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About this book

This book presents novel and fundamental aspects of metamaterials, which have been overlooked in most previous publications, including chirality, non-reciprocity, and the Dirac-cone formation. It also describes the cutting-edge achievements of experimental studies in the last several years: the development of high-regularity metasurfaces in optical frequencies, high-performance components in the terahertz range, and active, chiral, nonlinear and non-reciprocal metamaterials in the microwave range. Presented here are unique features such as tunable metamaterials based on the discharge plasma, selective thermal emission from plasmonic metasurfaces, and the classical analogue of the electromagnetically induced transparency. These most advanced research achievements are explained in understandable terms by experts in each topic. The descriptions with many practical examples facilitate learning, and not only researchers and experts in this field but also graduate students can read the book without difficulty. The reader finds how these new concepts and new developments are being utilized for practical applications.

Table of Contents


1. Modern Insights into Macroscopic Electromagnetic Fields

A new definition of refractive index is introduced to describe the idea of metamaterials. Their fundamental properties and some of their early investigations are explained. In addition, a basic problem of the macroscopic electromagnetic field is raised regarding the development of metamaterials in optical frequencies.
Kazuaki Sakoda

Metamaterials in Optical Frequencies


Chapter 2. Fabrication Techniques for Three-Dimensional Optical Metamaterials

Metamaterials have attracted much attention because they can provide unexemplified and favorable functionalities and applications in optics and related fields such as negative refractive index, perfect lenses, cloaking, perfect light absorbers, and so on. Because optical metamaterials are artificial sub-wavelength structures, their advancement strongly depends on the development of micro- and nanofabrication techniques. In particular, in spite of the recent progress of these fabrication technologies, the realization of three-dimensional (3D) metamaterials is still one of the big challenges. In this chapter, the recent progress in the fabrication technologies of 3D optical metamaterials is reviewed and discussed.
Takuo Tanaka

Chapter 3. Blackbody Metamaterial Composite Film of Nanoparticle and Polymer

Blackbody metamaterial composite films of nanoparticles and polymer are presented both theoretically and experimentally. Reflectance, transmittance and absorption of the film are calculated on the basis of the Mie theory and Clausius–Mossotti relation, which is equivalent to the Maxwell Garnett theory, at various conditions. We also fabricated the composite metamaterials in which gold nanospherical particles are dispersed in a polyvinylpyrrolidone film. Although the experimental results are in agreement with the calculated spectra in the composite of binary gold nanoparticles with different sizes, the results are somewhat deviated from the calculated spectra of the composite of single-element gold nanoparticles. This may be due to aggregation of the gold nanoparticles at high volume fraction.
Kotaro Kajikawa, Hisashi Karube

Chapter 4. Bottom-up Strategies for Fabricating Meta-atoms via Self-assembly of Polymers and Nanoparticles

In this chapter, bottom-up strategies for fabricating nanoscale ring structures to produce optical metamaterials are described. Co-assemblies of submicrometer-sized spherical polymer particles and metal nanoparticles spontaneously form three-dimensional (3D) nano-ring arrays among polymer particles through self-assembly of metal nanoparticles at the evaporation meniscus. Colloidal assemblies of submicrometer particles, which form 3D periodic structures, are used as templates to assemble metal nanoparticles and block copolymers. Block copolymers form phase-separated structures tens of nanometers in size; thus, metal nanoparticles can be self-assembled into the phase-separated block copolymers. These bottom-up methodologies are useful for fabricating optical metamaterials.
Hiroshi Yabu

Chapter 5. UV-Nanoimprinted Metasurface Thermal Emitters for Infrared CO2 Sensing

A polarization- and angle-independent dual-band metasurface thermal emitter for CO2 sensing was developed. The metasurface was based on a stacked Au/Al2O3/Au structure in which orthogonal rectangular Au patches were alternately arrayed, generating nearly perfect blackbody radiation with emittance as high as 0.98 at 4.26 and 3.95 μm. The metasurface was integrated on a Joule heater fabricated on a SiN membrane so that infrared light is radiated by applying voltage. Subwavelength-sized metasurfaces were manufactured by mass-producible, cost-effective ultraviolet nanoimprint lithography, and the emitter chip was mounted on a standard package compatible with conventional optoelectronic devices. A simple single-layer lift-off process was enabled by employing an organic-solvent-soluble UV resist. The metasurface emitter was applied to a CO2 sensor and was demonstrated to reduce required electric power by 31% as compared with a conventional blackbody emitter, due to the suppressed unnecessary radiation. Results demonstrate that commercialization of metasurface infrared thermal emitters is becoming a reality.
Hideki T. Miyazaki

Metamaterials in THz Frequencies


Chapter 6. Birefringent Metamaterials for THz Optics

Terahertz (THz) region is typically referred to as the frequencies from 100 GHz to 30 THz, which lies between the infrared and microwaves. Since the typical wavelength of the THz wave is hundreds micrometer, we can easily fabricate the metallic structure with the size comparable with its wavelength, and the bulky three-dimensional metamaterial is not huge. Recent development of the ultrafast-pulse-laser technique allowed the generation and detection of the THz electromagnetic pulse, which has led to easy characterization of the medium with the time-domain spectroscopy. Therefore, there are many reports on the metamaterials in the THz frequency region. Metamaterials have been used as the practical optics in the THz region. Many materials are not transparent in this frequency region, so the artificial media based on the periodic structures of the metal such as the metal slit array and metal hole array have been developed. In this chapter, we review the recent advances of the metamaterials in the THz frequency region.
Masaya Nagai

Chapter 7. Development and Applications of Metasurfaces for Terahertz Waves

The development of optical components, in the terahertz frequency range, composed of artificial metallic structures is reviewed, with particular focus on two-dimensional metamaterials (metasurfaces). Various electromagnetic responses and associated fundamental terahertz optical components such as polarizers, wave plates, lenses, and absorbers can be derived even from two-dimensional structures made from common materials. Such terahertz optical components are light and thin, made from readily available materials, and are easy to fabricate owing to the long wavelength of terahertz waves. Both linear and nonlinear optical responses in metamaterials have been developed. The generation of terahertz waves by the nonlinear optical response in silver nanostructures is investigated with a view to designing the nonlinear response of the light and terahertz waves in metamaterials.
Keisuke Takano, Boyong Kang, Yuzuru Tadokoro, Kosaku Kato, Makoto Nakajima, Masanori Hangyo

Chapter 8. Efficient Optical Modulation of Terahertz Metamaterials Utilizing Organic/Inorganic Semiconductor Hybrid Systems

We have utilized highly efficient optical modulation of terahertz (THz) transmission in organic/inorganic semiconductor hybrid system for active control of THz metamaterials. We have investigated highly efficient optical modulation of THz transmission through Si substrate coated with thin layer of organic π-conjugated material, copper phthalocyanine (CuPc) under various continuous-wave (CW) laser light irradiation conditions using THz time-domain spectroscopy. It has been believed that the charge carrier transfer from inorganic semiconductor substrate to π-conjugated material is crucial for efficient optical modulation of THz transmission. We found that the thickness of CuPc layer is a critical parameter to realize high charge carrier density for efficient optical modulation of THz transmission. We also investigated several solution-processable π-conjugated materials instead of CuPc and found that some of them show better modulation efficiency than CuPc. We fabricated a silver split-ring resonator (SRR) array metamaterial on CuPc-coated Si utilizing superfine ink-jet printer and succeeded in obtaining efficient modulation of THz resonant responses of SRR array metamaterials by CW laser light irradiation. Our findings may be utilized to fabricate various types of THz active metamaterials utilizing printing technologies.
Tatsunosuke Matsui, Keisuke Takano, Makoto Nakajima, Masanori Hangyo

Metamaterials in Microwave Frequencies


Chapter 9. Negative Refractive Index Materials Composed of Metal Patterns and the Applications

In this chapter, the aim is to highlight some negative refractive index (NRI) materials composed of metal patterns. First, the dielectric and the magnetic properties of opposite metal patterns are discussed. After the operation principle and the effective permittivity and the permeability are described, a NRI material composed of metal patterns on both sides of dielectric substrates is shown. Secondly, a bulk-type NRI material composed of metal patterns on side face of dielectric prisms is shown. The metal patterns constitute a slot line where a wave is guided. To understand how the structure causes the electric and the magnetic properties, the structure is expressed by the equivalent circuit for the guided modes and, using the circuit, the dispersion characteristics are calculated. A NRI slab lens is made of the material to measure the refocus distributions.
Hiroshi Kubo

Chapter 10. Functional Composites of Discharge Plasmas and Solid Metamaterials

Discharge plasmas are composed of electrons and ions, and their permittivity is dynamic and tunable. Conventional metamaterials are composed of designed functional microstructures of solid materials, and become extraordinary wave media such as negative-permeability materials. The composites of the plasmas and the metamaterials are well mixed to show dynamic properties coming from plasmas and extraordinary outputs based on metamaterials. Here, we describe their theoretical basis and topical features observed in microwave experiments. Beyond properties of tunability, such composite “plasma metamaterials” work well as nonlinear and high-energy-carrier metamaterials, unlike conventional solid-state metamaterials.
Osamu Sakai, Akinori Iwai

Chapter 11. Meta-atoms Emulating Quantum Systems

Electromagnetic property of a medium can be derived from electric and/or magnetic response of constituent atoms or molecules. If an artificial structure called meta-atom is designed to show the same response for the incidence of electromagnetic waves, the assembly of the meta-atoms, or metamaterial, is expected to exhibit the same functionality as that of the atomic medium. In this chapter, we focus on metamaterials mimicking electromagnetically induced transparency (EIT) effect, which has been extensively investigated in atomic systems composed of three-level atoms. We start with an analogy between a two-level atom and a meta-atom with a single resonant mode as a simplest example. Next, we provide rigorous analogy between an atomic medium with three-level atoms showing EIT effects and the metamaterial composed of coupled resonator-based meta-atoms, comparing the atomic response derived from Schrödinger equations of the quantum system and the response of the meta-atom derived from the circuit equations of its circuit model. Based on the coupled resonator model, several examples of metamaterials showing EIT-related effects such as sharp transparency and slow propagation are introduced. We also introduce a tunable metamaterial, which realizes storage of electromagnetic waves in the same way as the atomic EIT system.
Toshihiro Nakanishi, Masao Kitano

Chiral and Non-reciprocal Metamaterials


Chapter 12. Dispersion Relation in Chiral Media: Credibility of Drude–Born–Fedorov Equations

Dispersion relation of electromagnetic field in a chiral medium is discussed from the viewpoint of constitutive equations to be used as a partner of Maxwell equations. The popular form of Drude–Born–Fedorov (DBF) constitutive equations is compared with the one which is a simplified form of the first-principles macroscopic constitutive equations. Both of them describe [A] the dependence of the phase velocity of the EM wave in chiral media on the circular polarizations. However, there arises a decisive difference in the dispersion curve in the resonant region of chiral, left-handed character, as to [B] the ability of reproducing the linear crossing at k = 0, which is derived from the first-principles theory. DBF equations are a phenomenology applicable only to A but not to B.
Kikuo Cho

Chapter 13. Surface Waves of Isotropic Chiral Metamaterials

Phase diagrams of the surface electromagnetic waves in isotropic chiral metamaterials in contact with either the vacuum or metal are presented over a wide range of permittivity, permeability, and chiral parameters. Chirality is found to reduce the localized nature of the surface wave and modify strongly the surface wave phase diagrams. Exact analytical treatment of the chirality is presented which enables us to determine the surface wave phase diagrams and their boundaries completely.
Hiroshi Miyazaki, Yoji Jimba

Chapter 14. Magnetochiral Metamolecules for Microwaves

This chapter overviews magnetochiral (MCh) effects for the X-band microwaves by a single metamolecule consisting of a copper chiral structure and a ferrite rod. The directional birefringence due to the MCh effects is induced at the resonant optical activity frequencies by applying a weak DC magnetic field of 1 mT and increased with the magnetic field. The nonreciprocal differences in refractive indices by the MCh effects are evaluated to be \(10^{-3}\) at 200 mT, which is much larger than that observed in natural chiral molecules at the visible frequencies. Moreover, the enhanced MCh effects can be obtained at ferromagnetic resonance frequencies by the ferrite rod in the metamolecule. The present study paves the way toward the realization of synthetic gauge fields for electromagnetic waves and the emergence of meta material-science using microwave metamaterials. Furthermore, higher frequencies including the visible region are accessible by our concept, in which an interaction between magnetism and chirality in the metamaterials is realized without intrinsic electronic interactions.
Satoshi Tomita, Kei Sawada, Hiroyuki Kurosawa, Tetsuya Ueda

Chapter 15. Dispersion Engineering of Nonreciprocal Metamaterials

Nonreciprocal metamaterials using normally magnetized ferrite microstrip lines are reviewed, showing derivation of formula for the phase-shifting nonreciprocity based on the eigenmode solution in terms of the effective magnetization in ferrite and asymmetric boundary condition for the wave-guiding structures. Dispersion engineering of the nonreciprocity is also discussed for potential applications to leaky wave antennas with wide steering angles and reduced beam squint.
Tetsuya Ueda, Tatsuo Itoh

Novel Aspects


Chapter 16. Photonic Dirac Cones and Relevant Physics

In this chapter, we derive a necessary and sufficient condition for materializing the photonic Dirac cone, which is an isotropic linear dispersion relation, on the \(\varGamma \) point of periodic metamaterials and photonic crystals by the \(\mathbf{k}\cdot \mathbf{p}\) perturbation theory and the group theory. We analyze the coupling between the Dirac-cone modes in metamaterials/photonic crystal slabs and the free-space modes by the Green function method, and prove that the propagation direction of the Dirac-cone modes in the slab can be controlled by the polarization of the incident wave. We further analyze the shapes of dispersion curves of the slab modes in the presence of diffraction loss and show that the group velocity of the slab modes exceeds the light velocity in free space. This problem of superluminal propagation is often found for non-Hermitian systems. Finally, we extend our discussion to electronic waves and prove that we can also materialize the Dirac cone on the \(\varGamma \) point of periodically modulated quantum wells.
Kazuaki Sakoda
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