Recent Progress in Terahertz Metasurfaces
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In the past decade, the concept of metasurfaces has gradually dominated the field of metamaterials owing to their fascinating optical properties and simple planar geometries. At terahertz frequencies, the concept has been driven further by the availability of advanced micro-fabrication technologies that deliver sub-micron accuracy, well below the terahertz wavelengths. Furthermore, terahertz spectrometers with high dynamic range and amplitude and phase sensitivity provide valuable information for the study of metasurfaces in general. In this paper, we review recent progress in terahertz metasurfaces mainly in the last 5 years. The first part covers nonuniform metasurfaces that perform beamforming in reflection and transmission. In addition, we briefly overview four different methodologies that can be utilized in realizing high-quality-factor metasurfaces. We also describe two recent approaches to tuning the frequency response of terahertz metasurfaces using graphene as an active medium. Finally, we provide a brief summary and outlook for future developments in this rapidly progressing field.
KeywordsMetasurfaces Beamforming Fano resonance Electrically induced transparency Graphene Tunability
At the dawn of this new century, metamaterials had emerged as a promising scheme for exotic wave manipulation . The scheme promised access to bulk materials with virtually any combination of the effective permittivity and permeability values, including those not available from natural materials. Achieving full control over permittivity and permeability could lead to ground-breaking phenomena and applications such as negative refraction , subdiffraction imaging , and invisibility cloaking . More importantly, the concept of metamaterials was appealing to terahertz technology, for which suitable materials are limited. Although the concept of 3D metamaterials along with those unprecedented applications are very attractive, it poses several technological challenges. Since the concept is established on the resonance mechanism, dissipation loss becomes one great restriction for practical applications, in particular when involving multilayer structures. Gain materials can compensate the loss to a certain extent, but unfortunately such materials are not available at terahertz frequencies. Additionally, fabricating bulk structures must contend with stringent requirements on dielectric-metal arrangement and 3D geometrical tolerances.
In the past, metasurfaces was considered as a building block of metamaterials, since these surfaces were constructed as a simple proof of concept towards more complicated 3D structures. As those challenges of 3D metamaterials have yet to be fully overcome, the concept of metasurfaces itself has gradually evolved into an ultimate aim to wave manipulation. These metasurfaces are appealing from many different aspects. Their planar configuration is amenable to standard lithography techniques, and can readily incorporate tuning materials. Additionally, unlike 3D metamaterials, metasurfaces are fully compatible with integrated platforms. Owing to a relatively short interaction length and relaxed choices of materials, dissipation loss can be very low. As a consequence, a metasurface with multiple resonance modes can be designed for broadband operation. While this metasurface concept largely benefits from the long development of metamaterials, the definitions of effective permittivity and permeability meant for bulky materials become less relevant to the properties of these fully flat structures. The properties of interest are rather amplitude, phase, and polarization responses. Indeed, metasurfaces cannot entirely substitute metamaterials as some applications demand 3D constructions.
This recent evolution from metamaterials to metasurfaces motivates this review article. At terahertz frequencies, nearly 10 years ago, research activities on metamaterials focused on strong electric and magnetic responses in novel resonator designs, bandwidth broadening, frequency-agile operation, and perfect absorption . Lately, we have witnessed a shift in the research activities towards gradient metasurfaces (so-called flat optics), electromagnetically induced transparency (EIT) and Fano resonances, and graphene-based metasurfaces. Specifically, a recent revitalization of reflectarray and transmitarray concepts  via generalized Snells laws  have triggered enormous interest in gradient metasurfaces for beamforming applications. Moreover, Fano-like, EIT [8, 9], and toroidal dipole resonance  concepts have been thoroughly investigated for their potential to achieve high quality-factor (Q-factor) metasurfaces that can be used for plethora of applications such as sensing and slow-light devices [11, 12, 13, 14]. Furthermore, graphene with its unique optical properties has offered a new degree of freedom to enable different kinds of metasurfaces tunability through modifying its Fermi energy [15, 16, 17, 18]. Thus, this review article focuses on the latest progresses in these sub-areas of terahertz metasurfaces, and covers some relevant theories that should be accessible by a broad range of audience working in the terahertz field. The manuscript is organized as follows: Section 2 explains the concept of beamforming and related terahertz implementations in both reflection and transmission modes. In Section 3, we review four different approaches to achieve high Q-factor metasurfaces. Next, Section 4 discusses two approaches that effectively use graphene to tune the response of metasurfaces. Finally, the conclusion and outlook are presented in Section 5.
2 Metasurfaces for Beamforming
2.1 General Concept
Beamforming or wavefront shaping is a process that modifies the spatial phase distribution of free-space propagating waves to create particular beam patterns either in the near-field or far-field. These beam patterns are for example focal spot, deflection, vortices, contoured beams, and holograms. The concept is important to terahertz technology, since it delivers functionalities that are required by a wide range of applications. Particularly, beamforming for high-gain radiation can alleviate free-space path loss, which becomes more severe at shorter wavelengths . In principle, conventional passive components such as lenses and parabolic mirrors can be considered as a type of beamformers, because their curved geometries lead to different path lengths and thus different phase delays. More sophisticated components include phased arrays and leaky-wave antennas [20, 21, 22] that convert guided waves to free-space waves with designable phase profiles.
As an alternative, metasurfaces can realize beamformers by exploiting nonuniform resonant inclusions to impart spatially varying phase delays onto waves incident from free space. As in metamaterials, the spacing between these resonators must remain below a wavelength to avoid diffraction. In this form, nonuniform metasurfaces, so-called flat optics , reconcile well with the concept of transmitarrays and reflectarrays, well known in the microwave community . Nevertheless, the revitalization has led to novel designs and applications, with realizations across the electromagnetic spectrum. In general, these nonuniform metasurfaces possess compactness and a greater degree of freedom in beam control, compared with the conventional optics. They can be designed for polarization diversity and conversion. Existing planar fabrication technology streamlines the fabrication process, while offering sub-micron accuracy that is much needed for terahertz components. The surface can readily incorporate tunable components such as semiconductors and MEMs for active operation. All these benefits promise unprecedented functionalities not achievable with conventional optical components.
A typical design process for these beamforming metasurfaces is as follows. Initially, a set of different resonators are designed to cover the full phase cycle with either maximum transmission or reflection power. To attain this, the complex response of each resonator can be determined from simulation with a uniform resonator array that accounts for coupling with neighboring resonators. Separately, the required phase map for a metasurface can be calculated from either analytical or numerical approaches, depending on the desired radiation pattern. This calculated phase map is then wrapped into the 360-degree phase range and then spatially discretized to comply with the unit cell size. This wrapped and discretized phase distribution can then be readily realized by an array of subwavelength resonators chosen from a lookup table that relates the required phase response to the aforementioned resonator designs. It should be noted that some optimization of this nonuniform arrays might be necessary to mitigate the effect from coupling among different resonators.
2.2 Principle of Beamforming with Metasurfaces
We can further consider Eqs. 1 and 2 over a wide frequency range. If the phase difference between adjacent resonators Δϕ is designed to be constant over a certain bandwidth, we will observe the beam-squint effect where the direction of the outgoing wave becomes strongly frequency-dependent. This effect is not desirable in those applications requiring broadband operation. On the other hand, if Δϕ is a linear function of frequency, then the beam angle will remain fixed. A caveat is that spatial phase wrapping cannot take place at the same location for every frequency within the bandwidth.
2.3 Implementations at Terahertz Frequencies
The phase distribution discussed in Section 2.2 can be realized by using different types of subwavelength resonators. Typically, a complete set of these resonators must cover the 360-degree phase range and must have either maximum transmission (transmitarrays) or reflection (reflectarrays). This subsection overviews some implementations of terahertz metasurfaces, based on different resonator types. This overview does not intend to cover every implementation, but rather some explanatory designs with distinguishable features and functions.
Beamforming with metasurfaces in transmission requires distinctive resonator configurations. Although an electric dipole supported by a single metal layer can invert the phase of an incident electric field by 180 degrees, this results in minimal transmission. In those conventional transmitarrays at microwave and millimeter-wave frequencies, it was proven that at least three stacked layers of metallic resonators are necessary for independent control of a pair of electric and magnetic dipoles [34, 35]. This results in a full phase coverage with high transmission. This approach has been adopted in some terahertz transmitarrays. One numerical study involves two metal layers, each with a metal grid and patches with varying sizes . The simulation shows high transmission amplitude with a limited phase range. In another design, four metallic layers with ring slots were demonstrated to cover a phase cycle with good performance . Owing to a freedom in phase control, an anisostropic unit cell constructed from three metal layers can function as a half-wave plate that alters the sense of rotation for circular polarization. By progressively rotating every cell around its own optical axis, the spatial transmission phase can be controlled for beamforming with 76% efficiency observed in simulation . Apparently, terahertz transmitarrays of this type are not prevalent, most likely due to complexity in multi-layer fabrication.
An alternative design requires only a single metal layer of V-shaped resonators . These resonators sustain two resonance modes in the two orthogonal axes, and the phase can cover one cycle for the transmitted cross-polarization component. Many terahertz implementations for various beam patterns were based on this principle with V-shaped , complementary V-shaped [40, 41], C-shaped [42, 43], and complementary C-shaped  resonators. An example of complementary C-shaped resonators can be seen in Fig. 3c. In an attempt to counteract beam squint, two sets of resonators, namely C-shaped and complementary C-shaped resonators, were designed to operate at two discrete frequencies . The phase gradient for each resonator set is independently, as determined by using Eq. 2 for a fixed beam deflection angle. Nevertheless, in all these cross-polarization designs, the transmission efficiency is about 25% or lower. The efficiency can be improved to above 50% by sandwiching these V-shaped resonators between two layers of polarizers that are orthogonal to each other .
Most of the terahertz metasurfaces for wavefront control are not capable of tuning or beam steering. There are a few examples of tunable terahertz flat optics that are worth mentioning here. In a simplest form, the on/off switching of a transmitted patterned beam has been experimentally achieved by employing a Schottky junction underneath complementary C-shaped resonators  or thermally controlled VO 2 layer backing V-shaped resonators . It has been suggested via simulation that graphene in the form of square patches  or continuous stripes  on a ground plane can be used to achieve a full-cycle tunable phase response. Further to that, a similar graphene resonator reflectarray has been numerically shown to tune to a fixed focal spot in broadband . The application of graphene to terahertz metasurfaces will be expounded in Section 4.
3 High Q-Factor Metasurfaces
3.1 General Concept
Different terahertz applications such as thin-film sensing [51, 52, 53, 54], slow-light devices [55, 56, 57], and narrow-band filters rely on designing high Q-factors metasurfaces [58, 59]. For sensing purposes, high-Q-factor (defined as the ratio of resonance frequency to the full width at half maximum) metasurfaces enable high-sensitivity sample detection via precise measurement of a small resonance shift. Generally speaking, detecting biochemical analytes at a single-molecule level could lead to a new generation of label-free bioanalysis apparatus that will enable high-throughput applications [60, 61, 62, 63]. Moreover, slow-light devices can find applications in delay lines, dispersion compensation, improving light-matter interactions, and enhancing nonlinear effects [64, 65]. Conventional metasurface configurations consist of 2D arrays of sub-wavelength metallic resonators, and high-Q resonance can be achieved by suppressing dissipation and radiation losses. At terahertz frequencies, the losses associated with the dielectric substrates are negligible where high resistivity substrates are used. Moreover, Ohmic loss in metal is also very small. So, we are mainly left with the radiation losses that should be minimized in order to achieve high Q-factor resonances.
Far-field coupling through the diffraction modes of metasurfaces can have a strong impact on the effective response [66, 69, 70]. As such, one of the critical dimension of any metasurface is the periodic lattice constant that can affect far-field results. Hence, the metamaterial arrays have been measured in the far-field and indeed the eigenmodes of the structures are also observed as characteristic transmission minima as shown in Fig. 4b for different lattice periods of gy from 380 to 653 μm . There is a clear trend of resonance narrowing with the increase in the lattice constant. The effect of lattice constant has been thoroughly studied at the LC resonance and it was shown that the first order of diffractive lattice mode can simply be calculated as Pc = λ0/n, where P is the lattice constant, c is the speed of light in free space, λ0 is the wavelength at the resonance frequency, and n is the refractive index of the substrate . The highest Q-factor can be achieved by using a lattice constant that is very close to the above value, but a little bit less in order to avoid operating at the first order of diffraction. On the other hand, in order to evaluate the merit of any proposed scheme to achieve high Q-factor, it is advisable to choose the lattice constant to be much less than the first order of diffraction.
3.2 Approaches to High Q-Factor
4 Graphene-Based Metasurfaces
There has been a great deal of interest in utilizing the unique properties of graphene for various applications. The extraordinary quantum characteristics of graphene, represented by its relativistic massless Dirac-fermion physics [83, 84, 85], have great potential for pioneering applications in high-speed optoelectronics and photodetection [86, 87]. Moreover, the ability to tune the Fermi level, which can be adjusted via an applied gate voltage [88, 89], holds a great potential to develop new switching devices across the electromagnetic spectrum. This capability is highly relevant to metasurfaces that are typically functional within a narrow spectral band due to their resonance nature. By placing graphene sheets in contact with these metasurfaces, it is possible to tune the resonance frequency of the composite by tuning the optical conductivity of graphene. Due to the limited photon energy at the terahertz frequency range, intraband transitions in graphene have been utilized to demonstrate broadband electrical modulation , and patterned graphene structures have been shown to exhibit resonant response [15, 91]. While graphene itself has been used to achieve that, we are more interested in this paper on how graphene can be utilized to achieve tunable metasurfaces.
5 Conclusion and Outlook
In this review article, we have discussed how the field of metamaterials has been dominated by metasurfaces in recent years. This shift to planar structures has lifted many restrictions associated with fabrication and performance of metamaterials. This new perspective of the field has come with new functions and capabilities. For terahertz metasurfaces, we have seen increasing activities in beamforming, high-Q resonance, and graphene-based tunability. Yet, many challenges must be overcome. For beamforming metasurfaces, we can anticipate (i) adaptive beam patterns that can be achieved by incorporating tunable materials and (ii) bandwidth enhancement potentially with multilayer fabrication processes. With regard to the high-Q resonators, more practical applications can be foreseen such as high-throughput sensing of biomolecular and biochemical samples. Additionally, graphene and other novel monolayer materials will be more prominent in active terahertz metasurfaces. We expect that these recent and future contributions in the field will have an impact on terahertz technology that has been gradually migrating from lab-based equipment to practical devices. The concept of metasurfaces will be able to fulfill this goal with high-performance integrated components.
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