MODELING OF OPTICAL PROPERTIES OF HYBRID METAL-ORGANIC NANOSTRUCTURES

To model spectral characteristics of hybrid metal-organic nanostructures, the extended Mie theory was used, which makes it possible to calculate the extinction efficiency factor (Qext) and the scattering efficiency factor in the near zone (QNF) of two-layer spherical particles placed in an absorbing matrix. Two-layer plasmon nanospheres consisting of a metallic core (Ag, Cu) coated with dielectric shells and located into the copper phthalocyanine (CuPc) matrix were considered. The influence of dielectric shell thickness and refractive index on the characteristics of the surface plasmon resonance of absorption (SPRA) was studied. The possibility of the SPRA band tuning by changing the optical and geometrical parameters of dielectric shells was shown. It was established that dielectric shells allow to shift the surface plasmon resonance band of plasmonic nanoparticles absorption both to shortand long-wavelength spectral range depending on the relation between shell and matrix refractive indexes.


Introduction
Hybrid nanostructures which include both plasmonic and organic components are now under intensive investigation because of their great perspectives for the development and creation of effective modern nanophotonics, nanoplasmonics, and nanoelectronics devices [1,2]. Among hybrid nanostructures there are ultradisperse plasmonic nanocomposites that consist of metal-containing nanoparticles embedded in a matrix of organic semiconductors. The unique properties of plasmonic nanoparticles are connected with the surface plasmon resonance of absorption (SPRA) and with a strong increase of electromagnetic fields near the plasmonic nanoparticle surface in this spectral region. Optical properties of densely packed arrays of plasmonic nanoparticles depend on interparticle electrodynamic coupling associated with near-field scattering and coherent reirradiation by particles of each other. The extent of the near-field interparticle coupling is connected with the spectral position of the SPRA maxima and may be regulated by a special choice of a metal nanoparticle material and concentration as well as their morphological parameters such as nanoparticle size, shape, and its internal structure. The promising way to control the internal structure of plasmonic nanoparticles and in such way the SPRA spectra and the near-field scattering efficiency is an application of so-called two-layer nanoparticles with a metal core and a dielectric shell (M@D). Modeling and investigation of the optical properties of the M@D plasmonic nanoparticles was made based on the example of a spherical silver or copper core covered by a dielectric shell and embedded into a matrix of copper phthalocyanine.

Method
To model the spectral characteristics of such nanostructures, the extended Mie theory was used, which made it possible to calculate the extinction efficiency factor (Qext) and the scattering efficiency factor in the near zone (QNF) of two-layer spherical particles placed in an absorbing matrix [3,4]: ( 1) i ext n n n n n n n n n n n n n n n n n i r r Here 0 is the wavelength of the incident radiation, m = mr -imi is complex refractive index of the matrix, an, bn -Mie coefficients, a -particle radius, . Riccati-Bessel functions and their derivatives ( n  , n  , n  , n  ), as the spherical Hankel function of the first kind of order hn depend on the diffraction parameter  = 2a/0. In the case of two-layer spherical particles, the Mie coefficients are functions of the complex refractive indices of the nucleus and shell, the diffraction parameters of the particle as a whole and its nucleus.
The Qext value determines the attenuation of incident light beam intensity caused by the absorption in the particle and scattering on it. The QNF factor characterizes an increase in the intensity of the field along the surface of a sphere of radius R when nanoparticles are introduced into the center of this sphere.

Results
The spectral dependences of Qext and QNF factors for two-layer plasmon nanospheres consisting of a metallic core (Ag, Cu) coated with a dielectric shell, placed in the organic semiconductor matrix of copper phthalocyanine (CuPc) are shown in Fig. 1-3. The near-field scattering efficiency factor was calculated for R = R2, where R2 is an external radius of a two-layer nanosphere. The Ag and Cu optical constants, used at the calculations, are given in [5]. Fig. 1. Spectral dependence of the extinction efficiency factor (a) and the near-field scattering efficiency factor (b) for silver nanoparticle (curve 1) and two-layer nanospheres with silver core and dielectric shell (curves 2-4) placed in the CuPc matrix. The radius of the silver core R1 = 10 nm, the outer radius of the two-layer sphere R2 = 15 nm.
Refractive index of a dielectric shell n = 1.35, 1.5, 2.0 (curves 2, 3, 4 correspondingly) As can be seen from Fig. 1, the maximum of the SPRA band of a homogeneous silver nanosphere with a radius R1 = 10 nm placed in the CuPc matrix is located near the wavelength of 450 nm. In this spectral region, copper phthalocyanine absorbs insignificantly and its complex refractive index varies from mCuPc = 2 -i 0.12 for λ = 400 nm to mCuPc =1.6 -i 0.02 for λ = 500 nm. The CuPc absorption band maxima is located in the wavelength range of 370, 624, and 690 nm; the value of mCuPc = 1.7 -i 0.06 for λ = 450 nm [3]. As it is known, the presence of a shell on a small metal ball shifts the Frelich frequency, which determines the spectral position of the SPRA band dipole maximum [6].
The comparison of the curves 2-4 shows that at fixed core sizes and shell thicknesses the SPRA spectral shift may depend on the shell refractive index n. Using the Ag sphere nanoparticles in the CuPc matrix as an example, one can see that on covering the Ag core by a dielectric shell with n <1.7 the SPRA band moves to a short-wavelength region relatively to the SPRA band of a homogeneous silver nanosphere (see curves 2, 3). On covering by the dielectric shell with n >1.7, on the other hand, the SPRA band maximum moves to the long-wavelength region of the spectrum (see curve 4). This fact allows to conclude that both the value and the direction of the SPRA band spectral shift depend on the relative refractive index of the dielectric shell into the matrix surrounding the two-layer nanoparticle. Fig. 2 demonstrates the possibility of controlling the value of the spectral shift by changing the thickness of the shell on the metal core. First of all, we note that the maximum of the SPRA band for a homogeneous silver nanosphere R1 = 25 nm is shifted by the wavelength λmax = 480 nm due to the size effects. Herewith, Qext = 12.5, QNF = 320 at the maximum of the SPRA band. The application of quartz shells, for which the refractive index is n ≈ 1.45 in the spectral range 400 nm -600 nm, leads to a short-wave shift λmax, which increases with the quartz shell thickness increasing. As can be seen from Fig. 2, a, the spectral position of the SPRA maximum varies from 470 nm for a shell with a thickness of 5 to 450 nm for a shell with a thickness of 25 nm. For a given R1 = 25 nm of silver nanoparticles placed in CuPc, the available range of variation λmax,due to the changes in the thickness of the quartz shell, is 480-440 nm. The values of Qext and QNF in the maximum of the SPRA band decrease with the quartz shell thickness increase. а b Fig. 2. Spectral dependence of the extinction efficiency factor (a) and the near-field scattering efficiency factor (b) for two-layer Ag @SiO2 nanospheres placed in the CuPc matrix. The radius core R1 = 25 nm, the outer radius of the two-layer sphere R2 = 30 nm (curve 1), 40 nm (curve 2), 50 nm (curve 3) Comparison of the data shown in Fig. 1 and 2 allows us to evaluate the effect of the metal core size on the SPRA band characteristics and the amplification of the scattered field near the two-layer plasmon nanoparticle Ag@SiO2 placed in the CuPc matrix. As it was already noted, the growth of the silver core radius from 10 to 25 nm leads to a long-wave shift of the SPRA band of the homogeneous silver nanosphere from 450 to 480 nm, as well as to the increase in the Qext values in the maximum of the SPRA band (from Qext = 9.3 to Qext = 12.5). It is interesting to note that QNF decreases at the maximum of the SPRA band (from QNF = 800 to QNF = 320). Fig. 3 shows the results of calculations for Cu@SiO2 two-layer nanoparticles placed in the CuPc matrix. Comparison of Fig. 2 and 3 allows to estimate the effect of a plasmonic nanoparticle material on the ability to control the characteristics of their SPRA band by applying dielectric shells to the surface of metal nuclei. Unlike silver, copper has strong interband absorption.
Therefore, surface plasmon resonances in copper nanoparticles are less intense, and the SPRA bands are characterized by a large half-width. Besides, the peculiarities of the dispersion of the Cu and CuPc refractive indices lead to the possibility of the manifestation of two wide overlapping SPRA bands in the spectral range of 400-700 nm, with maxima λmax ≈ 480 nm and λmax ≈ 580 nm. As it can be seen from Fig. 3, when quartz shells are applied to a copper core with R1 = 25 nm, the SPRA bands are even more blurred. At the same time, the maximum attenuation is realized in the region of 460-540 nm. а b Fig. 3. Spectral dependence of the extinction efficiency factor (a) and the near-field scattering efficiency factor (b) for two-layer Cu@SiO2 nanospheres placed in the CuPc matrix. The radius of the copper core R1 = 25 nm, the outer radius of the two-layer sphere R2 = 30 nm (curve 1), 40 nm (curve 2), 50 nm (curve 3)

Conclusion
The results of numerical simulations show that the attenuation spectra of hybrid metal-organic nanostructures, as well as the near field effects at the spectral range of absorption bands of organic component, can be regulated by changing the plasmonic nanoparticle material, their size or shell refractive index and thickness. As one can see, a dielectric shell allows to shift the surface plasmon resonance band of plasmonic nanoparticles absorption both to short-and long-wavelength spectral range depending on the relation between shell and matrix refractive indexes. However, for cases under consideration, the appearance of dielectric shells on the plasmonic core leads to strong decrease of the Qext and QNF values. Besides, the degree of near-field interactions with dense packaging can be regulated by the choice of the matrix in which the nanoparticles are placed.