Exotic phenomena like negative refractive index and near-zero index were brought into the limelight by Pendry’s work on artificial materials. These materials have their individual scatterer resonant and are generally classified as metamaterials. We start with a brief introduction to such metamaterials, however, the primary focus of this review is on their two-dimensional counterparts called metasurfaces, which are at the forefront of contemporary research. The behaviour of metamaterials and metasurfaces can be analytically explained by the expansion of Floquet modes [1]. It also needs to be mentioned that when the periodicity of these individual scatterers becomes closer in size to the wavelength of operation, higher order propagating Floquet modes need to be taken into account, to accurately describe their behaviour, such structures, therefore are not classified as metamaterials or metasurfaces [1].

It is a widely established fact that when an electromagnetic wave strikes a composite medium, it induces electric and magnetic dipole moments in the inclusions. These dipole moments are closely related to the effective permittivity and permeability of the composite medium. Since the size, density, shape, and orientation of the inclusions can be controlled by the designer, materials with specific electromagnetic response can be synthesized. These artificially designed materials are called metamaterials. When the individual elements are resonant, such materials can possess negative values for both, relative permittivity and permeability. It needs to be emphasized that the negative refractive index is only possible with the resonant individual elements. This is due to the fact that “resonances have the characteristic that their phase response reverses as frequency changes around the resonance” [2]. Such materials are referred to in the literature as double negative media (DNG), left-handed media and backward wave media [3,4,5].

The electromagnetic properties of the metamaterials can be described by using the Lorentz classical theory. In this theory, the electron is treated like a damped harmonic oscillator in an electromagnetic field [6,7]. When the restoring force is negligible, the Lorentz model is reduced to the Drude model. The Drude model allows for the negative values of permittivity and permeability over a wide frequency range. Due to this property, the Drude model is sometimes preferred to than the narrowband Lorentz model for simulations [7].

Metamaterials with resonant individual elements can possess negative relative permittivity and permeability values. These left-handed materials, then according to Snell’s law of refraction, make the refracted angle negative, thus causing the incident and refracted wave to lie on the same side of normal. This phenomenon is called negative refraction. Negative refraction allows the complete control of electromagnetic waves (including light), in all four quadrants of a cartesian plane. Due to this unusual characteristic, metamaterials offer potential applications which would have not been possible by only using the naturally occurring materials [7]. One of the numerous applications of the metamaterials is the phase compensation medium. DNG and positive indexed materials are combined together in such a way that the phase difference across the slab of this medium is zero. By combining double positive and double negative metamaterials, the phase difference can be controlled. It can be shown that it is the ratio of the thicknesses and the refractive index, which cause the phase difference across the medium to be zero and not the total thickness [7]. This shows that the negative index part of the slab compensates for the phase propagation in the positive index part [8]. Another interesting phenomenon which can be observed by combining the positive and negative index materials is the concentrated resonance which occurs at the interface of such two materials [9]. This interface resonance (also known as a surface wave plasmon) can replace the aperture related resonance in a traditional waveguide thus making possible the existence of sub-wavelength thin waveguides. The dispersion relation for such waveguides is also related to the thicknesses ratio and is independent of the total thickness [10,11].

Metamaterials, with a negative refractive index equal to -1, can also be used to make a superlens [12]. A superlens (also called a perfect lens) breaks the limitations imposed on focussing by wave optics (for a traditional lens, an absolute limit on the area for focussing energy, is a square of wavelength). This is due to the fact that the amplitude of the evanescent waves decays exponentially in a naturally occurring medium, whereas DNG materials enhance their amplitude. The structure still obeys the law of conservation of energy as evanescent waves do not carry any energy. It also needs to be noted that even though the refractive index is negative, the characteristic impedance (being the ratio between the permittivity and permeability) is still positive, thus there are no reflections at the interfaces, and no (mismatch) energy is lost during the whole phenomenon [12,13].

Metasurfaces are two-dimensional or surface counterparts of metamaterials. Just like metamaterials, it is possible to characterise their response through their electric and magnetic polarizabilities. They are also referred to in the literature as metafilms [14]. Metamaterials control the propagation of light due to their bespoke permittivity and permeability values; however, they still use the propagation effect to manipulate the electromagnetic waves. This can result in a complicated relatively bulky structure whereas metasurfaces try to manipulate the wave over a single extremely thin layer [15,16]. The two-dimensional nature of metasurfaces, therefore makes them less bulky and offers the possibility of lower loss structures [1]. Due to their 3D nature, it is also difficult to fabricate metamaterials. Metasurfaces offer an extremely promising alternative. Due to their planar structure, metasurfaces can be easily fabricated using planar fabrication tools [17,18]. The planar fabrication process is also very cost-effective in comparison to the manufacturing of the complex 3D metamaterials [19]. Metasurfaces, being two-dimensional materials, can, therefore, be easily integrated into other devices which can make them a salient feature for nanophotonic circuits; this property will also allow them to be a part of “lab on chip” photonics [20].

The negative index of the metamaterials is due to the resonance of the individual meta-atoms. This property makes the metamaterials inherently dispersive, thus the electromagnetic properties of such materials are highly sensitive to the changes in the operating frequency, thus making such materials bandwidth limited. It has been shown in [21] that by using extremely thin metasurfaces with deep sub-wavelength notches in a two-layered fishnet structure, the dispersion characteristics can be engineered. This technique was then used to make a broadband metasurface filter. The (in-band) transmission and (out of band) rejection was achieved by respectively matching and mismatching the impedance of this metasurface (to the free space). The dispersion characteristics were controlled by tailoring the primary (and secondary) magnetic resonances, and the plasma wavelengths for permittivity. Both these properties (of the metasurface) were highly dependent on the design of the sub-wavelength deep notches. The design was optimized by the help of a genetic algorithm. This broadband metasurface also had a very low insertion loss in the transmission band [21]. Due to the variety of advantages offered by metasurfaces over metamaterials, the scientific community has shown a keen recent interest in this area. This has led to rapid development in the underlying physics which govern the behaviour of metasurfaces and their potential applications.

 

References

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