Optical characteristics of the nanoparticle coupled to a quantum molecular aggregate
Optical characteristics of a single nanoparticle, coupled to the one-dimensional quantum molecular aggregate is studied. Depending on the values of the coupling of the particle and its own frequency, with respect to the own frequency of the aggregated molecules, and the strength of the aggregation,...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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irk-123456789-1752532021-02-01T01:28:47Z Optical characteristics of the nanoparticle coupled to a quantum molecular aggregate Ropakova, I.Y. Zvyagin, A.A. Специальный выпуск. К 80-летию со дня рождения А.И. Звягина Optical characteristics of a single nanoparticle, coupled to the one-dimensional quantum molecular aggregate is studied. Depending on the values of the coupling of the particle and its own frequency, with respect to the own frequency of the aggregated molecules, and the strength of the aggregation, the dynamical relative permittivity of the nanoparticle manifests the contribution from the exciton band, or/and the ones from the local level(s) caused by the particle. The refractive index and the extinction coefficient of the nanoparticle is also calculated. 2017 Article Optical characteristics of the nanoparticle coupled to a quantum molecular aggregate / I.Y. Ropakova, A.A. Zvyagin // Физика низких температур. — 2017. — Т. 43, № 11. — С. 1594-1599. — Бібліогр.: 17 назв. — англ. 0132-6414 PACS: 78.67.Sc, 71.35.Aa http://dspace.nbuv.gov.ua/handle/123456789/175253 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Специальный выпуск. К 80-летию со дня рождения А.И. Звягина Специальный выпуск. К 80-летию со дня рождения А.И. Звягина |
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Специальный выпуск. К 80-летию со дня рождения А.И. Звягина Специальный выпуск. К 80-летию со дня рождения А.И. Звягина Ropakova, I.Y. Zvyagin, A.A. Optical characteristics of the nanoparticle coupled to a quantum molecular aggregate Физика низких температур |
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Optical characteristics of a single nanoparticle, coupled to the one-dimensional quantum molecular aggregate is studied. Depending on the values of the coupling of the particle and its own frequency, with respect to the own frequency of the aggregated molecules, and the strength of the aggregation, the dynamical relative permittivity of the nanoparticle manifests the contribution from the exciton band, or/and the ones from the local level(s) caused by the particle. The refractive index and the extinction coefficient of the nanoparticle is also calculated. |
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Ropakova, I.Y. Zvyagin, A.A. |
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Ropakova, I.Y. Zvyagin, A.A. |
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Ropakova, I.Y. |
| title |
Optical characteristics of the nanoparticle coupled to a quantum molecular aggregate |
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Optical characteristics of the nanoparticle coupled to a quantum molecular aggregate |
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Optical characteristics of the nanoparticle coupled to a quantum molecular aggregate |
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Optical characteristics of the nanoparticle coupled to a quantum molecular aggregate |
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Optical characteristics of the nanoparticle coupled to a quantum molecular aggregate |
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optical characteristics of the nanoparticle coupled to a quantum molecular aggregate |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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2017 |
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Специальный выпуск. К 80-летию со дня рождения А.И. Звягина |
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| citation_txt |
Optical characteristics of the nanoparticle coupled to a quantum molecular aggregate / I.Y. Ropakova, A.A. Zvyagin // Физика низких температур. — 2017. — Т. 43, № 11. — С. 1594-1599. — Бібліогр.: 17 назв. — англ. |
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Физика низких температур |
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AT ropakovaiy opticalcharacteristicsofthenanoparticlecoupledtoaquantummolecularaggregate AT zvyaginaa opticalcharacteristicsofthenanoparticlecoupledtoaquantummolecularaggregate |
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2025-07-15T12:30:43Z |
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2025-07-15T12:30:43Z |
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1837716098391212032 |
| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 11, pp. 1594–1599
Optical characteristics of the nanoparticle coupled
to a quantum molecular aggregate
I.Yu. Ropakova1 and A.A. Zvyagin2,3
1Institute for Scintillation Materials, STC “Institute for Single Crystals” of the National Academy of Sciences of Ukraine
60 Nauky Ave., Kharkov 61001, Ukraine
2Max-Planck-Institut für Physik komplexer Systeme, 38 Nöthnitzer Str., Dresden D-01187, Germany
3B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine
47 Nauky Ave., Kharkiv 61103, Ukraine
E-mail: ropakova@isma.kharkov.ua
Received April 18, 2017, published online September 25, 2017
Optical characteristics of a single nanoparticle, coupled to the one-dimensional quantum molecular aggregate
is studied. Depending on the values of the coupling of the particle and its own frequency, with respect to the own
frequency of the aggregated molecules, and the strength of the aggregation, the dynamical relative permittivity of
the nanoparticle manifests the contribution from the exciton band, or/and the ones from the local level(s) caused
by the particle. The refractive index and the extinction coefficient of the nanoparticle is also calculated.
PACS: 78.67.Sc Nanoaggregates; nanocomposites;
71.35.Aa Frenkel excitons and self-trapped excitons.
Keywords: J-aggregates, Frenkel excitons, permittivity, refractive index.
Low-dimensional optical materials like quantum wells and
wires, and organic systems like conjugated polymers, photo-
synthetic complexes of plants and bacteria, and molecular
aggregates were extensively studied during last years. The
interest to them is connected with their special optical prop-
erties, such as the fast transport of the electromagnetic ener-
gy, the strong (and color-tunable) optical absorption, optical
switching, and fluorescence [1]. Light in such molecular
systems is collectively absorbed by many molecules and
their optical properties reveal the collective coherent behav-
ior [2]. The changes of the shape of organic molecule, when
such molecules aggregate can help to understand the nature
of the interaction between monomers in such molecular ag-
gregates, and to determine the strength of such an interac-
tion. Aggregates of organic molecules are supra-molecular
complexes with the strong interactions between electronic
transitions. So called J-aggregates [3] manifest the red shift
and narrowing of the absorption spectrum for many molecu-
lar aggregates, e.g., for cyanine dyes with strong inter-
monomer coupling caused by the dipole-dipole interaction.
Unlike well-known concentration effects [4] (that manifest
themselves in broadening of optical spectra and decay of the
fluorescence of organic molecules for their chaotic associa-
tion), J-aggregates reveal ordered aggregation of molecules
with the new narrow absorption band, being shifted compared
to the monomer absorption. J-aggregates are related to the
class of large nanoclusters with the length 100L ≥ nM, with
the translation symmetry [5]. This is why, exciton excita-
tions of quantum molecular aggregates are used to be de-
scribed by the band theory [6].
It is known that optical properties of an excited atomic
state is not only the function of that single atom, but of its
environment [7]. That feature was observed, e.g., for atoms
closed to plane interfaces, in cavities and photonic crystals
[8]. For molecules, it was shown [9] that the strong interac-
tion of a molecule to the band exciton states can yield the
essential transformation of optical properties of the molecule
itself. However, the results of the experiments regarding
fluorescence of single molecules/particles coupled to the
environment are not consistent: Some of them demonstrate
the fluorescence enhancement, while others report fluores-
cence quenching [10]. Nanoplasmonics is the branch of the
modern optical science devoted to the optical phenomena of
the nanoscale in nanostructured systems [11]. Molecules (or
nanoparticles) coupled to the J-aggregate can serve as a
good example of such nanostructured subjects. Recently it
© I.Yu. Ropakova and A.A. Zvyagin, 2017
Optical characteristics of the nanoparticle coupled to a quantum molecular aggregate
was observed that the fluorescence of metallic nanoparticles
coupled to molecular aggregates strongly depends on the
distance between them [12].
The permittivity of nanoparticles is often used to describe
the behavior of optical characteristics of such systems [13]. In
this paper we study the optical characteristics of a metallic
nanoparticle (or a molecule) coupled to the exciton band of a
one-dimensional molecular aggregate: the permittivity and
the refractive index. We show that both can manifest contri-
butions from the local levels (caused by the coupling of that
single particle to the aggregate), and from the exciton band
states of the aggregate chain.
In molecular aggregates one usually deals with Frenkel
excitons, because the charge overlap in neighboring mole-
cules is small [14]. For Frenkel excitons the typical separation
between electron and hole is essentially zero, i.e., an electron
and a hole occur at the same molecule, and their binding ener-
gy is large. The main contribution to the exciton physics
comes from interactions between transition dipoles, which
form the exciton band. The Hamiltonian of a Frenkel exciton
in a single quantum molecule can be written as the one for the
two-level system sing = | | ( ) | |g eg g e eω 〉〈 + ω 〉〈 , where
| ,g e〉 and ,g eω are the wave function and the energy of the
ground (excited) state of the Frenkel exciton. It is useful to
denote the difference as 0 = e gω ω −ω , where 0ω is the tran-
sition frequency. The optical absorption of such a system is
the delta-function peak situated at the frequency of the light
0=ω ω . For the ensemble of interacting quantum molecules
one can neglect couplings between ground states and singly
and doubly excited states etc., and the interaction Hamiltonian
can be written as
int ,,= (| | | |)n m n m n m n m n mn mJ e g g e g e e g〉〈 + 〉〈∑ ,
where ,n mg and ,n me corresponds to the ground and excited
states of the nth (mth) molecule. Also the energy of a single
exciton can be renormalized due to the interaction. The in-
teraction between excitons in molecular aggregates is of
Coulomb nature, and it is dominated by the dipole-dipole
coupling between molecular transition dipoles. Within the
Hartree–Fock approximation the excited state of the exciton
is formed by the creation of an electron in an unoccupied
(excited) orbital and simultaneous destruction of an electron
state of the occupied (ground state) orbital, neglecting inter-
molecular charge transfer. Such creation and annihilation of
the nth two-level molecule can be described in terms of Pau-
li creation and destruction operators, †
nb and nb , which satis-
fy the following commutation relations at the same site
† † = 1n n n nb b b b+ , with 2 † 2( ) = ( ) = 0n nb b , and at different
sites [ , ] = 0n jb b , with †[ , ] = 0n jb b (for n j≠ ). The problem
with the quantum mechanical description of such an ensem-
ble of Frenkel excitons is in these commutation relations,
which are bosonic for different molecules and fermionic for
the same molecule. That produces so-called kinematic inter-
action between excitons. The number of excitons of the
same molecule is †=n n nn b b . Using these notations the Ham-
iltonian of the ensemble of excitons can be written as
†
0 0= [( )n n n
n
D b bω + −∑
††
, int( )] ,n j n j n gj
j
J b b b b H E− + + +∑ (1)
where nD is the difference between the ground state in the
Coulomb interaction of the first interacting molecule and the
excited state of the other interacting molecule, or vice versa
(we assume that molecules are situated symmetrically), int
is the part of the Hamiltonian, which contains higher-order in
nb and †
nb operators ( int is called the dynamic interaction),
and gE is the ground-state energy. Within dipole approxima-
tion the dynamic interaction part int can be neglected. How-
ever, the kinematic interaction persists, so the quadratic form
of Pauli creation and destruction operators still describes an
interacting system. It follows then that in linear optics one can
only examine properties of one-exciton states.
The molecules, forming aggregates, interact with electro-
magnetic fields in the optical range and the absorbed energy
of the latter transforms to excitons on a sub-micron scale.
From now on we limit ourselves with the one-dimensional
quantum molecular aggregates, and suppose the interaction
,n jJ to be limited to the nearest neighboring molecules.
Also we neglect nD , i.e., consider homogeneous aggregates.
In such a case we can write the Hamiltonian of the one-
dimensional ensemble of excitons as
† †
0 0 1= [ ( H.c.)] .n n n n
n
b b J b b +ω − +∑ (2)
Using the Jordan–Wigner transformation [15]
† †
<= (1 2 )n m m nm nb a a a−∏ , and † †
<= (1 2 )n n m mm nb a a a−∏ ,
where na ( †
na ) are destruction (creation) operator of a fer-
mion in the nth molecule, we can re-write the Hamiltonian
0 as † †
0 0 1= [ ( H.c.)]n n n nn a a J a a +ω − +∑ . The ad-
vantage of the transition to fermion operators is in the absence
of the kinematic interaction, present in the ensemble of Pauli
operators. Then the Hamiltonian 0 can be diagonalized us-
ing the Fourier transform, and we obtain †
0 = k kkk a a′ ′′′ε∑ .
The one-exciton eigenstates in the open aggregate chain
can be written as †| = 2 / 1sin( / 1) |nk L k L a g′〉 + π + 〉 with
the energy 0= 2 cos( / 1)k J k L′ ′ε ω − π + and integer
=1, 2, ,k L′
, L being the number of molecules in the
chain. For L →∞ the one-exciton state is a band centered
around 0ω with the bandwidth 4 | |J . The energy distance
between band states is = 2 | | / ( 1)E J L∆ π + . Notice that
the case > 0J the absorption of the molecular aggregate
is red-shifted comparing to the monomer absorption
(the case is called J-aggregates), and for < 0J it is blue-
shifted (H-aggregates).
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 11 1595
I.Yu. Ropakova and A.A. Zvyagin
Suppose that the one-dimensional molecular aggregate
is coupled to a single nanoparticle (or a molecule) (which
we enumerate with the number 0). Considering the main
effect we can model the Hamiltonian of the total system as
† † †
0 1 0 1 00 0 1= ( ) ,b b J b b b b′+ ω − + (3)
where 1ω denotes the transition frequency of that single
particle, and J ′ is the coupling strength of that single parti-
cle to the aggregate chain. Here we assume that the single
particle is coupled to the first molecule of the chain. One can
see that the single molecule differs in our model from other
molecules of the chain by 1ω and J ′. Obviously, the case
with 1 0=ω ω and =J J′ results in the same Hamiltonian
0 with 1L L→ + . For the infinite chain (L →∞ ) it is pos-
sible to obtain the characteristics of all states of the Hamil-
tonian , see, e.g., Ref. 16 using the unitary transfor-
mation ,= (2 / )n na L u aλ λλ∑ (for the homogeneous case
=J J′ and 1 0=ω ω it is the Fourier transformation), where
λ denotes either band eigenstates, or possible localized
levels. Analysis shows that there can exist band states and
localized states. The band states (with their wave functions
renormalized due to the coupled single molecule) have the
energy = 2 cosk J kε ω− , where k−π ≤ ≤ π. The localized
states appear if the following conditions hold. Let us define
1 0= ( ) / 2J∆ ω −ω and = /f J J′ . Then the local level
with the energy 1ε and the local level with the energy 2ε are
split from the upper/lower edge of the band if 2 > 2 2f − ∆,
or 2 > 2 2f + ∆ , respectively. The energies are [16]
2 1 2 2 2 2
1,2 0= ( 1) [ (2 ) 1]J f f f f−ε ω − − ∆ − ± ∆ + − . The
localization lengths for those local levels are
2 2 2
1,2 = ln[( 1) / ( 1)]f fξ ∆ ± ∆ + − − . For = 1f , we have
only one level with 2
0= (1 ) /Jε ω + + ∆ ∆ with the locali-
zation length = ln ( 2 )ξ − − ∆ .
The imaginary part of the dynamical susceptibility of the
particle can be written as ( ) ( )= b l′′ ′′ ′′χ χ + χ , where the imagi-
nary part of the susceptibility due to the band states of the
molecular aggregate is
( )
1= tanh
| | 2b
BJ k T
ω′′χ ×
2 2
2 2 4
2 1 (1 | |) ,
4( ) 4 ( )
f x x
x f x x f
−
× Θ −
∆ + − ∆ + +
(4)
where 0= ( ) / 2x Jω −ω , Θ is the Heaviside step function,
T is the temperature, and Bk is Boltzmann's constant. On the
other hand, the imaginary part of the susceptibility, caused
by the local levels, is
_____________________________________________________
2
2
( ) 1 2 2 2 2 2
2
2
2 2 2 2 2 2
1= tanh ( ) ( 2 2 )
2 1 2( 1 1)
1( ) ( 2 2 ) ,
1 2( 1 1)
l
B
ff
k T f f f
ff
f f f
ω ′′χ δ ε − ω Θ − + ∆ − + − ∆ + − + ∆ ∆ + −
+δ ε − ω Θ − − ∆ − +
− ∆ + − − ∆ ∆ + −
(5)
________________________________________________
where ( )xδ is the Dirac delta-function. One can see that for
= 0J ′ (i.e., for = 0f ) the contribution to the imaginary part
of the susceptibility from the second local level is zero, while
the one from the first level becomes ( ) 1" ( )lχ δ ω −ω , i.e., it
is the imaginary part of the susceptibility of a single nanopar-
ticle (a single molecule), and the contribution from the band
exciton states is zero. On the other hand, for = 1f and = 0∆
we obtain the imaginary part of the susceptibility ( )b′′χ be-
ing the one of the homogeneous one-dimensional J-
aggregate chain, 2
( ) 1 (1 | |)b x x′′χ − Θ − . Using the Kra-
mers–Kronig relations we can obtain the real part of the dy-
namical susceptibility 1( ) = ( ) / ( )d−′ ′ ′′ ′ ′χ ω π ω χ ω ω−ω∫ ,
where denotes the principal part of the integral. Then using
the relation
( ) = 1 ( )ω + χ ω (6)
we obtain the dynamical permittivity caused by the nanopar-
ticle coupled to the exciton system of the one-dimensional J-
aggregate (we normalize everything by the vacuum permittiv-
ity 0 , so we deal with the relative dynamical permittivity).
Notice that the imaginary part of the dynamical permittivity is
related to the dynamical conductivity σ via = /′′ σ ω . Fig-
ures 1 and 2 present the real and imaginary parts of that per-
mittivity (here and below we present the results as the func-
tion of the light wavelength = 2 /cλ π ω, where c is the speed
of light). In our calculations we used the fact that the relaxa-
tion rate in J -aggregates is usually much larger than in a sin-
gle molecule (or in a nanoparticle) 0γ [17].
For calculation of the results, presented in Figs. 1 and 2,
we used the following set of parameters: 0 0= 2 / =cλ π ω
=513 nm, 1 1= 2 / = 556cλ π ω nm, = 2 / = 20000T c Tλ π
nm, = 2 / = 11111J c Jλ π nm and = 5f (the strong cou-
1596 Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 11
Optical characteristics of the nanoparticle coupled to a quantum molecular aggregate
pling of the nanoparticle to the J-aggregate). Notice that the
wavelengths, related to the local levels, are very different
from 1λ (425 and 703 nm) due to the strong coupling of the
particle to the J-aggregate. For comparison, in Figs. 3 and 4
we present the results of calculation of the relative dy-
namical permittivity for the nanoparticle, weakly cou-
pled to the J-aggregate chain. In this case we use
= 0.5f with 1 = 541λ nm and = 7143Jλ nm (all other
parameters are the same as in Figs. 1 and 2).
Fig. 1. The real part of the relative dynamical permittivity (in
arbitrary units) of the nanoparticle (a molecule) strongly interact-
ing with the one-dimensional J-aggregate as a function of the
wavelength of the electromagnetic field λ. One can see the con-
tributions from the band exciton states and from the local levels
split below and above the band states.
Fig. 2. The imaginary part of the relative dynamical permittivity
(in arbitrary units) of the nanoparticle (a molecule) strongly cou-
pled to the one-dimensional J-aggregate as a function of the
wavelength of the electromagnetic field λ with the contributions
from the band exciton states (the dashed line) and from the local
levels (the solid line).
Fig. 3. The real part of the relative dynamical permittivity (in
arbitrary units) of the nanoparticle (a molecule) weakly interact-
ing with the one-dimensional J-aggregate as a function of the
wavelength of the electromagnetic field λ. Only band exciton
states contribute.
Fig. 4. The imaginary part of the relative dynamical permittivity
(in arbitrary units) of the nanoparticle (a molecule) weakly cou-
pled to the one-dimensional J-aggregate as a function of the
wavelength of the electromagnetic field λ with the contributions
from the band exciton states only.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 11 1597
I.Yu. Ropakova and A.A. Zvyagin
For this set of parameters there are no local levels, and
the dynamical permittivity of the nanoparticle is deter-
mined only by the exciton band states of the J-aggregate
chain. Notice that both the real and the imaginary parts of
the dynamical permittivity in this case is much larger than
the ones for the strong coupling case, see Figs. 1 and 2.
Then we calculate the dynamical refractive index ( )n ω
caused by the nanoparticle (or a molecule) coupled to the
J-aggregate chain 2( ) = ( )nω ω . (Notice that the refractivi-
ty is = 1N n− .) The real part of the refractive index (which
indicates the phase velocity) is related to the relative per-
mittivity as
1/2
1/2 2 2= 2 ( ) ( ) .n ' ' ''− + +
(7)
The imaginary part of the refractive index κ (also
known as the extinction coefficient, or the mass attenuation
coefficient, is related to the absorption coefficient α via
= / 2cκ α ω) can be written as
1/2
1/2 2 2
= .
2 ( ) ( )
''
' ' ''
κ
+ +
(8)
The absorption coefficient is connected with the penetra-
tion depth 1=p
−δ α , i.e., it shows how deep the light can
penetrate into the material. Notice that the skin depth eδ is
twice bigger than the penetration depth. The refractive index
and the extinction coefficient are related to the phase con-
stant β and the attenuation constant α (the imaginary and
the real part of the propagation constant γ ), respectively.
In Figs. 5 and 6 we present the results of calculation of
the dynamical refractive index and the extension coefficient
for the nanoparticle (a molecule) strongly coupled to the
one-dimensional J-aggregate. We used the same parameters
as in Figs. 1, 2.
In summary, we have shown that a nanoparticle (a sin-
gle molecule), coupled to the one-dimensional quantum
molecular aggregate manifests special features of its opti-
cal characteristics, like the dynamical permittivity and the
refractive index. Depending on the values of the coupling
of the particle and its own frequency, with respect to the
own frequency of the aggregated molecules, and the
strength of the aggregation, the real and imaginary parts of
the dynamical permittivity and the refractive index of the
molecule manifest the contribution from the exciton band,
or/and the ones from the local level(s) caused by the nano-
particle (or a single molecule). It is very different from the
dynamical characteristics of the single nanoparticle (or a
molecule). Hence, the optical characteristics of the nano-
particle coupled to Frenkel excitons of the J-aggregate are
stronly affected by the environment. In some cases, only
the exciton band contributes to the optical characteristics
of the nanoparticle (a molecule).
Acknowledgment
A.A.Z. acknowledges the support from the Institute for
Chemistry of V.N. Karazin Kharkov National University.
Fig. 5. The dynamical refractive index (in arbitrary units) of the
nanoparticle (a molecule) strongly interacting with the one-
dimensional J-aggregate as a function of the wavelength of the
electromagnetic field λ.
Fig. 6. The dynamical extinction coefficient (in arbitrary units) of
the nanoparticle (a molecule) strongly coupled to the one-
dimensional J-aggregate as a function of the wavelength of the
electromagnetic field λ.
1598 Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 11
Optical characteristics of the nanoparticle coupled to a quantum molecular aggregate
1. See, e.g., G.D. Scholes and G. Rumbles, Nature Mater. 5,
683 (2006).
2. For the reviews use, e.g., S.K. Saikin, A. Eisfeld, S. Valleau, and
A. Aspru-Guzik, Nanophotonics 2(1), 21 (2013); Yu.V. Malykin,
A.V. Sorokin, and V.P. Seminozhenko, Fiz. Nizk. Temp. 42, 551
(2016) [Low Temp. Phys. 42, 429 (2016)].
3. E.E. Jelley, Nature 138, 1009 (1936); ibid. 139, 631 (1937);
G. Scheibe, Angew. Chemie 50, 212 (1937); ibid. 52, 631 (1939).
4. J.R. Lacowitz, Principles of the Fluorescent Spectroscopy,
Springer, New-York (2006).
5. F. Wurthner, T.E. Kaiser, and Ch.R. Saha-Muller, Angew. Chem.
Int. Ed. 50, 3376 (2011); D. Möbius, Adv. Matter. 7, 437 (1995);
T. Kobayashi (ed.), J-Aggregates, World Scientific Publishing,
Singapore (1996); E. Lang, A. Sorokin, M. Drechsler,
Yu.V. Malyukin, and J. Köhler, Nano Lett. 5, 2635 (2005);
H. von Berlepsch and C. Böttcher, J. Phys. Chem. B 106, 3146
(2002); D.M. Eisele, J. Knoester, S. Kirstein, J.P. Rabe, and
D.A. Vanden Bout, Nat. Nanotech. 4, 658 (2009).
6. A.S. Davydov, Theory of Molecular Excitons, Springer Science
and Business Media, New York (1971); E.I. Rashba and
M.D. Sturge (eds.), Excitons, North-Holland, Amsterdam (1982).
7. E.L. Purcell, Phys. Rev. 69, 681 (1946).
8. K.H. Drexhage, Progr. Opt. 12, 163 (1974); R.R. Chance, A.
Prock, and R. Silbey, Adv. Chem. Phys. 37, 1 (1978); D. Kleppner,
Phys. Rev. Lett. 47, 233 (1981); P. Lodahl, A.F. van Driel,
I.S. Nikolaev, A. Irman, K. Overgaag, D.A.M. Vanmaekelbergh,
and W.L. Vos, Nature (London) 430, 654 (2004).
9. E.I. Rashba, Opt. Spectr. 2, 568 (1957) (in Russian).
10. K.T. Shimitsu, W.K. Woo, B.R. Fisher, H.J. Eisler, and
M.G. Bawendi, Phys. Rev. Lett. 89, 117401 (2002); A. Kramer,
W. Trabesinger, B. Hecht, and U.P. Wild, Appl. Phys. Lett. 80,
1652 (2002); E. Dulkeith, M. Ringler, T.A. Klar, J. Feldman,
A. Munoz Javler, and W.J. Parak, Nano Lett. 5, 585 (2005); W.
Trabesinger, A. Kramer, M. Kreiter, B. Hecht, and U.P. Wild,
Appl. Phys. Lett. 81, 2118 (2002).
11. M.I. Stockman, Opt. Express 19, 22029 (2011).
12. A.V. Sorokin, A.A. Zabolotskii, N.V. Pereverzev, S.L. Yefimova,
Yu.V. Malyukin, and A.I. Plekhanov, J. Phys. Chem. C 118, 7599
(2014); A.V. Sorokin, A.A. Zabolotskii, N.V. Pereverzev, I.I.
Bespalova, S.L. Yefimova, Yu.V. Malyukin, and A.I. Plekhanov,
J. Phys. Chem. C 119, 2743 (2015).
13. P. Törmä and W.L. Barnes, Rep. Progr. Phys. 78, 013901
(2015).
14. J. Knoester and V.M. Agranovich, in: Electronic Excitations in
Organic Based Nanostructures, Thin Films and Nano-Structures,
V.M. Agranovich and G.F. Bassani (eds.), Elsevier, Amsterdam,
(2003), vol. 31.
15. P. Jordan and E. Wigner, Z. Phys. 47, 631 (1928).
16. A.A. Zvyagin, Finite Size Effects in Correlated Electron
Models: Exact Results, Imperial College Press, London
(2005); A.A. Zvyagin, Phys. Rev. B 85, 134435 (2012).
17. S.K. Boer and D.A. Wiersma, Chem Phys. Lett. 165, 45
(1990); H. Fidder, J. Terpstra, and D.A. Wierssma, J. Chem.
Phys. 94, 6895 (1995).
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 11 1599
http://dx.doi.org/10.1038/nmat1710
http://dx.doi.org/10.1515/nanoph-2012-0025
http://dx.doi.org/10.1038/1381009a0
http://dx.doi.org/1038/139631b0
http://dx.doi.org/10.1002/ange.19370501103
http://dx.doi.org/10.1002/ange.19390524202
http://dx.doi.org/10.1002/anie.201002307
http://dx.doi.org/10.1002/anie.201002307
http://dx.doi.org/10.1002/adma.19950070503
http://dx.doi.org/10.1021/nl051132z
http://dx.doi.org/10.1021/jp0143701
http://dx.doi.org/10.1038/nnano.2009.227
http://dx.doi.org/10.1103/PhysRev.69.37
http://dx.doi.org/10.1016/S0079-6638(08)70266-X
http://dx.doi.org/10.1002/9780470142561.ch1
http://dx.doi.org/10.1103/PhysRevLett.47.233
http://dx.doi.org/10.1038/nature02772
http://dx.doi.org/10.1103/PhysRevLett.89.117401
http://dx.doi.org/10.1063/1.1453479
http://dx.doi.org/10.1021/nl0480969
http://dx.doi.org/10.1021/nl0480969
http://dx.doi.org/10.1364/OE.19.022029
http://dx.doi.org/10.1021/jp412798u
http://dx.doi.org/10.1021/jp5102626
http://dx.doi.org/10.1088/0034-4885/78/1/013901
http://dx.doi.org/10.1007/BF01331938
http://dx.doi.org/10.1103/PhysRevB.85.134435
http://dx.doi.org/10.1016/0009-2614(90)87010-O
http://dx.doi.org/10.1063/1.460220
http://dx.doi.org/10.1063/1.460220
Acknowledgment
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