International Journal of Antennas and Propagation

Volume 2015 (2015), Article ID 747580, 6 pages

http://dx.doi.org/10.1155/2015/747580

## Radiation-Induced Correlation between Molecules Nearby Metallic Antenna Array

Department of Physics and Electronics, Osaka Prefecture University, 1-1 Gakuen-cho, Sakai, Osaka 599-8531, Japan

Received 1 June 2015; Accepted 15 September 2015

Academic Editor: Shah N. Burokur

Copyright © 2015 Yoshiki Osaka et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We theoretically investigate optical absorption of molecules embedded nearby metallic antennas by using discrete dipole approximation method. It is found that the spectral peak of the absorption is shifted due to the radiation-induced correlation between the molecules. The most distinguishing feature of our work is to show that the shift is largely enhanced even when the individual molecules couple with localized surface plasmons near the different antennas. Specifically, we first consider the case that two sets of dimeric gold blocks with a spacing of a few nanometers are arranged and reveal that the intensity and spectral peak of the optical absorption strongly depend on the position of the molecules. In addition, when the dimeric blocks and the molecules are periodically arranged, the peak shift is found to increase up to ~1.2 meV (300 GHz). Because the radiation-induced correlation is essential for collective photon emission, our result implies the possibility of plasmon-assisted superfluorescence in designed antenna-molecule complex systems.

#### 1. Introduction

Optically illuminated metallic nanostructure, such as nanoparticles and nanoblocks, generates an extremely localized electric field due to localized surface plasmon resonance (LSPR), by which we can make individual molecules effectively couple with weak light [1]. In addition, the intensity gradient of the localized field becomes steep enough to break long-wavelength approximation and excite dipole-forbidden transitions even in a single molecule [2–4]. These features remind us of sophisticated antenna systems for photons and have attracted increased attention from various scientific fields with a view to efficient reaction fields [5–7]. We have theoretically examined optical responses of antenna-molecule coupled systems and found that, for certain set of parameters, one can efficiently excite only the molecule with the antenna excitation inhibited (energy transparency effect) [8, 9]. Actually, similar effect is experimentally verified using gold nanoantenna system [10]. Such a transparency is explained by considering the quantum interference between the molecular polarization and the plasmon, and it can be applied also to the nonlinear response by a few photons [11].

Besides, it is theoretically proposed that the plasmon-assisted enhancement of light-molecule interaction can be applied to cooperative photoemission such as superradiance and superfluorescence [12, 13]. According to Dicke’s theory, the ensemble of emitters can radiate coherent light after creating a macroscopic dipole moment through the incident and radiation fields [14, 15]. Then, in general, cooperative photoemission requires high-density emitters. Actually, in [12, 13], all the molecules are assumed to lie under the common localized field. However, if the molecules are efficiently excited by using the energy transparency effect, the radiated field from the molecule should be enlarged. Then, such plasmon-assisted radiations can enhance intermolecule correlation.

In the present work, we numerically analyze the optical absorption of molecules near a metallic nanostructure by using discrete dipole approximation (DDA) method [16–18] and investigate the correlation between the molecules. Here it is assumed that the metallic structure consists of dimeric gold nanoblocks with a spacing of a few nanometers. In such a system, the intensity of the localized electric field becomes ~10^{5} times larger than that of the incident light [19]. In addition, the periodic array of the dimeric blocks is also produced experimentally [20, 21]. It is found that the spectral peak of the optical absorption becomes largely shifted even when the molecules couple with different plasmons. We also find that radiation-induced correlation is further enhanced when the dimeric blocks and molecules are periodically arranged. The quantitative study of the intermolecule correlation is essential to explore the cooperative photoemission in the metallic antenna-molecule coupled system and may contribute to designing future photoemission devices.

#### 2. Model and Method

The system under consideration is shown in Figure 1(a). The size of each block is 40 × 40 × 4 nm^{3} and the spacing between the blocks is 2.83 nm. For a clear demonstration, we have considered the blocks to be sufficiently thin so that the mode volume of the localized light fields becomes comparable to the molecular volume. In order to obtain the optical absorption, we solve the discretized integral form of Maxwell’s equation within DDA [16–18]. In this calculation, we divide the whole space containing the metal blocks into small cubic cells, where microscopic quantities such as the electric field and polarization in each cell are averaged. The integral equation is given by where represents the total number of cells and are the cell number. The incident field is linearly polarized along the direction of the orange two-way arrows in Figures 1(b)–1(d), and the polarization in each cell is connected with the total electric field as Here, and are the optical susceptibility and the volume of the th cell, respectively. The free space Green’s function has both transverse and longitudinal electromagnetic components. The term including denotes the self-interaction, which is introduced in order to avoid unphysical divergence and can be calculated analytically as [22, 23] Here the parameter characterizes the size of the unit cell and is the wave number with being the frequency of the incident field.