ABSTRACT
Electromagnetic metamaterials are artificially constructed composite media that are composed of subwavelength-scale, periodic metallodielectric structures. They have emerged recently as a very promising platform for the manipulation of electromagnetic waves, such as microwaves and terahertz (THz) waves. To date, various exotic phenomena have been demonstrated experimentally as a result of the benefits derived from well-developed, microfabrication techniques. For example, negative indices of refraction as well as ultrahigh refractive indices, both of which are generally unattainable in nature, have been achieved successfully in the THz frequency regime with so-called “THz metamaterials.” Moreover, active control of THz waves, which is regarded as one of the most challenging issues in the field of THz science and technologies, can now be accomplished using THz metamaterials coupled with various active
media, such as conventional semiconductors, two-dimensional electron gas (2DEG) systems, phase transition materials, and carbon nanomaterials, including graphene and nanotubes. In this chapter, we briefly review the historical background, theory, and fabrication methods of THz metamaterials and then discuss recent progress on passive-and active-type THz metamaterials designed for many useful applications at THz frequencies. 10.1 IntroductionDespite the long history of the research on light-matter interactions, similar studies in the terahertz (THz) wave regime have been relatively underdeveloped in fields ranging from the fundamental sciences to practical applications [1]. The main reason for this is the fact that efficient THz sources and detectors have yet to be developed for those kinds of phenomena to be observed reliably. However, in recent years, THz waves have attracted the attention of physicists and material scientists because they offer the possibility of unveiling many important, low-energy physical properties of condensed matters in a noncontact, nondestructive way [2]. For example, the development of THz time domain spectroscopy (THz-TDS) and the quantum cascade laser (QCL) has paved the way for the characterization of a variety of materials as well as the development of many important THz components and devices. However, most naturally existing materials cannot respond efficiently to THz waves, so the development of practical devices to efficiently manipulate THz waves remains still challenging and currently is an important issue in THz research field. A metamaterial is an artificially constructed composite medium designed specifically to have certain desired electromagnetic responses at any frequency range of interest. Historically, the first practical design of such an artificial material was developed by Sir John Pendry, who modeled a metallic wire array with the Drude model, in which a plasma frequency is located in the microwave frequency range [3]. The plasma frequency can be controlled by modifying the geometrical parameters of the metallic wire array. Similarly, artificial magnetic response (i.e., magnetism) can be derived using nonmagnetic conducting structures as the basic
building block [4]. Due to the ability to control both electric and magnetic responses, many interesting phenomena have been observed at microwave frequencies, such as negative indices of refraction. At the same time, many efforts have been made to apply this principle to higher-frequency regimes, such as the THz and visible regimes. Metamaterials designed to operate in the THz frequency regime are of great importance due to their strong THz responses. The desired electromagnetic properties of THz metamaterials can be obtained by tailoring the electric and/or magnetic responses of so-called “meta-atoms,” which are the basic elements of metamaterials. Therefore, in the following sections, the basic concepts of electromagnetism that pertain to metamaterials are reviewed briefly. In addition, the representative fabrication methods for producing various THz metamaterials are addressed. As a specific example, several active-type THz metamaterials that possibly could be used for real-time manipulation of THz waves are discussed briefly, and notable recent works in this area are mentioned. 10.2 Theory of MetamaterialsMeta-atoms generally are made of a conducting material in which the application of an external electromagnetic field causes a surface current to flow. Therefore, the properties of a metamaterial are determined mostly by the geometry of the meta-atom (e.g., arrangement and morphology) rather than the elements that constitute the substance (especially for microwave and THz frequencies). Using innovative designs and arrangements of various resonant meta-atoms, metamaterials can be created that exhibit extraordinary electric and magnetic behaviors that are not likely to occur in nature. A necessary condition for the design of metamaterials is that the size of a unit cell (or the meta-atom) must be substantially smaller than the wavelength of interest so that the metamaterial can be considered as an effective homogeneous medium. Inside this medium, the meta-atom acts as an individual oscillator driven by an applied time-varying electromagnetic field. Therefore, carefully designed subwavelength-scale metallic structures that satisfy
the requirement of effective homogeneity can be used to create new optical properties. When the homogenization condition is satisfied, the electromagnetic properties of metamaterials can be characterized by defining effective optical parameters (e.g., effective permittivity and effective permeability). In the following two subsections, two representative structures of meta-atoms are reviewed that were designed to provide geometrically controllable electric and magnetic properties. 10.2.1 Tailoring Electric Response
To design a metamaterial to provide specific electrical properties, it is essential to understand the electromagnetic response of the basic substance of the metamaterial. Since the usual requirement of metamaterials is that they consist of conductive materials, it is useful to review the electromagnetic properties of metals. The response of a noble metal to the electric field of incident electromagnetic waves is described by its permittivity. Using the Drude model, the dielectric function of metals can be expressed as a function of frequency: e w w w gw
( )= - +
i (10.1)where g is the collision frequency and wp is the plasma frequency,
which is defined as w ep
∫ ne m
(10.2)where n, e, e0, and m are the electron density, elementary charge, vacuum permittivity, and mass of the electron, respectively. The plasma frequency is the natural frequency of a collective oscillation of free electrons. In noble metals, the plasma frequency is located in the UV regime. Among natural materials, it is difficult to identify materials that have plasma frequencies located in the THz or microwave regime. One exceptional example is the outermost part of the earth’s atmosphere, known as the ionosphere, which is partially ionized. In this zone, the electron density is very low, so the plasma frequency is approximately 1 MHz.
