many organic dye molecules exhibit linear absorption and emission dipoles

10,11

following the electric dipole

approximation. In some larger quantum conned systems, the optical matrix elements and optical transition selection rules deviate from the simple electric dipole approximation. In the specic case of wurtzite CdSe quantum dots (QDs), the lowest-lying emissive states are

2


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doubly degenerate in the plane perpendicular to the crystallographic c axis, giving rise to a twofold degenerate transition dipole.

1214

For most of these systems, single particle polariza-

tion spectroscopy has been utilized as an ecient tool in determining the dimensionality and orientation of the transition dipoles.

13,15

Compared to organic dye molecules and spherical

QDs, direct determination of transition dipoles in NPLs using polarization spectroscopy is nontrivial. This is because aside from the inuence of the intrinsic transition dipole properties, renormalization eect caused by the dielectric contrast between the NPLs and the surrounding medium can cause dierent degrees of internal electric eld attenuation for light polarized along dierent directions,

16

leading to polarization-dependent optical transition

probabilities of the NPLs. Moreover, since the transition dipoles are strongly related to the corresponding excitonic states among which the optical transitions happen, the absorption and emission transition dipoles of the NPLs could be substantially dierent.

13

In this Letter, we address these questions by studying the absorption and emission dipoles of core/shell CdSe/CdS NPLs using single particle spectroscopy.

The dimensionality and

orientation of the absorption dipoles are studied by using higher-order Bessel-Gauss laser beams, which when combined with confocal microscopy, are highly sensitive to surface eld gradients.

17

Comparing the experimentally obtained excitation patterns by raster scanning

individual NPLs through the higher-order laser beams with those from vector eld simulations, we nd that the absorption dipoles in NPLs are isotropic in three dimensions, disregarding their lateral dimensions. Further investigation of the emission dipoles of the NPLs using correlated polarization spectroscopy reveals that emission anisotropy of the NPLs is strongly dependent on the aspect ratio of the lateral dimensions. Numerical evaluation of the inuences of dipole degeneracy and renormalization eects on the emission anisotropy reveals that dielectric contrast-induced electric eld renormalization is the main reason for the observed emission anisotropy and the NPLs possess 2D degenerate emission dipoles. These ndings can provide new insights into the design of ecient optoelectronic and hybrid photonic devices based on NPLs.

3


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Figure 1: (a) Coordinate system used in this study. (b) Representative scanning PL images of the NPLs. (c) PL intensity proles from experiment (dots) and simulation (curve). (d), (e) Simulated excitation patterns of an emitter with a 2D (d) and 3D (e) degenerate absorption dipole at dierent tilt angles

α.

The 2D and 3D degenerate dipoles are simulated as two and

three superimposed perpendicular linear dipoles. Scale bars: 1

µm.

Four monolayer thick (∼1.2 nm) CdSe core NPLs with various lateral dimensions (∼70

2 nm to

∼440

2 nm ) were coated with 2 monolayer CdS conformal shells using a previously

published method.

18

PL spectra of the core/shell NPLs have a peak at

∼620

nm with no

apparent dependence on the lateral dimensions (Supporting Information S1). For single NPL optical measurements, diluted NPL suspensions were spin coated on glass cover slides and loaded onto a home-built confocal laser scanning microscope. To study the dimensionality and orientation of the absorption dipoles, individual NPLs were raster scanned at the speed of 10 ms/pixel through higher-order Bessel-Gauss laser beams to obtain the excitation patterns. A polarization converter was used to mode convert pulsed Gaussian laser beams (1 MHz) with a wavelength of 400 nm into higher-order azimuthally polarized beams. excitation power was kept below

∼5

The mean

nW, which is far below the multiexciton regime.

Excitation patterns of individual emitters obtained using higher-order laser beams are characteristic of the dimensionality and orientation of their absorption dipoles. proach has been applied to study absorption dipoles of molecules,

4


19

This ap-

SiO2 nanoparticles,

20

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and metallic nanoparticles.

21

Fig. 1(b) and its inset show representative doughnut-shaped

excitation patterns of NPLs by scanning them through the azimuthally polarized laser beams (see Supporting Information S2 for more examples). The NPLs experienced PL blinking during the scan, leading to a few dark pixels imposed on top of the excitation patterns. Change in the NPL lateral area has negligible inuence on the excitation patterns. To determine the dimensionality and orientation of the absorption dipoles from the experimentally obtained excitation patterns, we use a vector eld simulation method

22,23

implemented in a home-

written Matlab program to calculate the expected excitation patterns of dierent absorption dipoles (see Supporting Information S3 for a detail description of the simulation method). In the simulation, we assume that the laser beam propagates along the z-axis (Fig. 1(a)). Because azimuthally polarized laser beams do not create a longitudinal component and the total eld is transverse,

17

the excitation pattern of an emitter is determined by the projec-

tion of its absorption dipole in the xy-plane. This projection is dependent on the relative angle

α

between the transition dipole plane and xy-plane as well as the relative amplitudes

of the orthogonal composition dipole components. With the increase of angle

α,

the exci-

tation pattern of a 2D degenerate dipole undergoes a continuous change from the peculiar doughnut-shape to two bright o-axis lobes (Fig. 1(d)), whereas that of a 2D anisotropic dipole persistently presents two bright o-axis lobes (Supporting Information S4). The situation for an emitter with a 3D absorption dipole is fundamentally dierent.

For a 3D

degenerate dipole, its excitation pattern remains the same doughnut-shape regardless of its orientation (Fig. 1(e)). However, excitation patterns of an anisotropic 3D absorption dipole with unequal orthogonal dipole component amplitudes could either be doughnut-shaped or two o-axis lobes depending on its relative orientation (Fig. S5). These simulation results indicate that the experimentally observed excitation patterns of the NPLs result from absorption dipoles with isotropic projections in the xy-plane. These could either be isotropic 2D in-plane dipoles (Fig. 1(d)) or 3D dipoles with isotropic xy-plane projections (Fig. 1(e) and S5).

5


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Figure 2: (a), (b) AFM images of a at glass cover slide and a glass cover slide after being drying etched with SF6 for 3 minutes. (c), (d) Cross-section height curves for the glass cover slides in (a) and (b).

Since the NPLs lie mostly face-down on at glass cover slides, determination of the exact 3D nature of their absorption dipoles based on these experimental results is not conclusive. We therefore introduce certain degrees of roughness to the glass cover slides by dry etching them with SF6 (Fig. 2(b) and 2(d)). The roughness is controlled by the etch time in such a way that it causes negligible laser beam distortion but various NPL orientations. quantitatively determine the surface roughness, we estimate the values of force microscopy measurements by assuming that

tan α = ∆y/∆x.

value shows that the etched substrates have an average

10%

of the surface having a corresponding

α

value

(see Supporting Information S5 for details).

> 450

α

value of

α

To

from atomic

Calculation of the

∼ 300 ,

and more than

α

with more than

23%

with

α > 300

Although the detailed orientations of each

individual NPLs remain unknown, statistically, this would lead to some of the NPLs lying with certain tilt angles with respect to the substrates. In this way, if the absorption dipoles of the NPLs are only 2D degenerate, various excitation patterns and unequal intensity proles along dierent directions (Fig.

1(d) and Supporting Information S4) should be observed

from the NPLs dispersed on the etched substrates. However, scanning PL images of more than 150 NPLs from ve samples with dierent lateral dimensions show the same doughnutshaped excitation pattern with similar intensity proles along dierent directions (Fig. 1(b),

6


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S3 and S4). Moreover, a reasonable agreement between the experimental intensity proles and simulated proles of a 3D degenerate dipole can be obtained (Fig. 1(c)). These ndings reveal that regardless of the NPL orientations, projections of their absorption dipoles in the xy-plane are always isotropic. To fulll this condition, absorption dipoles of the NPLs at the excitation wavelength need to be 3D isotropic. This isotropic absorption dipole is most likely due to the relatively high density of electronic states at the excitation wavelength of 400 nm.

24

Figure 3: (a), (b) Projections of a linear (a) and 2D degenerate (b) transition dipole onto the sample plane. (c), (d) PL timetraces of a NPL (ρ

= 3.6) recorded by the detector behind

the rotating linear polarizer (c) and the detector without the linear polarizer (d). (e) Ratio of the intensity curves in (c) and (d). (f ), (g) PL timetraces of a NPL (ρ

= 1.5)

recorded by

the two detectors ((f ) with the linear polarizer; (g) without the linear polarizer). (h) Ratio of the curves in (f ) and (g). Marked areas indicate long "dark" periods of the NPLs.

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Having determined the 3D isotropic nature of the absorption dipoles of the NPLs at the excitation wavelength, we further investigate their emission transition dipoles. To rst order, the optical transition strength of an emitter is proportional to transition dipole vector, and

E

is the electric eld vector of the absorbed or emitted light.

For a linear transition dipole oriented at a tilt angle dipole and xy-plane) and an in-plane angle the light electric eld) (Fig.

| µ · E |2 , where µ is the

ϕ

α

(the angle between the transition

(the angle between the transition dipole and

3(a)), its emission intensity is proportional to its projection

along the light electric eld direction, i.e.

cos2 α cos2 ϕ.

Rotating the polarization in the

collection beam path using a linear polarizer is equivalent to changes in the angle leads to a detected polarization degree, which is dened as

Imin = 0,

respectively.

that here

ϕ

Imax =| µ |2 · | E |2 · cos2 α

If the emitter possesses a 2D emission dipole (Fig.

emission intensity is still dependent on the tilt angle

α

and it

P = (Imax − Imin )/(Imax + Imin ),

of 100% with the maximum and minimum intensities being and

ϕ,

and the in-plane angle

3(b)), its

ϕ,

except

refers to the angle between one of the transition dipole components and the

light electric eld. Recent ensemble studies

25,26

of CdSe NPL thin lms indicated that their

emission dipoles were oriented within the plane with no measurable out-of-plane component. Therefore, for a NPL with an in-plane 2D emission dipole lying on a at glass cover slide, the corresponding value of

α

is close to

00 .

Rotating a linear polarizer in the collection

beam path leads to maximum and minimum emission intensities of and

Imin =| µ⊥ |2 · | E⊥ |2 ,

with

µk , µ⊥

and

Ek , E⊥

Imax =| µk |2 · | Ek |2

being the transition dipole and light

electric eld components along the long and short axes, respectively. By dening a dipole degeneracy factor

η =| µk |2 / | µ⊥ |2 ,

the polarization degree is given by

P = (η· | Ek |2 − | E⊥ |2 )/(η· | Ek |2 + | E⊥ |2 ).

(1)

Therefore, photoluminescence polarization is determined by both the dipole degeneracy factor

η

and electric eld intensities along the dierent axes with

8


P = 0

corresponding to

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isotropic emission. It is worth noting that because we excite the NPLs far above their emission energy with excitation intensities below saturation, in a rst approximation, we can treat the absorption and emission processes independently. The overall experimentally observed PL polarization i.e.

P = Pex · Pem ,

P

with

is hence the product of the absorption and emission polarizations,

Pex

Pem

and

being the polarization degrees of the absorption and

emission processes. Moreover, even though we have known from the above higher-order laser studies of the NPLs that their absorption dipoles are isotropic and the excitation dipole degeneracy factor

ηex = 1,

the emission dipole degeneracy factor

could be fundamentally dierent from

ηex

ηem

remains unknown and it

due to the very dierent excitonic states involved

in the two independent processes. For quantum emitters with negligible size eects (such as small molecules) or isotropic geometries (such as spherical quantum dots), PL polarization of individual emitters has been used as a direct indication of their intrinsic transition dipole degeneracy because correspondingly in Eq. (1)

| Ek |=| E⊥ |.

However, in the case of NPLs which have anisotropic

geometries, the dierence in the dielectric constants of the NPLs and their surrounding medium can lead to a renormalization of the electric eld inside the NPLs with respect to the homogeneous external electric eld in the surrounding medium

16,27

(i.e.

| Ek |6=| E⊥ |).

This renormalization eect itself can alter the probability of optical transitions along different directions and lead to a dependence of the absorption and emission on the incident light polarization.

Thus, experimentally observed PL polarization of NPLs is a combined

result of intrinsic optical transition dipole degeneracy and dielectric contrast-caused electric eld renormalization eect. In the following, we present a general approach for disentangling these two eects and extracting intrinsic emission dipole degeneracy of a quantum emitter with an anisotropic geometry based on PL polarization spectroscopy. Due to PL blinking and PL uctuation of the NPLs commonly attributed to charge carrier trapping at surface and/or core/shell interface states,

4,28

direct measurements of the

polarization-dependent PL intensity was nontrivial. We therefore split the collected PL from

9


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the NPLs into two identical single photon avalanche diodes and place a linear polarizer in front of one of the diodes.

15

This technique enables simultaneous measurements of the PL

with the two detectors, and any PL intensity uctuation/blinking that is not caused by the linear polarizer can be compensated by comparing the signals from the two detectors. Fig.

3(c) and 3(d) show representative PL timetraces of a NPL from a sample with an

average length

L

of

∼15.9

nm and width

W

of

∼4.4

nm detected by the two diodes. The

timetrace in Fig. 3(c) was periodically modulated by a linear polarizer at an angular speed of

∼ 420 /s.

Despite the drastic PL uctuation, the ratio between the two timetraces (Fig. 3(e))

only reects the polarization modulation and it can be tted with a single Calculation of the polarization degree

P

sin2 ϕ

function.

gives a value of 23.2%. Fig. 3(f ) - (h) present PL

timetraces of a NPL from a sample with an average length of

∼16.2

nm and width of

∼11.1

nm, and a polarization degree of 5.9% is obtained. We investigate polarization degrees of more than 180 NPLs from ve samples with dierent lateral dimensions (See Supporting Information S6 for distribution), and plot the average polarization degree values from each sample as a function of the corresponding aspect ratio (ρ

= L/W ) in Fig.

4(a). The emission

polarization degree increases with the NPL lateral aspect ratio. Similar polarization behavior is observed for NPLs dispersed on the etched substrates, although the average polarization degree is slightly larger than those of the NPLs on at substrates.

Without knowing the

detailed orientations of each individual NPL on the roughened substrates, we approximate their eective" aspect ratio to be

ρe = L/(W ·cos α).

From the dierence in the polarization

degrees of the NPLs dispersed on the two dierent types of substrates, we can estimate that the tilt angle

α of the NPLs on the etched substrates could vary between 00

average value of

210 ,

and

900

with an

consistent with the values determined from the AFM measurements.

However, local electromagnetic eld variation caused by the roughened surface may also contribute to the discrepancy.

Due to the lack of knowledge of the exact orientations of

each individual NPLs, the observed discrepancy may be caused by either of the two or both eects.

10


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Figure 4: (a) Aspect ratio dependent polarization degrees of the NPL emission from experiment (red dots: NPLs on at glass cover slides; black dots: NPLs on dry-etched substrates) and simulation (dashed curve: FDTD simulation; solid curve: analytical calculation). (b) - (e) Local electric eld

|E|

distributions at the excitation wavelength for a normal inci-

dent plane wave polarized along the NPL width ((b) and (d)) and length ((c) and (e)). The 2 2 dimensions of the NPLs in (b), (c) and (d), (e) are 30×7.5 nm and 30×15 nm , respectively.

In principle, according to Eq. (1) the observed emission anisotropy (P attributed to:

(a) anisotropic emission dipoles (µem,k

6= µem,⊥ )

6= 0)

might be

determined by the band

structure of the NPLs which is related to their dimension, composition and crystal structure;

2932

(b) renormalization eect of the optical electric eld inside the NPLs caused by the

dierences in the dielectric constants of the NPLs and the surrounding environment.

3335

In

the second case, mismatch in the dielectric constants leads to dierent degrees of modulation to the optically-induced electric eld inside the emitter, with the internal electric eld for

E⊥ )

light polarized along the short axis (

Ek ). 34

(

attenuated stronger than that along the long axis

Because optical transition rate is proportional to the local electric eld inside the

NPLs, this in turn results in the probability of optical transitions for light polarized along the short axis being smaller. To determine the cause of the aspect ratio dependent PL polarization, we evaluate the inuences of the dielectric contrast and dipole degeneracy by calculating the attenuated electric eld intensities inside the NPLs using two approaches.

11


In the rst approach, we

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simulate the electric eld intensity distributions inside the NPLs using the three-dimensional nite-dierence time-domain (FDTD) method. NPLs with aspect ratios

ρ = 4

Internal electric eld distributions of two

and 2 at the excitation wavelength are plotted in (Fig.

4(b) - (e)). For both NPLs, the internal electric eld is attenuated strongly when the light is polarized along the width, with the attenuation being even stronger for the one with the larger aspect ratio (Fig. 4(b)). To calculate the polarization degree using Eq. (1), we numerically calculate the overall internal electric eld intensities in NPLs for light polarized along the NPL length (|

Ek |2 )

and width (|

E⊥ |2 )

at both the excitation and emission

wavelengths. In the second approach, we calculate the internal electric eld analytically. For a dielectric ellipsoid with a dielectric constant

ε

embedded in a medium (εm ), the internal

Ek/⊥ ) with the light polarized parallel and perpendicular to the

electric eld of the ellipsoid ( axial direction is given by

Ek/⊥ = E0 · (εm /(εm + (ε − εm ) · nk/⊥ )), 27,36

with

nk/⊥

being the

depolarization factors that are dened by the semimajor dimensions of the ellipsoid (a, c) as

nk = (1 − e2 ) · (ln((1 + e)/(1 − e)) − 2e)/(2e3 ), n⊥ = (1 − nk )/2,

where

e =

p

1 − a2 /c2 .

(2)

Because the depolarization factors of a dielectric ellipsoid and

rectangular plate are similar,

37

we apply this method to calculate the internal electric eld of

the NPLs. Since PL anisotropy is determined by both the absorption and emission processes, in principle from the simulated electric eld intensities we can calculate the polarization degrees

Pex

and

Pem

at both the excitation and emission wavelengths provided that the

corresponding dipole degeneracy factors polarization degree

ηex

and

ηem

are known, and as a result the overall

P = Pex · Pem .

Simulation results from both approaches are compared to the experimental values. Since we learn from the excitation patterns that the absorption dipole degeneracy factor only the value of the emission dipole degeneracy factor

12

ηem


ηex = 1,

is adjusted for tting. The best

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tting result is achieved with

ηem =

1 and the corresponding simulation results are plotted

in Fig. 4(a) (see Supporting Information S8 for other values of

ηem ).

These ndings reveal

that the dielectric contrast induced renormalization eect in the NPLs is the main reason for the observed PL anisotropy.

We also conclude that the 2D emission dipoles of NPLs

are isotropic irrespective of their extended plate geometries.

It is also worth mentioning

that the origin of PL anisotropy in NPLs and QDs is fundamentally dierent despite the similar isotropic 2D emission dipoles in both systems.

PL polarization of QDs is caused

by the random orientations of the 2D emission dipoles with respect to the sample planes, whereas for NPLs, it is mainly caused by the electric eld renormalization eect due to their anisotropic geometries. In conclusion, we have shown that despite their 2D in-plane emission dipoles, NPLs possess 3D isotropic absorption dipoles at the excitation energy.

This absorption isotropy is

because of the averaging over many electronic states at the excitation energy.

24

In contrast,

the isotropic in-plane emission dipoles of the NPLs might be due to the heavy hole level dominant valence band top which possesses mixed in-plane

px

and

py

symmetry.

26

Ultrafast

thermalization of charge carriers after absorption leads to their loss of memory of the initial absorption polarization, consequently leading to decoupled absorption and emission polarizations. We also present a general approach for disentangling the eects of dipole degeneracy and renormalized electric eld on PL anisotropy, which can be applied to a variety of systems for studying their intrinsic transition dipole properties. For NPLs, the aspect ratio dependent PL polarization indicates that their lateral dimensions and the dielectric constant of the surrounding medium can be designed to achieve the most ecient dipole coupling/light extraction for specic applications.

This, for instance, in combination with the size tun-

able LO phonon bottleneck in CdSe NPLs,

7

can be applied towards highly polarized lasing

applications.

13


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Acknowledgement We thank Ralu Divan for her assistance in the dry etching process. This work was performed, in part, at the Center for Nanoscale Materials, a U.S. Department of Energy Oce of Science User Facility, and supported by the U.S. Department of Energy, Oce of Science, under Contract No.

DE-AC02-06CH11357.

We also acknowledge support from NSF DMREF

Program under awards DMR-1629601 and DMR-1629383.

Supporting Information Available The following les are available free of charge. Ensemble characterization of CdSe/CdS core/shell NPLs; experimentally obtained excitation patterns of NPLs; numerical simulation of the excitation patterns; simulated excitation patterns of absorption dipoles with dierent orthogonal amplitudes and orientations; distribution of

α;

polarization degrees of NPLs on two dierent types of substrates; inuence

of CdS shell on the electric eld distribution; emission dipole degeneracy factor dependent polarization anisotropy.

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2009, 48, 68616864.

(2) Ithurria, S.; Tessier, M. D.; Mahler, B.; Lobo, R. P. S. M.; Dubertret, B.; Efros, A. L. Colloidal nanoplatelets with two-dimensional electronic structure. Nat. Mater.

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Anisotropic Photoluminescence from Isotropic Optical Transition

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