DOI 10.1515/ntrev-2012-0071 Nanotechnol Rev 2014; 3(2): 177–210 Review Kan Yao and Yongmin Liu* Plasmonic metamaterials Abstract: Plasmonics and metamaterials have attracted much smaller than the wavelength of interest [1–4]. From considerable attention over the past decade, owing to the deep subwavelength feature, the microscopic detail the revolutionary impacts that they bring to both the fun- of each individual structure cannot be resolved by the damental physics and practical applications in multiple electromagnetic waves. We can homogenize the assembly disciplines. Although the two fields initially advanced of these inhomogeneous elements, and assign effective along their individual trajectories in parallel, they started material properties at the macroscopic level [5]. Impor- to interfere with each other when metamaterials reached tantly, the effective material properties are predominantly the optical regime. The dynamic interplay between plas- determined by the size, shape, or structure of the building monics and metamaterials has generated a number of blocks of metamaterials, instead of the intrinsic properties innovative concepts and approaches, which are impossi- of the constituent materials that are used to construct meta- ble with either area alone. This review presents the fun- materials. Using different metamaterial designs (Figure 1), damentals, recent advances, and future perspectives in researchers have been able to engineer the material prop- the emerging field of plasmonic metamaterials, aiming to erties with unprecedented degrees of freedom and have open up new exciting opportunities for nanoscience and demonstrated extremely low-frequency plasmons [6], nanotechnology. artificial magnetism [7], negative refractive index [8], extremely large refractive index [9], and strong chirality Keywords: metamaterials; nanomaterials; nano-optics; [10]. The broad spectrum of material properties offered plasmonics. by metamaterials also propels the rapid development of transformation optics, which enables us to manipulate the flow of electromagnetic waves in almost arbitrary *Corresponding author: Yongmin Liu, Department of Mechanical manners [11–15]. and Industrial Engineering, Northeastern University, Boston, MA 02115, USA; and Department of Electrical and Computer After the proof-of-principle experiments in the Engineering, Northeastern University, Boston, MA 02115, USA, microwave regime, the operation frequency of metama- e-mail: [email protected] terials was quickly pushed to higher frequency from the Kan Yao: Department of Electrical and Computer Engineering, terahertz (THz) to mid-/near-infrared and to visible [16]. Northeastern University, Boston, MA 02115, USA Because most metamaterials are composed of metals, the plasmonic effect of metals plays an important role in optical metamaterials. For example, the magnetic reso- nance frequency of split-ring resonators (SRRs) inversely 1 Introduction scales with the structural dimension when the operation frequency is below ∼100 THz, where the metal can still Since the early 2000s, metamaterials have emerged be treated as a perfect metal with infinite carrier density as a new frontier of science involving physics, mate- and zero carrier velocity [4, 17]. However, this scaling law rial science, engineering, optics, and nanoscience. The breaks down when approaching the optical regime, and primary reason for the extensive interest in metamateri- the model for real metals must be adopted. At optical fre- als lies in the fact that metamaterials have implemented quencies, the kinetic energy of electrons can no longer a wide range of exceptional properties by engineering the be neglected comparing with the magnetic field energy internal physical structures of their building blocks. This driving the current in the loop, which contributes an addi- is distinctly different from natural materials, whose prop- tional term to the inductance of SRRs [18, 19]. This electron erties are primarily determined by the chemical constitu- inertia together with other plasmonic effects changes the ents and bonds. simple scaling law in a complicated way, leading to an ulti- Metamaterials comprise periodically or randomly mate saturation of resonance frequencies of SRRs at about distributed artificial structures with the size and spacing several hundred THz. Therefore, a more comprehensive Brought to you by | Northeastern University Library Authenticated | [email protected] author's copy Download Date | 4/3/14 8:31 PM 178 K. Yao and Y. Liu: Plasmonic metamaterials Figure 1 Schematics of some representative metamaterials. (A) Metallic wires to achieve low-frequency plasmons by reducing the electron density and increasing the effective electron mass. (B) Metallic SRRs to produce artificial magnetism. Around the resonance frequency, there is a strong current ()j circulating along the resonator, resulting in an effective magnetic moment ()m . (C) Chiral metamaterials made of metallic helices. exploration of plasmonic effects in metals will construct a respectively, the dispersion relation of surface plasmons solid foundation to develop optical metamaterials. is written as Plasmonics research focuses on the unique properties ω εε and applications of surface plasmon polaritons (SPPs), k = md (1) z c εε+ quasiparticles arising from the strong interaction between md light and free electrons in metals [20, 21]. At the interface between a semi-infinite metal and a semi-infinite dielec- where ω is the angular frequency, c is the speed of light in tric, SPPs behave as a surface wave that propagates along vacuum, and kz is the wave vector of SPPs along the prop- the interface while exponentially decaying into both the agation direction (z-axis). Figure 2C plots the dispersion dielectric and metal (Figure 2A and B). The dispersion relation for SPPs at the silver-air interface. The dielectric relation of SPPs at a dielectric-metal interface can be constant εm of silver is a frequency-dependent function 2 obtained by solving Maxwell’s equations and applying ω given by the Drude model, εω()=1- p , where proper boundary conditions. Denoting the dielectric con- m ωω()+iγ stant of the metal and the dielectric material as εm and εd, ωp is the bulk plasmon frequency and γ is the damping Figure 2 (A) Illustration of SPPs and oscillation of surface charges at the interface between a dielectric and a metal. (B) The electromag- netic field is maximum at the interface and exponentially decays in the direction perpendicular to the interface, reflecting the bound, nonra- diant nature of SPPs. (C) Dispersion curve (green) for SPPs at the silver-air interface. The red dashed line is the light line in air, and the black dotted line represents the surface plasmon resonant frequency at which Re(εm) = -εd. (D) and (E) Schematics of SPPs supported by a metallic nanowire and a metallic nanoparticle, which are confined in two dimensions and three dimensions, respectively. The false color indicates the electric field of SPPs. Brought to you by | Northeastern University Library Authenticated | [email protected] author's copy Download Date | 4/3/14 8:31 PM K. Yao and Y. Liu: Plasmonic metamaterials 179 frequency. Below the surface plasmon resonance fre- metamaterials. It is beneficial to reflect how the concepts quency ωsp (at which Re(εm) = -εd), the dispersion curve of of metamaterials inspire plasmonics and vice versa, SPPs (green solid line) always lies to the right of the disper- potentially creating more breakthroughs in both areas, sion curve of light in the dielectric medium, kc= εωd /, and in nanotechnology in a broader context. the so-called dielectric light line (red dashed line). The The rest of the review is organized as follows. We will large SPP wave vector results in a small SPP wavelength, first discuss different schemes to realize negative refrac- in comparison with the propagating light in the dielectric tive index and negative refraction at optical frequencies, medium at the same frequency. The wave vector along the followed by the review of recently developed metasur- surface normal direction (x-axis) is imaginary, implying faces that allow us to generalize the refraction and reflec- that SPPs are confined at the interface. Above the surface tion laws by controlling the phase front. Subsequently, plasmon resonance frequency, SPPs become lossy and we will present THz plasmonics and metamaterials based quasi-bound. By further reducing the geometric dimen- on graphene, which exhibit extraordinary tunability via sions, the imposed boundary conditions confine SPPs into electrical gating. One important application of plasmonic two dimensions (metallic nanowires) or three dimensions metamaterials is biomedical sensing, which will be pre- (metallic nanoparticles) at truly nanoscale beyond the sented in Section 5. We will then discuss some self-assem- Abbe diffraction limit (Figure 2D and E). Such localized bly techniques to implement sophisticated plasmonic SPPs are sensitive to the material property, size, and shape metamaterials with fine features and, finally, provide a of the metallic nanostructures. The unique properties of conclusion and a brief perspective on the fascinating area SPPs, that is, subwavelength confinement and strong field of plasmonic metamaterials. enhancement, promise a variety of novel applications in biomedical sensing [22], super-resolution imaging [23], energy harvesting [24], nano manufacturing [25], and next-generation optical circuits [26]. For instance, owing 2 Plasmonic metamaterials to to the