Substrate-Induced Chirality in an Individual Nanostructure | ACS

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Substrate-Induced Chirality in an Individual Nanostructure Sergey Nechayev, René Barczyk, Uwe Mick, and Peter Banzer ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.9b00748 • Publication Date (Web): 18 Jul 2019 Downloaded from pubs.acs.org on July 19, 2019

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ACS Photonics

Substrate-Induced Chirality in an Individual Nanostructure †,‡,¶

Sergey Nechayev,

René Barczyk,

†,‡,¶

Uwe Mick,

†

∗,†,‡

and Peter Banzer

†Max Planck Institute for the Science of Light, Staudtstr. 2, D-91058 Erlangen, Germany ‡Institute of Optics, Information and Photonics, University Erlangen-Nuremberg,

Staudtstr. 7/B2, D-91058 Erlangen, Germany ¶These authors contributed equally E-mail: [email protected]

Abstract

(CB), while the latter results in circular dichroism (CD)

4,5

. Importantly, circular anisotropies

We experimentally investigate the chiral optical

are invariant with respect to reversal of the

response of an individual nanostructure consist-

propagation direction of circularly polarized

ing of three equally sized spherical nanoparti-

light (CPL)

cles made of dierent materials and arranged in 90◦ bent geometry. Placing the nanostructure

requires some caution.

on a substrate converts its morphology from

of dierential extinction of CPL and therefore

achiral to chiral. Chirality leads to pronounced

necessitates polarization analysis of the trans-

dierential extinction, i.e., circular dichroism

mitted light , unless it is observed as an average

and optical rotation, or equivalently, circular

value of monodisperse solutions . In the pres-

birefringence, which would be strictly forbid-

ence of linear anisotropies, which are typical

den in the absence of a substrate or hetero-

for chiral structures

geneity. This rst experimental observation of

sity of the transmitted light (∆T ) for LCP and

the substrate-induced break of symmetry in an

RCP illumination along a certain direction does

individual heterogeneous nanostructure sheds

not necessarily represent CD as dened above,

new light on chiral light-matter interactions at

but rather a combination of circular and lin-

substrate-nanostructure interfaces.

ear anisotropies

611

and their proper measurement

For instance, CD is usually dened as a measure

7

5

12

, the dierence in inten-

7,10,11,13

.

Contrary to CD and

CB, linear anisotropies invert their sign upon wavevector reversal

Keywords

of

important

Lord Kelvin denes chirality as the property

for

the

12,13,15

optical .

response

of

In crystal optics,

dened with respect to the natural basis of

Chiral molecules and

the

2,3

specimen,

axes.

left- and right-hand circular polarizations

given

In contrast,

by

its

crystallographic

for nanostructures these

axes are in general unknown, whence the mea-

(LCP and RCP) experience dierent real and imaginary parts of the refractive index.

.

linear and circular anisotropies are commonly

mirror, ideally realized, cannot be brought to nanostructures exhibit circular anisotropies

role

anisotropic objects

of a geometrical gure who's image in a plane

1

7,10,11,14

The direction of illumination itself plays an

gence, heterogeneity, substrate-induced

coincide with itself .

and the average value

h∆T i for backward and forward illumination

represents CD

chirality, circular dichroism, circular birefrin-

7,10,11

sured anisotropies in general depend on the

The

7

chosen reference frame .

former is the origin of circular birefringence

ACS Paragon Plus Environment 1

Even achiral planar

ACS Photonics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 11

structures may show pronounced tunable CD

of our knowledge, substrate-induced emergence

and CB under oblique illumination, which is

of dierential extinction (CD) and CB in an

typically referred to as extrinsic or pseudo-

individual QPN under normal incidence and,

chirality

. Consequently, a measurement of

hence, its conversion into chiral morphology,

CD and CB along a xed direction of illumi-

have not been experimentally investigated to

nation does not necessarily indicate structural

date.

chirality.

Here,

A practically interesting case are quasi-planar

or

nanostructures (QPNs) with broken in-plane

try

reection symmetry (or asymmetric QPNs),

substrate-induced

such as a at spiral of nite thickness or an asymmetric planar arrangement of arbitrarily

asymmetric QPN. The QPN consists of three ◦ nanospheres of radii r = 90 nm arranged in 90

sized spheres.

bent geometry

1624

Since the sense of twist of a

we

k-space

7,10,11,41,42

apply

back-focal

Mueller

matrix

plane

(BFP)

spectropolarime-

to investigate the emergence of

35

chirality

in

an

individual

with estimated gaps of

2 nm

at spiral inverts with the reversal of the di-

between neighboring particles (Fig. 1a and

rection of observation and circular anisotropies

1b), which are positioned on a glass substrate

are

using a pick-and-place procedure

invariant

under

wavevector

reversal

611

,

43,44

. The in-

QPNs can not show any CD or CB when il-

plane reection symmetry of the nanotrimer is

luminated normally to their inherent plane of

broken by its heterogeneous material composi-

mirror symmetry. However, QPNs may show a

tion

strong chiroptical response in dierential trans-

are made of silicon (Si)

mission (∆T ),

dierential absorption (∆A),

35

the two upper nanoparticles in Fig. 1b

is made of gold (Au)

46

45

, while the third one

.

The glass substrate

dierential scattering and asymmetric polar-

breaks the forward-backward symmetry under

ization conversion of CPL

normal incidence and renders the whole system

mentioned

dierential

10,11,2536

measures

.

All afore-

must

invert

structurally chiral.

We experimentally recon-

their sign with the reversal of the illumina-

struct the emerging CD and CB spectra, which

tion direction, if the QPNs are embedded in a

would be strictly forbidden in the absence of a

homogeneous background.

substrate or heterogeneity.

This fundamental

dierence between the illumination directiondependent

∆T \∆A

and strictly forbidden cir-

Results

cular anisotropies attracted signicant attention and was discussed in the context of optical reciprocity

6,811,27,28,31,32,37,38

We start by theoretically investigating the scat-

.

tering properties of the nanosphere assembly.

However, for experimental investigation, QPNs

The sample exhibits a rich spectral behavior

are commonly positioned on a substrate, which

with several resonances, residing in the exci-

breaks the forward-backward symmetry for nor-

tation and interaction of various electric and

mally incident CPL. Furthermore, a substrate

magnetic multipoles in the nanospheres con-

converts the morphology of the system from

stituting the nanotrimer

achiral to chiral. Substrate-induced emergence

metric arrays of nanoholes time, non-zero

∆A

10

.

(σe ) cross-sections for normally incident plane-

and in asym-

wave CPL illumination

At the same

39

35,36

larizability is obtained from Mie theory in free-

.

space

Dierential scattering of CPL was shown for symmetric QPNs under oblique illumination

40

.

49

.

Each of these dipoles reacts to the

incident eld, to the eld of the other dipoles

22

and its own reected eld

and a variety of individual nanostructures under normal incidence

. In the CDM, each

dipole, whose electric- and magnetic-dipole po-

and single asymmet-

ric QPNs under normally incident CPL

47,48

of the nanoparticles is modeled as a point-

has been demonstrated for

individual nanohelices

We employ a

scattering (σs ), absorption (σa ) and extinction

tor reversal has been experimentally conrmed

8,11

.

coupled-dipole model (CDM) to calculate the

of CD and CB that are invariant under wavevecin arrays of asymmetric QPNs

24,35

47,48,50,51

. In Fig. 1c,

we plot the dierential cross-sections normal-

However, to the best


Page 3 of 11 (a)

(b)

Fig. 1c shows that the dierential scattering

∆Qs

in zero dierential extinction

z

∆Qa = 0.

x

0.12 (c)

Forward

∆Qs

With the reversal of the direc-

∆Qa

and

just interchange their ampli-

tudes, preserving

Backward

∆Qe = 0.

Fig. 1e shows the

dierential cross-sections in the presence of a

(d )

glass substrate (n

= 1.52) for incidence from the air side (+ˆ z). ∆Qs and ∆Qa no longer balance each other, resulting in a non-zero ∆Qe .

0.06 0 -0.06

Here, reversal of the direction of illumination

ΔQs ΔQa ΔQe

-0.12 0.24 (e) 0.12

∆Qa , resulting ∆Qe = ∆Qs +

tion of illumination (−ˆ z), as shown in Fig. 1d,

200 nm

y

z

Free-space

has the same magnitude and opposite sign

as the dierential absorption

x y

Substrate

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Photonics

(f )

(−ˆ z), as shown in Fig. 1f , strongly aects the

∆Qs and ∆Qa . ∆Qe 6= 0 is retained.

spectra of

Nevertheless, the

same

The CDM

47,48

al-

lows us to understand the origin of non-zero dif-

0

ferential extinction of normally incident CPL

-0.12

in the presence of a substrate.

-0.24 500 550 600 650 700 500 550 600 650 700 Wavelength λ [nm] Wavelength λ [nm]

the eld radiated by each of the nanospheres

Figure 1:

(a)

Schematic illustration and

reects from the substrate

5052

the nanospheres, we observe

(b)

ever, the CDM assumes only

Only when

and re-excites

∆Qe 6= 0.

How-

point-dipoles,

lo-

scanning electron microscope image of the in-

cated at the respective centers of the nanopar-

vestigated nanotrimer. The sample is composed

ticles. Therefore, the CDM cannot account for

of three nanospheres with radii r = 90 nm, ar◦ ranged in 90 bent geometry and positioned on

strong near-eld enhancement in the gaps be-

a glass substrate. The two upper nanoparticles

icantly contributes to the scattering, absorp-

in

(b)

tween the actual nanoparticles, which signif-

are made of silicon (Si), while the third

tion and extinction spectra. This eld enhance-

one is made of gold (Au). The estimated gap

ment originates from nonradiative higher-order

between neighboring particles is

2 nm. (c − f )

modes

48

and therefore requires full-wave sim-

Analytical cross-sections, derived from a cou-

ulations.

pled dipole model of the nanosphere system.

wards we employ nite-dierence time-domain

(c)

(FDTD) simulations

Normalized dierential scattering (∆Qs ),

For this reason, from this point on-

53

for a comparison with

absorption (∆Qa ) and extinction (∆Qe ) cross-

the experimental results.

sections for the nanotrimer in free-space, illumi-

A simplied sketch of the experimental scheme

nated with left- and right-hand circularly polar-

is depicted in Fig. 2a.

ized plane-waves along the positive direction of

jectives (MOs) in confocal conguration focus

the

z -axis (+ˆz). (e)

(c),

for the nan-

and collimate incident monochromatic light, l-

otrimer on a glass substrate with a refractive

tered from the output of a broadband super-

index of and

(e),

same as

Two microscope ob-

(c)

continuum white light source via an acousto-

respectively, for illumination from the

n = 1.52. (d)

optic tunable lter (AOTF) and guided into

and

(f )

same as

opposite side (−ˆ z).

the setup by a single-mode optical ber

35,54

. A

three-dimensional (3D) piezo actuator positions the mounted sample in the focal plane.

ized to the geometric cross-section (∆Qj ≡ LCP σj − σjRCP / [3πr2 ]) for the nanotrimer in free-space, illuminated with LCP and RCP along the positive direction of the

The

incident light only partly lls the aperture of the upper MO with numerical aperture (NA) of NA

z -axis (+ˆz).

= 0.9,

such that the nanotrimer is eec-

tively illuminated by a weakly focused Gaussian


ACS Photonics

(a)

(b)

Supercontinuum source + AOTF

(c)

-0.25

NA = 1.3

MO (NA=0.9)

y [μm ]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 11

sample on holder MO (NA=1.3)

0

NAeff = 0.4

BFP

0.25 -0.25

LCVR LCVR @22.5° @45° LP imaging lens CCD

Figure 2:

(a) Simplied experimental scheme.

0

x [μm]

0.25

min

max

The nanotrimer on a glass substrate is mounted on a

sample holder, which is attached to a three-dimensional (3D) piezo actuator for precise positioning in the focus. A broadband supercontinuum source generates white light which is spectrally ltered by an acousto-optic tunable lter (AOTF) and guided into the setup with a single-mode optical ber. The incident Gaussian beam partly lls the aperture of the upper microscope objective (MO) with numerical aperture (NA) of NA

= 0.9

and is focused onto the nanotrimer with an eective

NA of NAe = 0.4. The transmitted and scattered light is collected and collimated by the second ◦ MO with NA = 1.3 and passes two liquid crystal variable retarders (LCVRs, slow axes at 22.5 ◦ and 45 ) and a linear polarizer (LP) for Stokes analysis via projection onto dierent polarization states. The polarization-ltered intensity distribution in the back-focal plane (BFP) of the lower

(b)

MO is imaged onto a charge-coupled device (CCD) camera by a lens.

Raster scan image of the 2 total transmitted intensity, obtained by moving the nanotrimer sample in a 500 × 500 nm region

around the focus. We average the results of the polarimetric analysis on a 10 × 10 grid of positions 2 (250×250 nm ) around the estimated center of the sample, indicated by minimum transmission. (c) Typical BFP image of the lower MO, recorded for a specic polarization projection and position in the scan grid. White rings indicate the NA of the incident (NAe

= 0.4)

and collected (NA

= 1.3)

light. We perform our polarization analysis in the central angular region, where the incident and the scattered light interfere.

beam with NAe

= 0.4

from the air side (+ˆ z).

around the estimated center, which is indicated by reduced transmission in Fig. 2b.

The transmitted and scattered light is collected by a second oil immersion MO with NA

= 1.3.

To reconstruct the

The beam then passes two liquid crystal vari◦ able retarders (LCVRs) (slow axes at 22.5 and ◦ 45 ) and a linear polarizer (LP) for projection onto dierent polarization states

55

.

7

tem, we must invert the following identity :

So = MSi ,

Finally, a

lens images the polarization-ltered intensity

where

distribution in the lower objective's BFP onto

Si

and

So

(1)

are the input and the output

Stokes vectors, respectively.

a charge-coupled device (CCD) camera.

To this end, we

illuminate our sample with an overdetermined

The position of the sample relative to the exci-

set of six input polarization states, estimated to

tation beam is crucial for properly performing

be

the spectropolarimetry of an individual nanostructure.

4 × 4 Mueller matrix M, de-

termining the polarization response of the sys-

{RCP,

LCP, X, Y, diagonal, antidiagonal},

and analyze the transmitted light.

Fig. 2b shows a raster scan im-

position of the sample in the grid

age of the total transmitted intensity, obtained

For each

(x, y),

we

acquire angularly resolved output Stokes vec-

by moving the nanotrimer sample in a 500 × 500 nm2 region around the focus. We record

tors

ˆ o (x, y, k = (kx , ky )) S

and integrate them

over a region in the Fourier plane So (x, y) = RR ˆ o (x, y, k)d2 k encompassing the angular reS

and average the polarimetric properties over a 10 × 10 grid, covering an area of 250 × 250 nm2


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ACS Photonics

= 0.4,

where we detect the

spectively. In Fig. 3a and Fig. 3c, we present

far-eld interference of incident and scattered

the obtained experimental results for CB and

gion of NAe light

56

(Fig. 2c).

Finally, averaging

So (x, y)

CD, respectively, quantifying the chiroptical re-

over the grid provides us with the desired out-

So = So (x, y).

For comparison, Fig. 3b and Fig. 3d

sponse.

We also de-

show results obtained from FDTD simulations.

termine the actual experimental input Stokes

The nanotrimer is modeled as a system of three

put Stokes vectors vectors

Si

by performing the same procedure

on a plain glass substrate.

perfect spheres with radii

Using these six

2 nm, placed on a glass sub= 1.52) and arranged in the geometry in Fig. 1a. The Si nanospheres are sur-

strate (n

Eq. 1 and obtain the experimental Mueller ma-

shown

Mexp .

However, experimental noise, the

nite integration region of NAe

= 0.4

rounded by a SiO2

and

ness of

averaging of the Stokes vectors over the grid

Mexp ,

may result in a matrix

and inter-

particle gaps of

input and six output polarizations, we invert trix

r = 90 nm

45

shell with estimated thick-

8 nm, correspondingly reducing the core

diameter.

which is un-

The actual optical handedness of the hetero-

physical and contains depolarization, inhibit-

geneous trimer on substrate in Fig. 3 depends

ing the analysis of CB and CD. The experiexp mentally observed polarization fraction β = qP exp 2 exp 2 exp 2 ( ij [mij ] − [m00 ] )/(3[m00 ] ) provides a

on the wavelength and changes sign in the investigated spectral range of

700 nm.

7,57,58

β=1

strong. The experimentally measured CB corresponds to a maximum optical rotation of ◦ about −0.8 . Assuming a thickness of 180 nm

correspond to total and no depolar-

7,57,58

ization, respectively exp nd 0.998 ≤ β ≤

.

for the sample, this corresponds to a refractive

Experimentally we

1.008,

|∆n| ≈ 0.015, which is an extremely high value as comindex dierence for LCP and RCP of

wherefore we ap-

ply Cloude's sum decomposition

59

, providing us

pared to natural optically active media (typi−5 cally |∆n| ∼ 10 ). Remarkably, the spectra

with the closest physical and non-depolarizing

M of Mexp . In general, the elements M are rather complex functions of the

estimate

mij

of

show a characteristic ngerprint of the BornKuhn model dispersion

optical anisotropies. However, the absolute val-

, manifested by the

crossing for the bisignate CD, which appear

mens and individual nanostructures. Under the

around

small anisotropy approximation, CB and CD

600 nm

7

are given by :

= 0.5[m12 − m21 ], CD = 0.5[m03 + m30 ].

60

prominent dip in CB, accompanied by a zero-

ues of latter tend to be very small for thin speci-

CB

Moreover, for an isolated nanostruc-

ture, the chiroptical response is exceptionally

measure for the amount of depolarization , exp where mij are the elements of Mexp . Physical Mueller matrices satisfy 0 ≤ β ≤ 1, while β = 0 and

500 nm ≤ λ ≤

λ ≈ 580 nm in in Fig. 3b, 3d.

Fig. 3a, 3c and

λ ≈

Qualitatively, we achieve a good overlap between the numerically and experimentally re(2)

trieved spectra.

The blue-shift of the CB

and CD spectra with respect to FDTD simu-

The denition of CB in the Mueller matrix for-

lations may be attributed to underestimation

malism given by Eq. 2 corresponds to twice the

of the SiO2 shell thickness.

average rotation angle of the plane of polariza-

deviations of the actual sample from the ide-

tion of incident linearly polarized light after be-

ally assumed geometry, clearly visible under

ing transmitted through the sample, due to cir-

the scanning electron microscope in Fig. 1b,

cular anisotropies only and after excluding the

are not accounted for in simulations.

contribution of linear anisotropies. CD in Eq. 2

cussed earlier, any asymmetry aects the cir-

measures the dierence of energy attenuation

cular anisotropies, reasoning the observation

(normalized to the average transmission) for in-

of

cident LCP and RCP waves under preserved

periment.

polarization, i.e., if projecting the transmitted

assembly is extremely sensitive to the inter-

polarization state back onto LCP and RCP, re-

particle gaps, which cannot be determined ex-

substantially


higher

CB

Additionally, the

and

CD

As dis-

in

ex-

Most importantly, our nanosphere

ACS Photonics

CB [rad.]

Experiment 0.01

Simulation

(a)

0.01

0 -0.01 -0.02

0.02

(b)

in arrays which support lattice resonances. Secondly, owing to the heterogeneous environment, each of the nanoparticles in the nanotrimer assembly responds dierently to the incident

-0.01

(c)

0.01

eld

(d)

550

600

650

700

Wavelength λ [nm]

(a, c)

Figure 3:

dent beams

62,63

, paving the way towards novel

nanoscopic sensors and sorters.

500

550

600

650

Wavelength λ [nm]

In conclusion, we have experimentally investi-

700

gated a geometrically symmetric heterogeneous nanotrimer on a glass substrate. The in-plane

Experimentally measured and

circular birefringence (CB) and

(c, d)

reection symmetry of the system is broken by

(a, b)

its heterogeneous material composition, while

circular

the glass substrate breaks the mirror symmetry

dichroism (CD) of the investigated nanotrimer The error-bars in

The latter suggests that such systems

charge of orbital angular momentum of inci-

numerically calculated spectra of

sample.

.

citation eld and distinguish the topological

-0.01

-0.02 500

35

can potentially sense the gradient of the ex-

0

0

(b, d)

stituents and by arranging the nanostructures

0

-0.03

CD [rad.]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 11

(a, c)

of the whole system, transitioning its morphol-

denote the

ogy from achiral to chiral. We have experimen-

standard-mean deviation for the spatial aver-

tally reconstructed the circular birefringence

age performed over the scan grid.

and circular dichroism spectra. The study of an individual nanostructure allowed us to preclude

actly and which considerably inuence the op-

any contributions of delocalized lattice eects,

tical response

Lastly, the individual het-

collective resonances and near-eld coupling

erogeneous nanotrimer is strongly anisotropic

eects, otherwise present in arrays of nanos-

and exhibits linear birefringence (LB) and lin-

tructures.

ear dichroism (LD), which are orders of magni-

a clear-cut distinction between the material-

tude larger than CB and CD. Strong LB and

and

LD are known to induce artifacts in measure-

in a system exhibiting a heterogeneity- and

ments of CB and CD

substrate-induced break of symmetry,

material

61

48

.

7,13

. In the supplemental

Additionally,

geometry-induced

our study provides

chiroptical

responses shed-

ding light on chiral light-matter interactions at

, we compare the experimentally re-

substrate-nanostructure interfaces.

constructed and the simulated spectra of LB and LD. Additionally, we numerically investi-

Acknowledgement

gate forward and backward illumination of the sample, a nanotrimer in a homogeneous envi-

acknowledge fruitful discussions with Israel De

ronment and a nanotrimer of opposite handedness

61

The authors gratefully

Leon, Gerd Leuchs and Paweª Wo¹niak.

.

Supporting Information Avail-

Discussion and Conclusion

able

Owing to the relatively high chiral response of an individual nanostructure, such heteroge-

Experimental and numerical spectra of linear

neous systems hold promise for constructing

anisotropies, simulations for forward and back-

at chiral and on-chip optical elements. First,

ward illumination, simulations in free space and

the chiral response may be signicantly en-

on substrate, simulations for nanotrimers of op-

hanced by utilizing a higher refractive index

posite handedness.

substrate, by introducing structural chirality, by tailoring individual resonances of the con-


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ACS Photonics

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2019,

arXiv:

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Extinction Circular Dichroism

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Wavelength Ȝ [nm]

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Substrate-Induced Chirality in an Individual Nanostructure | ACS

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