Molecular chirality detection using plasmonic and dielectric nanoparticles
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Nanophotonics 2022; 11(9): 1897–1904
Research Article
TaeHyung Kim and Q-Han Park*
Molecular chirality detection using plasmonic and
dielectric nanoparticles
https://doi.org/10.1515/nanoph-2021-0649 spectroscopy, such as chiral metasurfaces [1–5], achiral
Received October 29, 2021; accepted December 30, 2021; nanoarrays [6–11], achiral plasmonic nanoparticles [12–21],
published online January 11, 2022 and dielectric nanoparticles [12, 14, 15, 22, 23]. In these
studies, CD enhancement was usually achieved near the
Abstract: Nanoscale particles and structures hold promise
resonance frequency of the nanostructures. The most stud-
in circular dichroism (CD) spectroscopy for overcoming the
ied resonant nanostructures, both theoretically [12–15, 24]
weakness of molecular CD signals. Significant effort have
and experimentally [16–22], are achiral nanoparticles,
been made to characterize nanophotonic CD enhancement
whether plasmonic or dielectric. The main advantage of
and find efficient ways to boost molecular chirality, but the
using achiral nanoparticles is separating the molecular CD
best solution is yet to be found. In this paper, we present a
signals from the unwanted strong background CD signals
rigorous analytic study of the nanophotonic CD enhance-
occurring in chiral nanostructures. In addition, achiral
ment of typical nanoparticles. We consider metallic and
nanoparticles in the form of colloidal solutions do not
dielectric nanoparticles capped with chiral molecules
require complex measurements while, for example, nano-
and analyze the effect of multipolar nanoparticles on the
arrays coupled with chiral molecules require additional
molecular CD. We identify the spectral features of the
experimental processes to obtain measurable CD signals
molecular CD resulting from the electric and magnetic
[1, 7, 9, 10]. Despite the growing interest in achiral nano-
resonances of nanoparticles and suggest better ways to
particles, theoretical studies on the effect of achiral nano-
boost molecular chirality. We also clarify the contribution
particles on chiral molecules have mostly continued to
of particle scattering and absorption to the molecular CD
apply conventional dipole approximation [12–14]. Although
and the dependence on particle size. Our work provides an
exceptionally some studies report chiroptical responses by
exact analytic approach to nanophotonic CD enhancement
higher-order multipoles [23, 24], these works do not consider
and offers a rule for selecting the most efficient particle for
the scattering-induced CD of a nanoparticle which results
sensitive molecular chirality detection.
from nearby chiral molecules. Large-sized achiral nano-
Keywords: chiral molecules; chiral sensing; chiroptical particles capped with chiral molecules can be synthesized
spectroscopy; circular dichroism (CD); dielectric nano- experimentally [16, 17, 19, 20] and offer better efficiency
particles; plasmonic nanoparticles. for CD enhancement through an enlarged surface area.
However, a non-static analytic approach has remained
unexplored.
1 Introduction In this paper, we investigate achiral nanoparticles
capped with chiral molecules and obtain exact Mie scat-
Nanoparticles and nanostructures are a promising new di- tering solutions. We identify the multipole resonances of
rection for circular dichroism (CD) spectroscopy. They can both plasmonic and dielectric nanoparticles and their effect
generate locally enhanced electromagnetic fields, which are on the surrounding chiral molecules. The spectral features
necessary for sensitive molecular CD measurement. Various of CD enhancement caused by electric and magnetic reso-
approaches have been tried to utilize nanostructures for CD nances, are presented in detail. We find that, although
plasmonic nanoparticles show only electric resonances,
high index dielectric nanoparticles possess magnetic reso-
*Corresponding author: Q-Han Park, Department of Physics, Korea nances which can boost the molecular CD more efficiently
University, Seoul 02841, Republic of Korea,
than electric resonances. By solving Mie scattering analyti-
E-mail: qpark@korea.ac.kr. https://orcid.org/0000-0002-6301-2645
TaeHyung Kim, Department of Physics, Korea University, Seoul 02841,
cally, we also clarify the contribution of nanoparticle
Republic of Korea, E-mail: john101kr@korea.ac.kr. https://orcid.org/ scattering and absorption to the molecular CD and their
0000-0001-5147-0625 dependence on particle size. We also show that scattering by
Open Access. © 2022 TaeHyung Kim and Q-Han Park, published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0
International License.
1898 T. Kim and Q.-H. Park: Molecular chirality detection
larger nanoparticles can significantly enhance the mole- ∞ 2n + 1
QsR = ∑ in [(QL γn + QR δn )(M(3) (3)
o1n (k b ) − No1n (k b ))
cular CD. In particular, the scattering of a high-index n=0 n(n + 1)
nanoparticle combined with chiral molecules contributes + i( − QL γn + QR δn )(M(3) (3)
e1n (k b ) − Ne1n (k b ))],
critically to the overall higher-order induced CD. Conse- (4)
quently, we find that the higher-order resonances of large-
sized achiral nanoparticles, especially magnetic resonance, where αn , βn , γn , and δn are scattering coefficients, QL, R is
are more effective for enhancing weak molecular CD signals. the amplitude of the left- and right-circularly polarized
Our analytic approach based on Mie theory can provide both components of an incident plane wave and k b = nb k 0 is the
a qualitative understanding of and a good approximation to wavenumber of the achiral background surrounding the
other non-spherical nanostructures for which analytic so- core–shell system with the refractive index nb .
lutions are possible and is applicable to the development of We solved the chiral Mie theory explicitly and calcu-
more sensitive molecular chirality detection methods. lated the rate of extinction, scattered, and absorbed en-
ergies normalized by the incident light energy (detailed
derivations are given in SI). The resulting extinction,
scattering and absorption cross sections are expressed by
2 Chiral Mie theory for achiral ∞ QL 2 Reαn
core-chiral shell nanoparticle C NP@mol
ext = −4π ∑ (2n + 1)[
n=1 QL + QR 2 k b 2
2
(5)
QR 2 Reδn
To understand analytically the chiroptical activity of chiral + 2 ],
QL + QR 2 kb 2
molecules, we consider a core–shell system with spherical
core nanoparticles and a shell made of chiral molecules, as
shown in Figure 1, and solve the associated Mie scattering
problem. Firstly, we introduce the constitutive relation of a
chiral medium D = ϵE + iκH and B = μH − iκE where ϵ, μ
and κ are the permittivity, the permeability and the
chirality parameter of a chiral medium, respectively [25]. To
solve the Mie problem for a chiral medium, we express the
incident, scattered and internal fields of our system in
terms of {QL (k L ), QR (k R )} by using the wave-field decom-
position method. In the chiral medium, the wavenumber of
two circularly polarized lights of opposite handedness is
given by k L, R = (nc ± κ)k 0 with the refractive index nc and
vacuum wavenumber k 0 = 2π/λ. Plus and minus signs
correspond to left and right circularly polarized light
wavenumbers k L and k R , respectively. Using the vector
spherical harmonics M and N of the Mie theory, we express
the incident field by (see SI)
∞ 2n + 1
QiL = ∑ QL in [(M(1) (1)
o1n (k b ) + No1n (k b ))
n=0 n(n + 1) (1)
− i(M(1)
e1n (k b ) + N(1)
e1n (k b ))],
∞ 2n + 1
QsR = ∑ QR in [cn (M(3)
o1n (k b )
n=0 n(n + 1) (2)
− N(3) (3) (3)
o1n (k b )) + idn (Me1n (k b ) − Ne1n (k b ))],
and the scattered field by
∞ 2n + 1 Figure 1: Schematic figure of CD measurement for (A) achiral
QsL = ∑ in [(QL αn + QR βn )(M(3)
o1n (k b )
n=0 n(n + 1) plasmonic and dielectric nanoparticles capped with chiral
molecules (B) schematic figure of Chiral Mie theory for large-sized
+ N(3) (3) (3)
o1n (k b )) − i(QL αn − QR βn )(Me1n (k b ) + Ne1n (k b ))], achiral core-chiral shell nanospheres embedded in achiral
(3) background.
T. Kim and Q.-H. Park: Molecular chirality detection 1899
∞ QL 2 |αn |2 + |γn |2 available in the literature [26, 27]. Optical constants and the
C NP@mol
sca = 4π ∑ (2n + 1)[ chirality parameter of the chiral molecule shell are
n=1 QL + QR
2 2
kb 2
(6) modeled using the Condon model [28] in accordance with
QR 2 |βn |2 + |δn |2
+ ], the behavior of typical chiral molecules in the ultraviolet-
QL 2 + QR 2 kb 2
visible wavelength range [29] (see SI). We chose an
CNP@mol
abs = CNP@mol
ext − C NP@mol
sca , (7) aqueous background of permittivity ϵb = 1.332 . By imple-
menting all the constitutive relations of the chiral medium
where the scattering coefficients are determined from the
parameters and other material parameters in COMSOL, we
boundary condition and n accounts for the order of reso-
calculated ΔC NP@mol
ext , ΔCNP@mol
sca , and ΔC NP@mol
abs numerically.
nance. We define the circular differential extinction cross
Figure 2 indicates that the results from the chiral Mie theory
section as the difference of extinction cross section for two
agree nicely with the electromagnetic simulation, thereby
opposite circularly polarized incident lights and hold the
confirming the validity of the analytic solutions.
same definition for scattering and absorption. Then, the
calculated circular differential extinction, scattering and
absorption cross sections are
∞ Reαn − Reδn 3 CD of plasmonic and dielectric
ΔC NP@mol
ext = −4π ∑ (2n + 1)[ ], (8)
n=1 kb 2 nanoparticles capped with chiral
∞ |αn |2 − |βn |2 + |γn |2 − |δn |2 molecules
ΔCNP@mol
sca = 4π ∑ (2n + 1)[ ], (9)
n=1 kb 2
Equipped with these analytic tools, we are now able to
ΔCNP@mol
abs = CNP@mol
abs (QL = 1, QR = 0)
(10) uncover the role of nanoparticles in CD enhancement. The
− C NP@mol
abs (QL = 0, QR = 1), extinction cross section in Eq. (5) and the circular differ-
ential extinction cross section in Eq. (8) allow a quantita-
where the polarization states of the incident light are used
tive description of enhanced molecular CD by nanoparticle
with (QL , QR ) = (1, 0) and (QL , QR ) = (0, 1) for the left- and
resonances, such as electric/magnetic dipole (n = 1),
right-circular polarization respectively.
quadrupole (n = 2), and octupole (n = 3) resonances. The
To test the validity of our analytic solutions in Eqs.
scattering coefficients αn , βn , γn and δn reflect the chirality
(8)–(10), we compared the analytic results from (8)–(10)
parameter κ of the chiral shell as they are determined
with direct full-field numerical simulations, and present
through the boundary matching conditions. Note that the
the results in Figure 2. In the electromagnetic simulation,
complex value chirality parameter κ contains the infor-
we used a silicon core particle of radius 50 nm and a chiral
mation on the optical rotatory dispersion (ORD) and CD
molecule shell 5 nm thick. The material parameters for
simultaneously. Our chiral Mie theory considers both the
silver and silicon are chosen from the tabulated data
ORD and the CD of chiral molecules, unlike a previous work
[15] which considered only the ORD of a chiral molecule
medium.
Figure 3 shows the extinction cross sections of nano-
particles with a 1 nm thick chiral molecule shell which is
the typical thickness of a self-assembled molecular
monolayer [30]. The extinction cross section and circular
differential extinction cross section of both the silver core
case (Figure 3A and B) and the silicon core case (Figure 3C
and D) are plotted varying the core size and wavelength.
Note that the silver core case shows only electric resonance
whereas the silicon core case shows both electric and
magnetic resonances. Earlier works focused mostly on the
electric dipole resonance and the enhanced CD signal
[12–15] without paying much attention to the higher-order
Figure 2: The circular differential cross sections calculated by electric resonance modes and induced CD signals. It was
analytic solution and numerical simulation. The results obtained by considered that dipole resonance plays the dominant role
the two methods are perfectly matched. in CD enhancement by nanoparticles and nanostructures,
1900 T. Kim and Q.-H. Park: Molecular chirality detection
Figure 3: The extinction and circular differential extinction cross section of plasmonic core-chiral shell and dielectric core-chiral shell nanoparticles.
(A) The extinction cross section and (B) the circular differential extinction cross section of silver core-chiral shell nanoparticle. (C) The extinction cross
section and (D) the circular differential extinction cross section of silicon core-chiral shell nanoparticle. The thickness of the chiral molecular shell is
fixed at 1 nm. The ED (black solid), EQ (black dashed), EO (black dotted), MD (blue solid), MQ (blue dashed), and MO (blue dotted) resonance
positions are plotted. The black dashed-dotted line shows the molecular intrinsic CD resonance at 220 nm.
and that complicated higher-order resonances, although Importantly, the FWHM of the induced CD signal in
present in large-sized particles, have less significant effect Figure 4B shows that the values at the peak positions of
on CD enhancement. Contrary to these expectations, our EQ (red arrow) and EO (blue arrow) are 65 nm and 57 nm,
analytic solution reveals the important role of higher-order respectively, which are smaller than the FWHM value of
resonances. 117 nm at the ED (black arrow). Thus, we found that,
To clarify the role, from Figure 3, we traced the advantageously for CD spectrum measurement, higher-
⃒⃒ ⃒⃒
maximum value of ⃒⃒⃒ΔC NP@mol
ext
⃒⃒ and the full-width half
⃒
order resonances can provide lager CD magnitudes and
smaller CD linewidths than dipole resonance. We point
maximum (FWHM) at each resonance for a fixed size of
out that the maximal efficiency of ED resonance may be
achiral core particle. The results plotted in Figure 4 show
⃒⃒ ⃒⃒ larger than those of higher-order resonances if extinction
the maximum value, Max( ⃒⃒⃒ΔC NP@mol
ext
⃒⃒), around the electric
⃒ is normalized by the particle surface area. However, for
dipole (ED), the electric quadrupole (EQ) and the electric CD measurement, since the absolute value of a CD signal
octupole (EO) resonance, of which the peak values occur at and the high quality factor of resonance is more impor-
silver core radii of 40 nm (black arrow), 80 nm (red arrow) tant than efficiency, higher-order resonances are more
and 120 nm (blue arrow), respectively. The maximum preferable.
⃒⃒ ⃒⃒ The strong CD signal of chiral molecules is usually
values of Max( ⃒⃒⃒ΔCNP@mol
ext
⃒⃒⃒) around the EQ and the EO
located in the UV region and the CD signal enhancement by
resonance are 2 times and 3.2 times larger, respectively, nanoparticle resonances arises in the visible region where
than the induced CD signal around the ED resonance. molecular CD is much weaker. In fact, the induced CD
T. Kim and Q.-H. Park: Molecular chirality detection 1901
⃒⃒ ⃒⃒
Figure 4: The maximum value of ⃒⃒⃒ΔC NP@molext
⃒⃒ and FWHM of each resonance for varied core radii. (A) And (B) show silver core-chiral shell
⃒
nanoparticle, (C) and (D) show silicon core-chiral shell nanoparticle. In (A) and (B), the arrow denotes the core radius position at which the
⃒⃒ ⃒⃒
Max( ⃒⃒⃒ΔC NP@mol
ext
⃒⃒⃒) is maximized. In Figure 4D, the FWHM for electric resonances are not well defined and thus not plotted.
signal by the ED resonance of a silver nanoparticle is conclude that the magnetic resonances of high index
approximately 0.07 times the magnitude of the molecular dielectric nanoparticles induce larger CD signals with
intrinsic CD signals. However, the situation changes if we smaller CD linewidths than electric resonances or the res-
consider dielectric core particles. Figure 3C and D show the onances of plasmonic nanoparticles. All these features are
C NP@mol
ext and ΔC NP@mol
ext of the silicon core case, which pos- summarized in Table 1.
sesses both electric resonance and magnetic resonance. As
noted in the previous circular differential Mie scattering Table : Advantages of different multipole resonances for induced
(CDMS) study [15], magnetic resonances show positive CD. X denotes that there are no induced CD signals. The triangle and
differential CD signals while electric resonances show circle symbols indicate which resonant properties are more advan-
negative ones. Compared to the silver nanoparticle case, tageous for obtaining the measurable induced CD signals (△ ⟨ :
the silicon core-chiral shell exhibits much stronger ⟨ ○ ⟨ ●). △ indicates small magnitudes and broad spectral line-
shape CD signals. ● indicates large magnitudes and sharp spectral
induced CD signals at magnetic resonances, as shown in
⃒⃒ ⃒⃒ lineshape CD signals.
Figure 4C. For example, the Max( ⃒⃒⃒ΔC NP@mol
ext
⃒⃒) around the
⃒
Core resonances Core particle
MD (MQ) exhibits 6.4 times (7.2 times) larger magnitudes
than the ED (EQ) for a silicon core of radius 85 nm. The Low-index Plasmonic High-index
⃒⃒ ⃒⃒ dielectric (Silver) dielectric (Silicon)
Max( ⃒⃒⃒ΔCNP@mol
ext
⃒⃒) at the electric resonances of dielectric
⃒
Electric dipole X △ △
nanoparticles show similar values to the plasmonic silver Higher-order electric X : :
nanoparticle case. Figure 4D shows that higher-order resonances
magnetic resonances also possess smaller FWHM values Magnetic dipole X X ○
Higher-order magnetic X X ●
compared to those of MD. The FWHM of electric resonances
resonances
are not well defined and thus not plotted. Thus, we can1902 T. Kim and Q.-H. Park: Molecular chirality detection
4 Scattering and absorption
contribution to CD
Large-sized particles provide an efficient platform for
enhancing weak molecular CD signals because they sup-
port multipole resonances and a large surface area on
which chiral molecules can be adsorbed. When the particle
size becomes comparable to the light wavelength, not only
the absorption but also the scattering by the particles
contributes critically to molecular CD. The CD signals we
measure consist of the sum of circular differential scat-
tering and absorption (ΔCNP@mol
ext = ΔCNP@mol
sca + ΔC NP@mol
abs ). In
the previous study, only circular differential absorption
was considered for the CD signals of achiral nanostructures
coupled with chiral molecules, neglecting scattering [6].
Also, in the CDMS study [15], the scattering contribution
was considered only for the spectral change of molecular
CD, but not for the intrinsic absorption of the chiral mo-
lecular medium. Our chiral Mie theory solution in (5)–(7)
allows a qualitative and quantitative understanding of
these effects.
Figure 5 shows the effect of particle scattering and
absorption on the induced CD. We choose a chiral molec-
ular medium with a CD peak in the UV region to surround a
nanoparticle of 75 nm radius and 1 nm shell thickness.
Figure 5A shows a low-index (n = 1.33) dielectric core
particle possessing no resonance and no resulting CD
spectral change. In this case, the CD is determined only by
the circular differential absorption of the chiral molecular
medium and the scattering effect is not noticeable. In the
presence of resonance modes, as in Figure 5B (silver core)
and C (silicon core), the contribution of scattering to the
induced CD cannot be ignored. Particularly, in the present
case of the 75 nm particle size, with induced CD at dipole
resonances (ED at 428 nm in Figure 5B and MD at 628 nm in
Figure 5C), scattering is a dominant factor. This suggests
that particle scattering plays a key role in inducing the CD
near the multipole resonances as the particle size in-
creases. Thus, it is essential to analyze the scattering
properties of nanostructures when designing structures for
nanophotonic CD enhancement.
5 Conclusions Figure 5: The circular differential extinction (black solid), scattering
(red dashed) and absorption (blue dashed) cross section of (A) low-
index dielectric core (B) silver core and (C) silicon core particle of
In this paper, we investigated the effects of the multipole
radius 75 nm. The refractive index of the low-index dielectric mate-
resonances of plasmonic and dielectric nanoparticles on rial is the same as the achiral background medium.
the surrounding chiral molecules. We first developed the
chiral Mie theory for an achiral core-chiral shell nano- scattering. Based on the analytic solution, we identified the
particle system and obtained an exact solution for the Mie role of higher-order resonances on CD enhancement. TheT. Kim and Q.-H. Park: Molecular chirality detection 1903
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