Journal of Nanomaterials

Volume 2018, Article ID 8540805, 9 pages

https://doi.org/10.1155/2018/8540805

## Optical Conduction Resonance in Self-Assembled Metal Nanoparticle Array-Dielectric Thin Films

Department of Physics, Physical Sciences, and Geology, California State University-Stanislaus, Turlock, CA 95382, USA

Correspondence should be addressed to Liangmin Zhang; ude.natsusc@gnahzl

Received 31 May 2018; Revised 21 September 2018; Accepted 14 November 2018; Published 10 December 2018

Academic Editor: Yogendra Mishra

Copyright © 2018 Liangmin Zhang. 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

Optical conduction resonance- (OCR-) enhanced third-order optical nonlinearity of two dimensional (2D) periodic gold nanoparticle array-dielectric thin films has been investigated. The third-order optical susceptibility of periodic gold nanoparticle array embedded in silica thin film shows ~10^{4} enhancement comparing to gold nanoparticle colloids. The 2D gold nanoparticle arrays were synthesized by using the electrostatic self-assembly (ESA) technique. During the fabrication process, the positively or negatively functionalized gold nanoparticles are automatically self-aligned to establish a 2D array with a very small interparticle spacing due to the polymer shell on the metal particles. Then, a monolayer of silica can be coated on the top of the 2D metal nanoparticle array. This type of 2D gold nanoparticle array-dielectric thin films has high volume fraction of gold nanoparticles. According to the extended Maxwell-Garnett theory, this kind of films can exhibit OCR. The OCR frequency can be tuned from visible to mid-infrared by controlling the gold nanoparticle volume fraction. During OCR, the real part of the composite dielectric constant is zero to make the induced electromagnetic waves in gold nanoparticles to couple effectively within the film. The open-aperture z-scan technique is used to measure the nonlinear optical properties of the ESA films.

#### 1. Introduction

Gold (Au) nanoparticles and clusters are known to possess a fast and extremely large nonlinear optical susceptibility (third-order susceptibility of can be as much as 10^{6} times larger than that of the standard reference of CS_{2}) [1, 2]. Although linear optical properties of small metal particles and metal colloids have been studied for at least a century based on Mie and Maxwell-Garnett (MG) theories [3–5], because pure metal thin films have large optical attenuation constants and do not normally transmit optical radiation, embedding metal nanoparticles in a dielectric matrix to provide a smart way to investigate the nonlinear optical properties is currently an intensive research area. The experimental investigation of nonlinear optical phenomena in Au nanoparticle-incorporated systems started in the 1980s [6–8], most of the research work is concentrated on low metal particle volume fraction. After Richard and coworkers performed the first measurement of the nonlinear optical response of metal colloids in 1985 [6], subsequently, in the last three decades, numerous other research work has contributed to our understanding of such composites, in which the concentration of metal particles is usually very low (~10^{−6}–10^{−5} in volume fraction). To my knowledge, only quite a small volume of research has been directed toward the composites with high volume fraction of metal nanoparticles [9–11]. In particular, few experimental investigations concentrated on the OCR-enhanced nonlinear optical susceptibilities have been performed. After the year 2000, giant enhancement (up to 10^{10}–10^{15}) of optical susceptibility in metal nanocomposites consisting of metal nanoparticles and dielectrics has been reported [12–16]. This has led to a resurgence of activities both in the design of plasmon resonance-based materials and the understanding of fundamental mechanisms [17–25]. Although some questions on the exact origin of the enhanced nonlinear optical susceptibility still remain [20, 26], it is generally agreed that closely ordered periodic metal nanostructures and aggregated nanometal clusters can provide a large local-field enhancement because of small interparticle spacing and collective oscillation of conduction electron gas [12–15] that is called OCR. The OCR phenomenon in high-volume Au particle systems has been theoretically predicted in the 1970s [27, 28]. Microscopically, when light is incident on the system, the free electrons in metal nanoparticles are driven by a periodic field. The free electrons respond to the periodic local field, sloshing back and forth within the volume of the nanoparticles. This is actually a periodic conduction current within the particles causing a periodic polarization field around the particles—both periods being equal to that of the incident radiation. At a certain frequency the phases of the conduction currents in all the particles become nearly equal, resulting in a strong oscillation field, which enhances the local field. The collective resonance of photoconductivity occurs at this optical frequency. This resonance is not the normal free-electron plasmon resonance [27, 28]. Instead, at the OCR frequencies, the photoconductivity of the system is maximized. Only at a very low concentration of metal nanoparticles, the OCR and surface plasmon resonance (SPR) occur at the same frequency [27, 28]. As far as I know, the ion implantation laser ablation [29], electron beam deposition [30], and sputtering techniques are commonly used to fabricate metal nanoparticle-dielectric thin films with high volume fraction of metal nanoparticles. This work reports using the electrostatic self-assembly (ESA) technique to fabricate two-dimensional (2D) Au nanoparticle array-dielectric thin films containing high volume fraction of Au nanoparticles to investigate this type of resonance through theoretical calculations and experimental characterizations. In the theory section, I will first review some fundamental theoretical work and show the computed results based on the fundamental work. In the sample preparation section, I will briefly present the sample fabrication process. In the characterization section, the measured results of third-order susceptibility from the thin films containing high-volume Au particles will be shown.

#### 2. Theory

In the 1970s, Marton and Lemon developed the MG theory to explain several resonance features in aggregated metal systems and metal-dielectric thin films with high volume fraction of metal nanoparticles [27, 28]. In addition to bulk plasmon and SPRs, this model predicts that there is OCR in the system with a high volume fraction of metal nanoparticles. If metal nanoparticles are much smaller than the wavelength of light and they can be approximately treated as spheres, optical properties of the dielectric-metal nanoparticle system may be described in terms of the refractive index of the dielectric, the frequency-dependent complex dielectric constant of the metal particle, and the volume fraction of the metal by the MG theory where is the complex dielectric constant for the composite system, is the imaginary unit, and is the volume fraction of metal nanoparticles. Manipulating equation (1) and equating the real and imaginary parts, one gets

In order to obtain the complete resonance frequency dependence on , one needs to examine the optical properties of the system at a frequency of . Let us assume that the dielectric constant of the metal nanoparticles can be described by the Drude theory as where is the plasma frequency of the free electrons. , , and are the element charge, the number density, and the effective mass of the conduction electrons, respectively.

##### 2.1. Optical Conduction Resonance

Following the definition of conductivity, the conductivity of the system can be written as where is the permittivity of vacuum. For the OCR frequency, one should find the maximum value of . Substituting and from equations (4) and (5) and taking we can find that one of the solutions is which corresponds to the OCR frequency [27, 28]. One can see this frequency depends on the metal particle volume fraction . The computed results are shown in Figure 1. If we substitute from equation (8) into equation (2), after manipulating, one can get . Since is related to the phase change of a propagating electromagnetic wave, this is an important factor to recognize the OCR phenomenon. This result will be used in the next sections.