ISSN 1062-8738, Bulletin of the Russian Academy of Sciences: Physics, 2018, Vol. 82, No. 4, pp. 453–458. © Allerton Press, Inc., 2018. Original Russian Text © N.T. Lam, A.D. Kondorskiy, V.S. Lebedev, 2018, published in Izvestiya Rossiiskoi Akademii Nauk, Seriya Fizicheskaya, 2018, Vol. 82, No. 4.

Effects of Plasmon–Exciton Interaction in the Spectra of Light Absorption by Hybrid Systems Consisting of Two- and Three-Layer Organometallic Nanoparticles N. T. Lama, b, A. D. Kondorskiya, b, *, and V. S. Lebedeva, b aLebedev

Physical Institute, Russian Academy of Sciences, Moscow, 119991 Russia Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow oblast, 141700 Russia *e-mail: [email protected]

b

Abstract—The effects of plasmon-exciton interaction on the spectra of light absorption by hybrid systems of two- and three-layer nanoparticles that consist of a metallic nucleus, the outer shells of ordered molecular dye J-aggregates, and an intermediate passive organic spacer between them is analyzed theoretically. It is established that the type of the absorption spectra and the efficiency of a near-field electromagnetic coupling between the particles in the system depends largely on the distance between the centers of concentric spheres and the direction of light polarization. DOI: 10.3103/S1062873818040111

INTRODUCTION Studying the spectral properties of different hybrid nanostructures and the effects of their interaction with visible-band radiation is of great interest when solving a broad range of problems in nanophotonics. Hybrid nanostructures are used to create light-emitting diodes [1–3], solar panels [4, 5], and nanolasers [6, 7]. Composite materials are employed in solving a number of problems in subwavelength optics that are related to investigating the spatial localization of electromagnetic fields on the nanometer scale in metalized conical optical probes with dielectric [8, 9] or semiconductor [9–11] cores and studying the propagation of light in nanowaveguides [12–14]. Research on and development of hybrid nanomaterials containing organic and metallic components are currently also of great interest. This field, which is now expanding rapidly, falls between nanoplasmonics and organic photonics. This is exemplified by today’s extensive research into the spectral properties of hybrid organometallic nanostructures in which the organic component is ordered molecular dye aggregates. In these aggregates, the electronic excitations of separate molecules are collectivized to form Frenkel excitons. They therefore have unique optical properties, including great transition-oscillator strength and ultrashort radiative lifetimes. Electromagnetic coupling between Frenkel excitons and plasmons localized in nanoparticles [15‒17] or travelling along the plane metal–dielectric interface between the two media [18] play a major role in shaping the optical properties of hybrid nanostruc-

tures containing a metallic component and molecular dye J-aggregates. A great many experimental and theoretical works have studied the spectral characteristics of hybrid nanostructures that differ in composition, shape, and size and consist of a metallic nucleus and the outer shell of ordered molecular cyanine-dye J-aggregates. Among these is a series of works on modeling the spectra of two- [19–22] and three-layer [23–25] organometallic nanosystems of spherical shape. The spectral characteristics of organometallic nanosystems have also been studied and modeled for structures in the form of spheroids [26, 27]; nanorods [28–33]; stars [34]; and dumbbell-shaped figures [27]. These works studied the effects of electromagnetic coupling between molecular excitons and localized plasmons using the example of systems that consist of gold or silver nuclei and the J-aggregates of different cyanine dyes that act as outer shells. In [35], we also examined the experimental and theoretical research into the optical properties of hybrid metallic-nucleus nanoparticles and nanorods in which ordered molecular dye H-aggregates formed the outer shell. Let us recall that the structures of J- and H-aggregates differ in the angle of molecular packing, making the optical properties of these ordered molecular systems distinctly different. The aim of this work was a theoretical study of the spectral characteristics of nanosystems that consist of two- and three-layer organometallic Ag/TMA/Jaggregate and Au/TMA/J-aggregate nanospheres (see

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Fig. 1). Each nanosphere has a silver or gold nucleus, the outer shells of ordered molecular cyanine-dye J-aggregates, and an intermediate organic layer of TMA[N,N,N-trimethyl(11-mercaptoundecyl)ammonium chloride] that serves as a passive dielectric spacer between the metallic system nucleus and its outer organic layer. We chose the materials TC [3,3'-disulfopropyl-5,5'-dichlorothiacyanine sodium salt] and PIC [1,1'-disulfopropyl-2,2'-cyanine triethylammonium salt] as cyanine dyes that are capable of forming molecular J-aggregates and differ greatly in the positions of the J-band absorption maxima and transitionoscillator strengths [20, 25]. The main goal was to determine how the absorption spectra in the systems of two and three organometallic particles change, as compared to a single three-layer sphere. The absorption spectra of the considered systems were calculated for two possible polarizations of incident light—along and perpendicular to the axis that passes through the centers of concentric spheres. To establish the type of reduction in the efficiency of electromagnetic coupling between the particles in the system as its geometrical parameters are varied, we calculated and analyzed photoabsorption spectra for different distances L between the centers of concentric spheres.

CALCULATION PROCEDURE We used the method of Finite Differences in Time Domain (FDTD) [36] for solving Maxwell equations when numerically modeling absorption spectra in the relevant systems of two and three hybrid organometallic nanoparticles. Based on the MEEP open-source code library [37, 38], we developed software that enabled us to calculate absorption cross sections with allowance for contributions from all multipoles. The optical properties of the materials constituting the studied organometallic systems were governed by their dielectric functions. As in [20, 25, 27, 35], the parameters of the dielectric function of a silver (or gold) nucleus in a single three-layer particle were selected with allowance for contributions from free and bound electrons, and a dimensional effect produced by the scattering of electrons at the interface between a silver (gold) nucleus and a passive organic layer. The parameters of the dielectric functions of TC and PIC cyanine-dye molecular J-aggregates, along with the dielectric permittivity of the intermediate organic TMA layer, are also available in [20, 25]. All calculations in this work were performed for particles immersed in an aqueous solution, so the value εw = 1.78 was used as the dielectric permittivity of the surrounding medium in the visible spectral band. CALCULATION RESULTS Figures 1a and 1b show the scheme of the considered systems consisting of two and three closely adjacent three-layer organometallic nanoparticles, respectively. The Z-axis of the coordinate system is directed along the line that joins the centers of the particles. We denote the metallic nucleus radius by r, the intermediate layer thickness by h1, the outer J-aggregate shell thickness by h2, and the distance between the centers of the particles by L. Absorption cross sections were calculated for particles of radius r = 7.5 nm and intermediate- and outer-layer thicknesses h1 = 1.5 nm and h2 = 3 nm, respectively. The distance L between the centers of concentric spheres varied within a range of 24–29 nm. Figure 2 compares the results from calculating the spectral dependence of the cross section of light absorption by a system that consists of two three-layer Ag/TMA/TC nanoparticles (curve 1) and the same results for a single three-layer Ag/TMA/TC sphere (curve 2). The radiation incident on the system was polarized along the Z-axis (see Fig. 1), and distance L between the centers of concentric spheres was set at 25 nm. We can see there are two spectral peaks that are notably different in amplitude in the absorption spectrum of a single three-layer sphere. The left-hand peak with the maximum at wavelength λmax = 422 nm is primarily due to plasmon resonance in the silver nucleus, while the right-hand peak of relatively low amplitude at wavelength λmax = 486 nm can be attributed to a

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Frenkel exciton in the J-aggregate shell. It should be noted that for an uncovered silver sphere of radius r = pl 7.5 nm, plasmon resonance occurs at λ max = 408 nm, with the absorption-band center for TC dye molecular J-aggregates being at λ0 = 462.6 nm. Certain differpl ences in the positions ( Δλ max = 14 nm and Δλex max = 23.4 nm) and shape of the resulting spectrum of a single hybrid three-layer Ag/TMA/TC particle from the straightforward sum of the nucleus and shell spectra are due to near-field electromagnetic coupling of a localized plasmon and Frenkel exciton, with the plasmon and exciton interacting in the weak-coupling mode, as the plasmon-resonance peak maximum in the particle’s silver nucleus is relatively far from the exciton peak in the TC dye shell (Δλ = 54.6 nm). Located at λmax = 419 and 489 nm for a system consisting of two three-layer spheres, these two peaks are also somewhat displaced with respect to their positions in the case of a single three-layer sphere. At the same time, their intensity is to some degree redistributed over the spectrum. This is due to near-field electromagnetic coupling between two organometallic particles in the system. In addition to these two peaks, the effect of electromagnetic coupling between two three-layer spheres produces one more peak at wavelength λmax = 444 nm. Analysis shows that a key role in the emergence of this peak is played by the outer J-aggregate shell in the hybrid particles of which the studied systems consist. To demonstrate this and form a clearer idea of how the spectra are transformed upon the buildup of the organic shells in a particle, Fig. 2 additionally presents the results from calculating the dependences of absorption cross sections σ on the in vacuo light wavelength λ for two bare silver spheres (curve 3) and two silver spheres coated with a TMA organic layer (curve 4). We can see that in both ca, there is only one absorption-spectrum peak, attributed to localized plasmon resonance in the silver nuclei, for a system of two particles that consist of purely metallic spheres (Ag) or two-layer spheres (Ag/TMA). As for the additional spectral peak in the system of two three-layer Ag/TMA/TC particles, our calculations show its amplitude falls with distance L between the centers of concentric spheres. Figure 3a shows the cross sections of absorption by a system that consists of two three-layer Ag/TMA/TC particles as distance L between the centers of the spheres changes from 24 to 29 nm. The radiation incident on the system is in this case polarized along the Z-axis, i.e., along the line that joins the centers of the spheres. This figure visually demonstrates that the electromagnetic near-field coupling between nanoparticles, an effect that accounts for the additional spectral peak near wavelength λmax = 444 nm, occurs only for short distances between the nanoparticles. Increasing distance L ruptures the near-field electromagnetic bond between two organo-

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Fig. 2. Comparison of spectral dependences of light absorption cross sections by a system consisting of two three-layer Ag/ТМА/TC particles (curve 1) and the same results from calculations for an isolated single three-layer Ag/TMA/TC sphere (curve 2). Curve 3 is the absorption cross section for a pair of bare silver particles, while curve 4 is the absorption cross section for a pair of two-layer Ag/ТМА particles. The following geometrical parameters of the examined systems were used in calculations: r = 7.5, h1 = 1.5, h2 = 3 nm; the distance between the centers of concentric spheres was selected at 25 nm. Light was polarized along the Z-axis, i.e., along the line joining the centers of the concentric spheres.

metallic Ag/TMA/TC particles and thus to additional peak vanishing. Figure 3b shows the similar dependences of the photoabsorption cross section on in vacuo wavelength λ for light polarized in the direction perpendicular to the axis joining the centers of the spheres (i.e., in plane XY; see Fig. 1). Calculations show that in this case, varying distance L between the centers of organometallic particles affects the light absorption cross sections only slightly. As the number of particles in the system grows from two to three, the emergence of an additional spectral peak becomes more noticeable, with the total light absorption cross section contour widening. This is shown in Fig. 4 for a system that consists of three identical Ag/TMA/TC particles with a silver nucleus, an outer TC-dye J-aggregate shell, and an intermediate passive ТМА layer. In this work, we analyzed field distribution patterns inside systems consisting of two and three identical hybrid Ag/TMA/TC nanoparticles. It was established that for light wavelength λ = λmax, which corresponds to the maximum of the additional spectral peak (due to the near-field electromagnetic coupling between particles in the system), the field is strongly localized in the domain between the particles. The corresponding results from calculating the distribution of electro-

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Fig. 3. Spectral dependences of light absorption cross sections by a system consisting of two three-layer organometallic Ag/TMA/TC nanoparticles for two different directions of incident-light polarization, (a) along the Z-axis and (b) in plane XY. The geometrical parameters of the nucleus and shells of the spheres were set at r = 7.5, h1 = 1.5,  h2 = 3 nm. Calculation results are shown for L = 24, 25, 27, and 29 nm.

εE 2 + μH 2 (μ = 1) 8π in plane ZY at the wavelength of the additional peak are presented in Figs. 5a and 5b for the cases schematically depicted in Figs. 1a and 1b, respectively. The values of λmax for the systems of two and three Ag/TMA/TC particles are, respectively, 444 and 448.5 nm. magnetic-field energy density w =

The above additional peak in the absorption spectra of systems consisting of two or three hybrid organometallic Ag/TMA/TC particles is thus an important characteristic of their optical properties (compared to

A different situation is observed for systems composed of identical hybrid Au/TMA/PIC nanoparticles with a gold nucleus and an outer PIC-dye J-aggregate shell. In this case, the positions of the peaks of plasmon resonance in a particle’s gold nucleus and the exciton peak in the J-aggregate shell are, respectively, pl = 521 and λ0 = 582.1 nm, with the spectral disλ max tance between these peaks being Δλ = 61.1 nm, a value on the same order as in the system considered above and consisting of three-layer Ag/TMA/TC particles. Our calculations for the cross sections of photoabsorption by the system of two Au/TMA/PIC particles for different distances L between the centers of the spheres nevertheless show there is no additional (compared to a single Au/TMA/PIC sphere) spectral peak for either of the two possible mutually orthogonal incident light polarizations (see, e.g., Fig. 6 for L = 25 nm). Comparing the shapes of curves 1 and 2 in Fig. 6, we also conclude that the dependence of the cross section of light absorption by the system of two hybrid Au/TMA/PIC particles on light wavelength λ generally yields the same spectral dependence for an isolated single sphere. This is most likely explained by the effect of the near-field coupling between a localized plasmon in the metallic nucleus of the concentric Au/TMA/PIC system and a Frenkel exciton in its

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outer shell predominating over the weaker (in this case) near-field electromagnetic coupling of separate particles that constitute the system of two Au/TMA/PIC spheres. In contrast to a system of two (or three) Ag/TMA/TC spheres, this phenomenon is thus masked by a stronger effect for the system of Au/TMA/PIC particles. CONCLUSIONS (1) Our calculations and analysis of their results show that in addition to the plasmon-resonance peak caused by the silver nucleus of a hybrid Ag/TMA/TC particle, and the peak that corresponds to a Frenkel exciton in the particle’s J-aggregate shell, the absorption spectra of the studied organometallic systems contain an additional peak that results from the electromagnetic coupling between two or three particles in the system. A key role in the emergence of this peak is played by the presence of the outer J-aggregate shell in

Fig. 6. Comparison of the spectral dependences of the light absorption cross sections obtained in this work for a system that consists of two three-layer organometallic Au/TMA/PIC spheres (curve 1) with the same results from calculations for a single three-layer Au/TMA/PIC sphere (curve 2), two bare gold spheres (curve 3), and two gold Au/TMA spheres coated with an organic ТМА layer (curve 4). All results were obtained for light polarized along the Z-axis. The geometrical parameters of the system were L = 25,  r = 7.5, h1 = 1.5, and h2 = 3 nm.

the particles that constitute the examined systems. The height of this peak was shown to diminish as the particles move apart, an effect explained by the near-field electromagnetic interaction rapidly decaying with the distance between the particles. (2) In studying the pattern of spatial field distributions inside the considered systems of Ag/TMA/TC nanoparticles, it was established that at the wavelength that corresponds to the maximum of the additional peak, the field is strongly localized in the domain between the particles. It was also shown that increasing number of particles in the system from two to three widens the total light-absorption cross section. (3) It was found that the type of interaction between light and nanoparticles in the system depends largely on the polarization of incident radiation with respect to the directions that correspond to particle ordering. For example, it was shown that for the light polarization directed perpendicular to the axis of the system, varying the distance between the nanoparticles of the particles affects the absorption cross sections only slightly. (4) An important element of this work was establishing that the intensities and widths of spectral peaks, along with their total number in a light absorption spectrum, are determined not only by the transition-oscillator strength in the dye J-band, the radius of a particle’s nucleus, and the thicknesses of the outer

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and intermediate shells; they also depend largely on the spectral distance ∆λ between the molecular Jaggregate absorption-band center and the position of the peak of plasmon resonance in a hybrid particle’s nucleus. It was established in particular that due to electromagnetic coupling, there are no new additional peaks in the light absorption spectra of systems consisting of two and three organometallic particles if the wavelengths in the relevant isolated-particles absorption spectra that correspond to the peak of plasmon resonance in the metallic nucleus and the absorptionband center of Frenkel exciton in the dye J-aggregate shell are close to one another. This follows from our calculations for systems composed of two and three Au/TMA/PIC hybrid particles with a gold nucleus and a PIC dye J-aggregate shell. ACKNOWLEDGMENTS This work was supported by the Russian Foundation for Basic Research, project no. 15-02-07777. REFERENCES 1. Vashchenko, A.A., Lebedev, V.S., Vitukhnovskii, A.G., Vasiliev, R.B., and Samatov, I.G., JETP Lett., 2012, vol. 96, no. 2, p. 113. 2. Shirasaki, Y., Supran, G.J., Bawendi, M.G., and Bulović, V., Nat. Photonics, 2013, vol. 7, p. 13. 3. Vitukhnovsky, A.G., Lebedev, V.S., Selyukov, A.S., et al., Chem. Phys. Lett., 2015, vol. 619, p. 185. 4. Guo, C., Lin, Y.-H., Witman, M.D., et al., Nano Lett., 2013, vol. 13, no. 6, p. 2957. 5. Chang, L.-Y., Lunt, R.R., Brown, P.R., et al., Nano Lett., 2013, vol. 13, p. 994. 6. Ma, R., Oulton, R.F., Sorger, V.J., and Zhang, X., Laser Photonics Rev., 2012, vol. 7, no. 1, p. 1. 7. Khurgin, J.B. and Sun, G., Nat. Photonics, 2014, vol. 8, p. 468. 8. Naber, A., Molenda, D., Fischer, U.C., et al., Phys. Rev. Lett., 2002, vol. 89, no. 21, p. 210801. 9. Kuznetsova, T.I. and Lebedev, V.S., Quantum Electron., 2002, vol. 32, no. 8, p. 727. 10. Yatsui, T., Isumi, K., Kourogi, M., and Ohtsu, M., Appl. Phys. Lett., 2002, vol. 80, no. 13, p. 2257. 11. Kuznetsova, T.I. and Lebedev, V.S., JETP Lett., 2004, vol. 79, no. 2, p. 62. 12. Kuznetsova, T.I. and Lebedev, V.S., Phys. Rev. B, 2004, vol. 70, no. 3, p. 035107. 13. Kuznetsova, T.I. and Lebedev, V.S., Phys. Rev. E, 2008, vol. 78, no. 1, p. 016607. 14. Gramotnev, D.K. and Bozhevolnyi, S.I., Nat. Photonics, 2014, vol. 8, p. 13.

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