Metamaterials

There have been increasing interests in metamaterials in the past 10 years in the scientific communities. However, metamaterials are sometimes regarded as left-handed materials or negative refractive index materials by a lot of people including researchers. In fact, the rapid development in this exciting area has shown that metamaterials are far beyond left-handed materials. In this chapter, we will clarify what metamaterial is and report the recent progress on metamaterials. We also summarize the important issues for the development and future of metamaterials, including the optical transformation, effective medium theory for periodic structures, broadband and low-loss metamaterials, rapid design of metamaterials, and potential applications. The impact of computational electromagnetics on metamaterials is briefly discussed.

In the past few years, a rapid progress has been achieved in the subject of optical transformation, which is based on the property of form invariance in Maxwell’s equations. The optical transformation, also termed as transformation optics, allows artificial metamaterials to be tailor-made according to practical needs and desires. In this chapter, we introduce the general theory of optical transformation and discuss the recent development on the optical transformation devices, such as invisibility cloaks, beam bends and splitters, wave-shape transformers, EM concentrators, rotators, antennas. The methodology of optical transformation can also be applied when the sources are included in the transformed space. Such a technique is expected to have further impact on the real-life applications.

In this chapter, we present a general theory of effective media to establish the relationship between the local field responses on metamaterial structure and the macroscopical behaviors for artificial metamaterials composed of periodic resonant structures. By treating the unit cell of the periodic structure as a particle, we average the local field to define the local average permittivity and permeability for different unit structures and derive a general form of discrete Maxwell’s equations in macroscale. We obtain different wave modes in metamaterials including propagation mode, pure plasma mode, and resonant crystal bandgap mode. The distortion in the electromagnetic parameters has been well explained by the derived spatial dispersion model. Thus, the unfamiliar behaviors of metamaterials from the numerical S-parameter retrieval approach is further verified and described. The excellent agreements between the theoretical predictions and the numerical retrieval results indicate that the new defined model and method of analysis fit better to the physical structures and is thereafter a more advanced form of fitting formula for the effective electromagnetic parameters of metamaterials.

Metamaterials are generally composed of sub-wavelength structures with designable geometries. The macroscopic properties of metamaterials are harnessed by engineering the geometric dimensions of the particles. During the past few years, designing metamaterials has become increasingly time-consuming due to the growing complexity of their electromagnetic properties and the complexity has been spurred by the arising interest in generating inhomogeneous and anisotropic metamaterials. Motivated by accelerating the design process for metamaterials with excellent accuracy, rapid design for metamaterials is introduced in this chapter. This method is based on full-wave simulation, S-parameter retrieval technique, and the effective medium theory for metamaterials. The rapid design algorithm for metamaterials is widely applicable to all particles with or without resonances from microwave to optical regime. Its efficiency is validated and demonstrated by a few examples.

Loss and bandwidth have been major problems that limit the potential applications on metamaterials for a long time. To bring the ultimate opportunity to metamaterials, we analyze and discuss, in this chapter, another type of metamaterials that perform at low loss and broad bandwidth. Although the range of structures is limited to those having only electric response, with an electric permittivity always equal to or greater than unity, there are still numerous metamaterial design possibilities enabled by leveraging the non-resonant elements. For example, a gradient, impedance matching layer can be added that drastically reduces the return loss of the optical elements, making them essentially reflectionless and lossless. In microwave experiments, we demonstrate the broadband design concepts with a gradient-index lens and a beam-steering element, both of which are confirmed to operate over the entire X-band (roughly 8–12 GHz) frequency spectrum.

In this chapter, we will discuss the approach of utilizing transformation optic approach and metamaterial technology to construct various cloaking devices in experiment. We take the advantage of rapid design approach to demonstrate the reduced cloaking device in free space. Then we discuss the next-generation cloaking device of broadband and low-loss feature. The experiment at microwave verifies the broadband complex cloaking design.

A radially dependent dispersive finite-difference time-domain (FDTD) method is proposed to simulate electromagnetic cloaking devices. The Drude dispersion model is applied to model the electromagnetic characteristics of the cloaking medium. Both lossless and lossy cloaking materials are examined and their operating bandwidth investigated. It is demonstrated that the perfect “invisibility” of electromagnetic cloaks is only available for lossless metamaterials and within an extremely narrow frequency band. Spherical cloaks are simulated and investigated with a parallel dispersive FDTD technique. Finally, ground-plane cloaking devices are examined and analyzed with non-orthogonal and orthogonal FDTD methods.

In this chapter, I will discuss the image focusing, rotation, lateral shift, as well as the image magnification with sub-wavelength resolutions through differently designed structures of compensated anisotropic metamaterials. The verifications of all the proposed structures by full wave electromagnetic simulations will be demonstrated, as well as the experimental proof of imaging with sub-wavelength resolution through a compensated bilayer lens realized by TL metamaterials. Utilizing the proposed structures, planar optical image of sub-wavelength objects can be magnified to wavelength scale allowing for further optical processing of the image by conventional optics.

We investigate the dynamical characteristics of metamaterial systems, such as the temporal coherence gain of superlens, the causality limitation on the ideal cloaking systems, the relaxation process and essential elements in the dispersive cloaking systems, and extending the working frequency range of cloaking systems. The point of our study is the physical dispersive properties of meta-materials, which are well known to be intrinsically strongly dispersive. With physical dispersion, new physical pictures could be obtained for the waves propagating inside metamaterial, such as the “group retarded time” for waves inside superlens and cloak, the causality limitation on real metamaterial systems, and the essential elements for design optimization. So we believe the dynamical study of meta-materials will be an important direction for further research. All theoretical derivations and conclusions are demonstrated by powerful finite-difference time-domain simulations.

We review our effort in understanding the rich electric, magnetic, and plasmonic properties of photonic metamaterials based on a planar fractal geometry. We employed both experiments and finite-difference time-domain simulations to study the electromagnetic properties of such systems and established effective medium models to characterize these complex structures. These fractal photonic metamaterials are shown to exhibit subwavelength and multiband functionalities with many interesting potential applications.

Magnetic metamaterials consist of magnetic resonators smaller in size than their excitation wavelengths. Their unique electromagnetic properties were characterized by the effective media theory at the early stage. However, the effective media model does not take into account the interactions between magnetic elements; thus, the effective properties of bulk metamaterials are the result of the “averaged effect” of many uncoupled resonators. In recent years, it has been shown that the interaction between magnetic resonators could lead to some novel phenomena and interesting applications that do not exist in conventional uncoupled metamaterials. In this chapter, we will give a review of recent developments in magnetic plasmonics arising from the coupling effect in metamaterials. For the system composed of several identical magnetic resonators, the coupling between these units produces multiple discrete resonance modes due to hybridization. In the case of a system comprising an infinite number of magnetic elements, these multiple discrete resonances can be extended to form a continuous frequency band by strong coupling. This kind of broadband and tunable magnetic metamaterial may have interesting applications. Many novel metamaterials and nanophotonic devices could be developed from coupled resonator systems in the future.

We describe in this chapter development of plasmonic optical antennas for light concentration and near-field enhancement. A set of bow tie nanoantennas are fabricated and characterized with optical and electron excitation methods. Optical spectroscopy of these subwavelength antennas displays pronounced extinction peaks at resonant wavelength, showing total extinction cross sections as much as 10 times of their physical dimensions. On the other hand, coherent excitation of the bow tie antennas allows tuning the peak wavelength of the scattered light by changing the periodicity. Under dark-field microscopy, we observed the scattered waves from arrays of different bow tie antennas in complete visible spectrum. The local resonant modes of the bow tie antennas are also probed by focused electrons. Such cathodoluminescence spectroscopy reveals the fine details of enhanced field on the optical nanoantennas at resolution down to 20 nm. Finally, we show examples of surface-enhanced Raman spectroscopy on the nanoantennas. Effective designs based on local enhancement and radiation engineering of the plasmonic optical antennas would promise revolutionary changes in highly compact and integrated photonics for photon energy conversion, adaptive sensing, and image processing.

In this chapter, a fast solver, i.e., adaptive integral method (AIM) which is based on hybrid volume–surface integral equation, is utilized in the numerical simulation of electromagnetic scattering from composite left-handed materials (LHM) such as split-ring resonators (SRR) with rods/wires. The volume electric field integral equation (EFIE) is applied to the dielectric region of this LHM, and the surface EFIE is applied on the conducting surface. The method of moments (MoM) is used to discretize the integral equation into a matrix solution and AIM is employed to reduce the memory requirement and CPU time for the matrix solution. Numerical results and computational complexity analysis have shown that the AIM solver can significantly reduce the computational cost while maintaining a good accuracy. Inspired by the periodicity of SRR, the ASED-AIM, a new adaptive integral approach based on accurate sub-entire-domain method, has been proposed to solve the electromagnetic scattering by large-scale finite periodic arrays, especially the LHM structures like SRR. Several results are shown to demonstrate the efficiency of the method in solving periodic structures. Additionally, further computational time saving scheme for calculating the near-zone interaction matrix has been proposed. Both 2-D and 3-D periodic structures can be solved by this fast solver with impressive efficiency and accuracy. In the last section of this chapter, a novel rectangular patch antenna was specifically designed using planar-patterned LHM concepts. This new antenna has demonstrated to have left-handed characteristics. It is shown to have great impact on the antenna performance enhancement in terms of the bandwidth significantly broadened and also in terms of high efficiency, low loss, and low VSWR. A good agreement is achieved between the simulation and measured results. This new antenna designed has strong radiation in the horizontal direction within the entire working band, which is desirable for some special applications.

In this chapter some experiments and applications of metamaterials in the microwave regime have been presented. Although metamaterials are composed of structures with finite periodicity, they can still be regarded as effective medium when the periodicity is far smaller than the wavelength. We discuss some interesting experiments such as the tunneling structure and the partial focusing phenomenon and investigate several applications like gradient index circuit and the Luneberg lens antenna. The simulation and experimental results show that metamaterials may have great potentials in the design of microwave devices and antennas.

We introduce a novel left-handed (LH) transmission line (TL), which is based on a structure of identical symmetrical lattice type. While all the LH-TLs reported previously are of high pass, the present LH-TL has a wide left-handed low-pass band. Compared with a conventional right-handed transmission line, this LH-TL has a phase shift difference of 180° independent of the frequency. We also analyze the effect of a non-ideal component in a practical case, i.e., when the inductance of the shorted line in the lattice section cannot be neglected. The dispersion relations between the practical case and the ideal case are given and compared. It is shown that the introduction of the inductance of the shorted line will not change the left-handedness and low-pass property of the LH-TL, but make the phase response vary slightly. In the application example of broadband 180° hybrid ring, the constant-phase-shift property of the proposed LH-TL is utilized. The broadband hybrid ring is shown to have a very high isolation and about 42% bandwidth ratio.