Competition between Local Field Enhancement and Nonradiative

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Competition Between Local Field Enhancement and Nonradiative Resonant Energy Transfer on the Linear Absorption of a Semiconductor Quantum Dot Coupled to a Metal Nanoparticle Xiaona Liu, Qu Yue, Tengfei Yan, Junbin Li, Wei Yan, Jianjun Ma, Chunbo Zhao, and Xin-Hui Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b03637 • Publication Date (Web): 21 Jul 2016 Downloaded from http://pubs.acs.org on July 22, 2016

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The Journal of Physical Chemistry

Competition Between Local Field Enhancement and Nonradiative Resonant Energy Transfer on the Linear Absorption of a Semiconductor Quantum Dot Coupled to a Metal Nanoparticle Xiaona Liu,*,† Qu Yue,‡ Tengfei Yan,† Junbin Li,† Wei Yan,† Jianjun Ma,§ Chunbo Zhao† and Xinhui Zhang*,† †

State Key Laboratory of Superlattices and Microstructures, Institute of

Semiconductors, Chinese Academy of Sciences, Beijing 100083, P. R. China. ‡

College of Science, National University of Defense Technology, Changsha 410073,

Hunan Province, China. §Department of Physics, New Jersey Institute of Technology, 322 King Blvd., Newark, New Jersey 07102, USA.

ABSTRACT. In this work, we systematically investigate the linear absorption associated with the excitons’ interband transition of a semiconductor quantum dot (SQD) in proximity to a metal nanoparticle (MNP), where the competition between local field enhancement and nonradiative resonant energy transfer (NRET) plays a critical role. It is shown that the linear absorption coefficient of SQD depends strongly on the geometrical parameters of the hybrid nanostructure. In particular, a continuous 1 ACS Paragon Plus Environment


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transition from absorption enhancement to quenching by varying the size of MNP and location of SQD is clearly observed. Three regimes are identified unambiguously where the NRET or local field enhancement governs the absorption response of SQD hybrid nanostructure. In the first regime where there exists strong SQD-MNP when the separation distance between SQD and MNP is relatively short, the dominant contribution to the absorption response of SQD is the NRET effect, and the multipole effect must be considered beyond the dipole effect. With increasing the separation distance between SQD and MNP, the coupling is slightly weakened and the local field enhancement becomes the dominant contribution to the optical response of SQD in second regime. When the coupling is further weakened by increasing the distance between SQD and MNP, the strong coupling interaction is diminished and the optical response approaches to the case of bare SQD. Controlling over the geometrical parameters of the nanostructure not only provides a further engineering degree of freedom to elucidate the underlying physics of these structures, but also offers a guide for optimal design of SQD-MNP hybrid nanostructures towards their novel optoelectronics application.

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Ⅰ. INTRODUCTION Tailoring over optical properties of semiconductors has been an ever increasing demand to the implementation of the novel optoelectronic application. This ongoing thrust leads to the development of nanoscale semiconductors that exhibit size, shape and composition dependent electronic and optical properties. However, as the dimension of semiconductors is reduced, light-matter interplay is typically weakened, thus limiting the optoelectronic applications. To further optimize the material properties, many approaches have been utilized to improve the light-matter interactions, such as synthesizing hetero-nanostructure1-4, doping metal into semiconductor nanostructure5-6 as well as coupling semiconductor nanomaterials with metal nanoparticles (MNP)7-13 to form hybrid nanostructures. Hybrid nanostructures possess unique properties in comparison to their individual counterparts, which has been under a great deal of attention both theoretically and experimentally8-9, 11, 14-22. On one hand, colloidal semiconductor quantum dots (SQD), exhibiting rich physical phenomena of quantum-confined systems23-26, are especially attractive in this context since they can be prepared in highly monodisperse form to show optical response in a widely tuned spectral range and easily form the multifunctional nanostructure in the presence of other nanomaterials27-28. On the other hand, MNP supports the localized surface plasmons that are tightly confined spatially, enables the concentration of the electromagnetic energy, and thus enhances their ability for focusing optical fields. The coexistence of SQD and MNP profoundly modifies the light-matter interaction with the potential tunability and control. The excitons (the discrete quantum confined electronic 3 ACS Paragon Plus Environment


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states in SQD) and plasmons (the dielectric-confined electromagnetic modes in MNP) in the hybrid nanostructure influence each other indirectly due to the long-range Coulomb interaction. A SQD plays the role of quantum emitter, whereas the MNP plays the role of damper or amplifier in this hybrid nanostructure. Novotny et al.29 showed that the fluorescence of single-molecule can be enhanced and quenched depending on the interparticle distance. Subsequently, similar behavior from the closely packed monolayers of CdSe quantum dots doped with MNPs was experimentally reported8, but this transition was explained by the single particle emission and collective emission. Enhanced emission of the CdSe/ZnS SQD was further demonstrated experimentally in the presence of bimetallic nanoparticles30. Such enhancement or quenching of optical response is attributed to the interaction between the quantum emitter and MNP31-34. Moreover, by varying the density of the embedded gold nanoparticles, emission quenching and enhancement in quantum dot films can be achieved35. Interestingly, it is found that different materials such as two-dimensional sheets of graphene, hexagonal bornon nitride and MoS2, as well as their layer thickness play an important role in the photoluminescence response of the core-shell SQD in the hybrid nanostructures36-37. Very recently, the enhanced photoluminescence properties of Bi2S3 quantum dots with the Ag@SiO2 nanoshell hybrid have been experimentally demonstrated by modulating the thickness of the silica shell and the concentration of Ag nanoparticles38. Besides, recent theoretical studies have also suggested that the linear optical response can be either quenched or enhanced by the addition of a MNP17, 31-32. Although these works offer an extensive study for the interaction of the 4 ACS Paragon Plus Environment

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exciton-plasmon coupling, revealing that such coupled systems exhibit enhanced or quenched optical response and larger tunability of their optical response compared to the uncoupled systems, there has been no clear distinguishment of the crossover from the quenching to enhancement with the two competing effects: NRET and local field enhancement induced by the plasmon resonance39. Our motivation in this work is to investigate the critical material design parameters and to find out the crossover point from the NRET to local field enhancement, resulting in the absorption quenching or enhancement of quantum dots, respectively. The results presented in this work will offer useful reference from the experimental point of view to optimize the hybrid nanostructure design for their novel optoelectronics application.

In this paper, a semiclassical theory has been adopted to systematically investigate how plasmons modify the linear optical absorption associated with the excitons’ interband transition of SQD in proximity to an Au nanoparticle. A non-monotonic variation of absorption peaks with the increased distance between SQD and MNP is observed, which corresponds to a crossover phenomenon arising from the competition between the local field enhancement and SQD-MNP near-field energy transfer. Three regimes are identified to distinguish unambiguously the two competing mechanisms by continuously varying the geometrical parameters of SQD-MNP hybrid nanostructure. Furthermore, the close dependence of the optimum surface-to-surafce distances dopt and the optimal absorption peaks of SQD on the size of MNP are demonstrated. It is found that these optimum parameters for the considered nanostructure are located in the region Ⅱ , where the local field enhancement 5 ACS Paragon Plus Environment


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dominates the optical response of SQD. Our results presented in this work provide a general guide for proper hybrid nanostructure design in order to take full advantage of their optical properties towards novel optoelectronics application.

Ⅱ. MODEL AND THEORY The hybrid nanostructures composed of colloidal CdSe/ZnS quantum dots and Au nanoparticles have been constructed experimentally27. These systems are commonly realized when the low-dimensional semiconductor structures are brought into the vicinity of metallic nanoparticles. The main feature of such systems interacted with a laser field is the fact that they combine different types of excitations (excitons and plasmons) forming coupled excitations. In this section we consider the linear absorption of the core-shell SQD coupled to a nearby spherical MNP in a dielectric background with permittivity of εb . SQD is characterized with a core radius of R1, the shell radius (core radius plus the shell thickness) of R2 and the dielectric function of ε s . The radius of MNP is taken as Rm and the dielectric function of MNP is εm . The two nanoparticles have a center-to-center distance d and the surface-to-surface distance ds. The radius Rm of the MNP and the size of the SQD R2 as well as the surface-to-surface spacing ds in the interaction regime are small enough compared to the optical wavelength, thus allowing the use of the quasistatic approximation. Also, the retardation effects are negligible because the interaction between the SQD and MNP is dominated by the near-field dipole-dipole (multipole) coupling. However, retardation must be considered in the case of the hybrid nanostructure composed of the MNP nanorod and SQD40, where the length of nanorod can be comparable to the 6 ACS Paragon Plus Environment

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wavelength of incident light. Two excitonic states of SQD are considered here and they are labeled as 1 for the ground state and 2 for the excited state. The exciton frequency of transition between 1 ↔ 2 is denoted as ω21 . The entire system is subjected to an external

field

oriented

along

form

the

z

direction

in

the

. A schematic diagram of the hybrid

nanostructure is shown in Figure 1.

Figure 1. A schematic diagram of hybrid nanostructure composed of a core-shell CdSe/ZnS quantum dot coupled to an Au nanoparticle. A SQD with the core radius R1 and shell radius R2 locates at ds from the surface of a MNP which is characterized by a radius Rm and permittivity ε m. An external optical electric field is applied to orient along z direction.

A semiclassical approximation is adopted as usually used in most of previous works on this hybrid nanostructure, i.e., the optical response of the SQD is treated quantum mechanically, and the two-level exciton model is used to describe SQD in the hybrid system, with the Hamiltoian

H =−

h2 1 ∇ ∗ ∇ + Vα (r ) − µES (t), 2 mα

(1) 7

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while the optical response of the plamons in the MNP is treated classically, considering its polarizability. The total electric field applied inside the SQD41-42 can be calculated using

(2)

is the local electric field induced by E0 inside a SQD in the absence of a MNP, where εb, background,

εs, and εeff 1 = (ε s + 2εb ) / (3εb ) are

SQD

and

the

effective

the dielectric constants of permittivity,

respectively.

comes from the surface charges of MNP induced by E0 , and

is the effective electric field induced by the

dipole (n=1) and multipole (n>1) interactions between the exciton and plasmon, where

εeff 2 = (ε s + 2εb ) / 3,

γ n = [ n(ε m − ε b )] / [ n(ε m + ε b ) + ε b ],

ε m (ω )

γ 1 = [ε m (ω ) − ε b ] / [ε m (ω ) + 2ε b ], is

the

dielectric

function

of

Au, g1 = 2 and gn = (n +1) for the electric field polarization parallel to the major axis of 2

the system. In the simplest approximation, we describe MNP with the local uniform dielectric function εm (ω), obtained from reference43.

We then calculate the exciton transition energy levels of the hybrid system based on the single band effective-mass approximation, by adopting the general theoretical approach for the exciton energy eigenvalues and carrier wave functions44-45. The stationary Schrödinger equation is written as


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[−

h2 1 ∇ ∗ ∇ + Vα (r )]ψ α (r ) = Eαψ α (r ). 2 mα

(3)

Here the subscript α = e (electron) or h (hole), and a spherically symmetric confinement potential V(r)=V(r) depends only on the radial coordinate r as follows： Vα = 0 for 0 ≤ r < R1 , Vα ( r ) = Vα0 for R1 ≤ r < R2 , and Vα ( r ) = ∞ for r ≥ R2 . The single

carrier envelope wave functions may be expressed as

ψα (r) =ψα (r,θ ,ϕ) = Rα,nl (r) Ylm (θ ,ϕ),

(4)

Rα ,nl ( r ) is the radial wave function, a linear combination of the spherical Bessel and Neumann functions jl and nl , or a linear combination of the modified spherical Bessel and Neumann functions il and kl , which can be determined by the relative position of 0

the carrier confinement (kinetic) energies and the band offset Vα of the heterostructure. Ylm (θ , ϕ ) is a spherical harmonic function. The Coulomb interaction energy of an exciton can be treated as a heliumlike perturbation term

Ec = −

e2 4π

∫ ∫ dre drh

ψ e∗ (re )ψ h∗ (rh )ψ e (re )ψ h (rh ) re − rh

⋅

1 , ε (re − rh )

(5)

and the new band gap of the core-shell quantum dot material is the sum of the confinement energies, Coulomb energy and the bulk band gap energy, i.e.

Egap = Ee,1s + Eh,1s + Ec + Egap,bulk .

(6)

The eigensolutions of the exciton are obtained numerically based on the continuous and smooth boundary conditions in SQD.



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The optical response of the exciton in the SQD is described in terms of the interband polarization and the occupancy by the optical Bloch equations

(7)

(8)

Time-dependent

density

matrix

operator

ρ(t)

can

be

written

and we set ∆ = ρ11 − ρ 22 . The equations of motion for

as

the density matrix elements should satisfy

Putting these into the Eqs.(7)

and (8), we obtain the first-order density matrix element under the rotating wave and steady state approximation

(9)

where we have defined G as ∞

G=∑ n =1

g nε bγ n Rm 2 n +1µ 2 = GR + iGI . ε eff 1ε eff 2 d 2 n + 4 h

(10)

G is known as the self-interaction of the SQD41, 46. It arises firstly when SQD is polarized by the applied field, the oscillating dipole moment in SQD produces an oscillating electric field that acts on MNP to produce a field which in turn interacts with SQD. The G factor stems from the Coulomb interaction between SQD and MNP,


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which is crucial in determining the frequency shifts and lifetime of the exciton, and is also responsible for the Förster energy transfer and Dexter energy transfer. The electronic polarization P(t) and susceptibility χ47caused by the applied laser electric field can be expressed through the dipole operator and the density matrix as

(11)

where N0 is the density of carriers, ε 0 is the permittivity of free space. By using Eqs.(9) and (11), we obtain the linear susceptibility of the SQD coupled to a MNP given by 2

N0 µ ∆ g1γ1Rm3 χ (ω) = − (1+ ) . εeff 1ε0 d3 h(ω − ω21 + G∆ + iγ 21 ) (1)

εb

(12)

We can see from Eq. (12) that the exciton transition frequencies, ω → ω − ω21 + GR ∆ are renormalized and the damping rates γ 21 → γ 21 + GI ∆ are also renormalized. The latter term plays an important role in the nonradiative energy transfer process31, 33 due to the presence of the MNP close to SQD. The susceptibility χ is related to the absorption coefficient α(ω) by

α (ω) = ω

µs Im ( ε 0 χ (1) (ω) ) , ε

(13)

where µs is the permeability of the system. This formalism is used to analyze the exciton-plasmon interaction as a function of the MNP’s size and the distance between SQD and MNP. In our case we have ignored the coupling with phonons for SQD 11 ACS Paragon Plus Environment


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emitter, thus the absorbed energy and emitted energy are the same at the equilibrium state. In most cases, absorption of the SQD is reduced in the presence of the MNP due to the nonradiative energy transfer to MNP and energy dissipation in the metal. However, it will be found that the absorption of SQD increases in the presence of the MNP under some condition. We will give the numerical solutions in the following section.

Ⅲ. NUMEIRICAL RESULTS AND DISCUSSION In this section, the calculated absorption spectra associated with the excitons’ interband transition of SQD coupled to MNP based on equation(13) with different hybrid material parameters are presented and discussed. Here we mainly focus on three different regimes for the optical response of SQD-MNP hybrid system. First, we investigate the absorption quenching in the regionⅠ, where the NRET is dominant. Second, we show the absorption enhancement in the regionⅡ, where the optical field felt by SQD is amplified by the plasmon resonance. And then the region Ⅲ where the interaction between SQD and MNP is negligible and the optical response approaches to the case of bare SQD. All the enhancement and quenching for the optical responses of the hybrid system are compared to that of the bare SQD.

In all calculations, the SQD is considered initially in the exciton ground state, leading to ∆ =1. Assuming the aqueous solution as the enviroment of SQD, the dielectric constant of the background is taken to be ε b =1.8. The effective electron and hole mass of CdSe and ZnS in the colloidal core-shell SQD used in the calculation are 12 ACS Paragon Plus Environment

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chosen as me∗,CdSe =0.13m0, mh∗,CdSe = 0.45m0, me∗,ZnS =0.28m0, mh∗,ZnS =0.49m0 (m0 is the free electron mass), and the adopted bandgap of CdSe and ZnS are E band gap, CdSe=1.84 eV, E band gap, ZnS=3.9 eV44, the conduction band offset parameter Ve is 0.9 eV48 and the valence-band offset Vh is concluded to be 1.16 eV, the relaxation time T2 is taken as 0.3 ps and ε s =6.249. The core-shell radius of SQD is fixed to be R1=2.0 nm and R2=2.6 nm, respectively. The multipole polarization up to N=10 as included in previous works modeling the optical property of the hybrid nanocrystals41 is considered as well in our calculation. The influence of band bending and alloying on the energy levels of the exciton is neglected in this work. Besides, charge exchange correlation or tunneling between the SQD and MNP is not considered for shorter surface-to-surface

distance,

thus

the

interparticle

Coulomb

interaction

(dipole-dipole/multipole) becomes the main coupling mechanism of in the hybrid nanostructures.



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Figure 2. (a) The absorption spectra of SQD in the hybrid nanostructure as a function of detuning pump photon energy from the exciton resonance, calculated for different surface distances ds with Rm=20 nm. For comparison purpose, the absorption spectrum of the bare SQD is also included in the figures (gray solid line).

(b)The

absorption peaks corresponding to the absorption spectra in (a) as a function of the surface-to-surface distance ds. (c) The influence of the multipole effect (solid lines) and dipole effect (dashed lines) on the absorption spectra of SQD in the hybrid nanostructure.


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The characteristic of the absorption spectra of the SQD hybridized with MNP is shown in Figure 2, where the radius of MNP is taken as Rm=20 nm. It is clearly seen that the effect of MNP on the absorption of SQD can be tailored by moving SQD away from MNP. Figure 2 (a) shows the dependence of the absorption spectra on the detuning of the pump photon energy from the exciton resonance for several different surface-to-surface distances ds. For comparison purpose, the absorption spectrum of the bare SQD is also included in the figure. There appears a non-monotonic variation of the peak absorption coefficient, along with red shifts and broadening of the spectra with the decreased surface-to-surface distances ds between SQD and MNP, which is a manifestation that the NRET and the local field enhancement compete with each other in the entire studied separation distance. At substantially small distances when SQD and MNP are in close contact, the progressive red shifts lead to the transparency of SQD at the frequency that it was previously absorbing most strongly. In addition, NRET from SQD to MNP results in the absorption quenching compared with that of bare SQD. Since this energy transfer process is a short-range effect and is very sensitive to the separation distance between SQD and MNP, NRET would be weakened with distance much faster than the enhanced local filed responsible for the absorption enhancement. Thus the optical absorption would exhibit a maximum value at a certain separation distance, which is calculated to be in the range of 10~14 nm by using numerical simulation, depending on the size of the components. This means that there exists an optimal distance dopt for a fixed size of SQD and MNP (the details can be seen later in Figure 5). Further increase in the SQD-MNP distance results in a 15 ACS Paragon Plus Environment


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decrease of absorption to the level of that for bare SQD. It is apparent in Figure 2 (b) that the absorption peak exhibits the continuous transition from quenching to enhancement and eventually approaches to the value of the bare SQD. In the hypothetical case where the NRET is absent, a monotonic variation will be expected and a stronger absorption enhancement will show up. Moreover, it is worth noting that there exists a transition point at distance of ds=2.91 nm , at which the absorption peak of the SQD-Au hybrid nanostructure is coincident with that of the bare SQD, implying that the impact of two competing mechanisms (NRET and the local field enhancement) on the absorption spectra cancels out at this crossover point. The influence of the MNP polarization effect on the absorption response of the hybrid system for three typical surface-to-surface distances is presented in Figure 2(c). The dashed curves are calculated using the dipole approximation (N=1), while the solid curves include the contributions from the higher-order polarization up to N=10 beyond dipole polarization, such as the quadrupole, octopole and so on. Previous work41 has emphasized the important role of multipole effects on the coupled metal-semiconductor system. Here we show a more detail comparison of the absorption response for the hybrid system to that of the bare SQD, with both the dipole and multipole polarization effects included. At a short separation distance, ds=1 nm, it is readily seen that the peak absorption coeffeicient at higher-order polarizaiton (N=10) is smaller than that of the bare SQD, while it is the opposite case for the dipole polarization, the absorption coefficient is larger than that of the bare SQD. For larger surface-to-surface distance (i.e. when the exciton moves away from the 16 ACS Paragon Plus Environment

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plasmon), ds=20 nm, the dipole-dipole and dipole-multipole interaction are hardly resolvable. Therefore, the high-order polarization has a dominant contribution to the absorption response at small SQD-MNP distance. However, when SQD moves away from MNP, one only needs to consider the lowest polarizaiton effect (N=1), multipole polarization effect is approximately negligible. Furthermore, tunneling electrons from the photoexcited electron-hole pairs in SQDs could be captured in MNPs, which is beyond the scope of this work and is not consider here.

The effects of MNP can also be tailored by tuning the MNP size as shown in Figure 3. With increasing the separation distance between SQD and MNP, the absorption spectra seen in Figure 3(a) with Rm=5.0 nm have similar features with Figure 2 (a), but with lower peak absorption coefficient. Moreover, the transition point from the absorption quenching to enhancement occurs at ds=9.46 nm as shown in Figure 3 (b), being farther away from the surface of MNP compared with the case of Rm=20 (see Figure 2(b)). When SQD approaches closely to MNP, entering the strong coupling regime where the decay rates are predominantly nonradiative due to the Dexter energy transfer related to the dipole-multipole interaction and Förster energy transfer induced by the dipole-dipole interactions, a strong absorption quenching occurs39. It is seen that a maximum absorption peak appears when SQD locates at ds=14 nm, implying that this is an optimal surface-to-surface distance for the SQD-MNP hybrid. Nevertheless, the overall absorption enhancement is fairly weak compared with the case of bare SQD, as illustrated in Figure 3(b). Therefore, it



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is concluded that the MNP with smaller size exhibits much more pronounced absorption quenching effect than the enhancement on the optical response of SQD.


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Figure 3. (a) The linear absorption coefficients as a function of the detuning pump photon energy from the exciton resonance calculated for various surface-to-surface distances ds and a fixed small size of MNP with Rm=5 nm. (b) Absorption peak corresponding to the absorption spectra in (a) versus the surface distances ds. (c) and (d) exhibit the same content as (a) and (b), respectively, but for a larger size of MNP with Rm =40 nm.

The effect of MNP’s size on the absorption response is further investigated in Figure 3(c) with larger size of Rm= 40. It is seen that, with a larger size of MNP and shorter surface-to-surface distance of ds=1 nm, the contributions from both the dipole and multipole polarization effects are nearly negligible, with no observable quenching effect. By comparing with Figure 3 (a), it is found that the local field enhancement is increased dramatically and the nonradiative decay rate is efficiently reduced by increasing the size of MNP. In particular, it is seen that the absorption coefficient becomes negative with the energy detuning slightly above the exciton resonant energy of SQD for a certain range of the surface-to-surface distance. This suggests that the 19 ACS Paragon Plus Environment


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coherent interaction between SQD and MNP reverses the energy transfer process which is from the MNP to the SQD as previously reported50. Moreover, it is clear that the enhanced absorption peak is observed within widely tuned surface-to-surface distance as shown in Figure 3 (d). This is a direct consequence of the local field enhancement resulting from the strong MNP-induced surface plasmon win over the NRET. The different results presented in Figure 3 (a)-(b) and Figure 3 (c)-(d) reveal that the radiation feedback from MNP towards SQD is proportional to the size of MNP, which is also indicated in Figure 5 later.

To get a full insight into the dependence of different types of optical absorption response on the hybrid nanostructure parameter, Figure 4 provides a clear look of continuous variation of the absorption response that quenching or enhancement is exhibited in different regimes, respectively, by tuning the surface-to-surface distance ds and size of MNP Rm. Here one can see three regions divided by the two isograms which correspond to the absorption peak of the bare SQD. In the first regime, the Coulomb interaction including the multipole effect besides the dipole approximation has to be included, it is seen that the dominant contribution to the absorption response is the NRET which is responsible for the absorption quenching. This indicates the strong coupling between SQD and MNP, which is a direct consequence of strong interaction between SQD and its own polarization. As the coupling is slightly weakened, the local field enhancement becomes the dominant contribution in the second regime where the absorption enhancement wins over the quenching. When the coupling is further weakened with increasing the distance between SQD and MNP, 20 ACS Paragon Plus Environment

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the optical response of the hybrid nanostructure approaches to that of the bare SQD, thus the interaction of exciton-plasmon coupling disappears in the third regime. Our results presented in Figure 4 show that the size of MNP and the surface-to-surface distance between SQD and MNP are key parameters in determining the optical response of SQD-MNP hybrid nanostructure. These results provide a useful reference for the optimum hybrid nanostructure design in the related experiments. However, there could exist large deviation for our current results from the real case at very short surface-to-surface distance, about ds

Competition between Local Field Enhancement and Nonradiative

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