1 Introduction

Metamaterials with engineered periodic unit cells have expanded the boundaries of naturally occurring materials in the field of electromagnetic application since the concept was proposed [1,2,3,4,5,6,7,8,9,10]. Metasurfaces are two-dimensional metamaterials, they have electromagnetic properties that are difficult to achieve in natural materials by designing appropriate microstructure, and selecting appropriate materials [11,12,13,14]. Metasurfaces (or metamaterials) with unique properties have been intensively studied for negative refraction [15,16,17], electromagnetically induced transparency (EIT) [18, 19], and Fano resonance [20,21,22]. As a promising type of structured medium with balanced complexity and performance, metasurfaces attracted widespread interest in the technically important terahertz band in recent years, various narrowband or actively tunable terahertz metasurfaces have been developed [23,24,25,26,27,28,29,30,31]. The strong interaction of metasurface with terahertz radiation overcomes the weak response deficiencies naturally exhibited by conventional materials [32,33,34] and also enables terahertz near-field imaging [35,36,37]. Such optical properties open up the probability for the development of innovative devices [38,39,40,41,42,43].

The emergence of resonance has provided new ways to study the modern physical, and different resonance models are essential elements of modern optoelectronics research [44,45,46,47,48,49,50,51,52,53]. The discovery of Fano-type resonances has provided a new understanding of radiation-matter interactions [54,55,56,57,58,59]. Here we will focus on the unique resonance generated by metasurfaces and its promising applications [60,61,62,63,64]. Theories of Fano-type resonance contributed to the study of devices in radiation-included systems, from nanostructures to radar with various functions. Metasurfaces can precisely modulate the amplitude, phase, and polarization of electromagnetic waves, offering new opportunities for the design of high-performance terahertz devices [47, 65]. Tightly linking of Fano resonance with metasurfaces could lead to even more promising applications. Terahertz technology has attracted much attention because of its value in applications such as wireless communications, spectral detection, and non-destructive imaging.

In this review, we start with the generation and development of Fano resonance, combined with the research progress of terahertz metasurfaces. Then the research progresses of mixed structures of metal, graphene, liquid crystal, and phase change materials are introduced for the Fano metasurfaces with different materials or structures. Finally, the applications of Fano resonators in chemical sensors and biosensors are described, and the development trend and potential applications of Fano resonance in terahertz metasurfaces have been discussed.

2 A review of the theory: from Fano’s to device-adapted

The Fano resonance model was first proposed in quantum physics to account for the scattering line shapes appearing in the inelastic scattering of electrons with helium and later referred to the coupling between discrete and continuous states [21, 66]. Later, Fano resonance was introduced into micro- and nano-photonics, it can be generated by coupling between two optical resonators, and temporal coupled-mode theory was developed in order to better characterize the fundamental mathematical model of Fano resonance. The temporal coupled-mode theory allows a unified description of the properties of the Fano resonance. Various new physical mechanisms such as EIT [67, 68] and the Kerker effect [69] with coupled resonant modes are introduced in metasurfaces for demonstrating and controlling the Fano line-shaped resonances.

2.1 Fano’s theory

The shape of the Fano resonance arises from the interference of the excited continuous state and the discrete state. By breaking the symmetry, an interference discrete resonance can be obtained between the spectrally broad continuous resonance and the narrow continuous resonance, with the mathematical expression Eq. 1, resulting in the asymmetric peaks and valleys spectral profile shown in Fig. 1a. In complex plasmonic nanostructures like metasurface, dipole-radiation coupling and multipole resonance can generate Fano resonances [70].

Fig. 1
figure 1

Schematic of the Fano effect a discrete and continuum phenomenon for Fano effect, b Line shapes of Eq. (1) for different values of q [21]

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According to Fano [21], the asymmetric line shape is represented by the form of:

$$\sigma (\varepsilon ) = \frac{{q^{2} - 1}}{{\varepsilon^{2} + 1}} + \frac{2q\varepsilon }{{\varepsilon^{2} + 1}} + 1 = \frac{{(\varepsilon + q)^{2} }}{{\varepsilon^{2} + 1}}$$
(1)

where ε describes how close the energy is to the resonance level, and Γ denotes the linewidth of the Fano resonance state. q is an indicator of the line shape, known as the Fano parameter, which varies arbitrarily. A series of curves with different q values are plotted in Fig. 1b according to Eq. (1). With a higher q value, the line shape generates a more distinct peak. Notice that the σ(ε) reaches zero at ε = −q and maximum value at ε = 1/q and defined by 1 + q2, therefore flips entirely when considering the case of the limits of q, i.e. q → 0 or q → ∞. At the points, the asymmetric line shape degenerates to a Lorentzian shape. In the opening study of the Fano resonance, the square of q parameter was introduced to be a ratio of probabilities of two atomic state transitions in line: either to the mixed state or the continuum, from the original unperturbed state. And while the atomic system concerned here is specific, and also the q parameter representing the cotangent of the phase shift caused by states interaction is applicable for other systems. For the common physical configuration of this review, the q parameter tunes the resonant by its between-modes phase shift.

2.2 A step to application: typical structures and temporal coupled-mode theory

Mode coupling is the cornerstone of modern photonics, whereby many significant phenomena arise, such as Fano resonance, EIT, the bound state in continuum (BIC), and parity-time symmetry. The most basic coupled system consists of two resonant modes, and strong coupling between the modes can be achieved when the rate of energy exchange between the two is greater than their respective decay rates. The typical configuration of generating Fano resonance in devices can be extracted and presented in Fig. 2a. Such basic models were first brought up and analyzed by Haus [71] and Xu [72], and reviewed by Andrey [73]. The graphics representing waveguides and resonators are the main compositions of a wave-structure interaction system that generates Fano resonance, coupled either directly or by side. The schematic allows port signals to be tuned with resonance by applying any external perturbance, yet sensitive enough due to the nature of Fano resonance. In 1984, Haus introduced the temporal coupled mode theory to analyze multi-port systems [74]. Later, it turned out to be a successful method for analyzing periodic structures with a simplified approach. For metasurfaces, it is significantly helpful, as long as the array of resonant cells holds the prior property, although the theory was first verified in some more compact photonic crystals.

Fig. 2
figure 2

Schematic of the typical resonant structures a Direct coupling and side-coupling [73], b–c A holey dielectric slab as photonic crystal structure radiated by a normal incident wave and the intensity transmission spectrum. The circles are the results from the FDTD simulations. The solid curve is calculation by analytic couple mode theory [75]

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The coupled mode theory is on the basis of a time-dependent deduction, holding the dynamics of mode interaction in resonators. In general, the equations of the wave-structure interaction system take the form of [75]:

$$\frac{da}{{dt}} = (j\omega_{0} - \frac{1}{\tau }\alpha ) + (\left\langle \kappa \right| * )\left| {\sigma_{ + } } \right\rangle \,,\,\left| {s_{ - } } \right\rangle = C\left| {s_{ + } } \right\rangle + a\left| d \right\rangle$$
(2)

where a is the normalized resonant amplitude and |a|2 equals the total energy inside the resonantor. τ is the corresponding lifetime of the frequency with ω0 being the eigenfrequency determined by the actual structure, and j is a positive integer. The wave vectors and coupling coefficients are in the form of Dirac’s bracket notation, among which s+ and s- refer to the incoming and outgoing waves. And respectively, κ and d are the efficiencies of the localizing and radiate process. In addition, C is the direct coupling coefficient standing for the port-to-port scattering and therefore is a unitary and symmetric matrix. In the precondition, if we take the time-reversal condition into consideration, the intensity reflection coefficient R can be extracted. According to Fan et al. [75], in a simple two-port system with a mirror symmetric resonator, R is in the form:

$$R = \frac{{r^{2} (\omega - \omega_{0} )^{2} + t^{2} ({1 \mathord{\left/ {\vphantom {1 \tau }} \right. \kern-0pt} \tau })^{2} \pm 2rt(\omega - \omega_{0} )({1 \mathord{\left/ {\vphantom {1 \tau }} \right. \kern-0pt} \tau })}}{{(\omega - \omega_{0} )^{2} + ({1 \mathord{\left/ {\vphantom {1 \tau }} \right. \kern-0pt} \tau })^{2} }}$$
(3)

Again, the equation generates a Lorentzian line shape when either r or t is zero and a Fano asymmetric line shape otherwise. To verify the universality of the theoretical derivation, Fan et al. compared the intensity transmission spectrum of a holey dielectric slab obtained by the finite-difference time-domain (FDTD) method and coupled mode theory calculation separately (Fig. 2b, c). It turned out that the theory and simulations excellently agree.

2.3 Damping model: a more accurate revision for application

In 2011, Martin et al. [76] pushed the analytical method for Fano resonance even further, by introducing a damping to the equation and considered a general situation of material dispersion characteristic, from dielectric to plasmonic. With such efforts, the results are distinct and explicable when it comes to actual and complex systems with losses. The modified Fano resonance equation is given as:

$$\sigma (\varepsilon ) = \frac{{(\varepsilon + q)^{2} + b}}{{\varepsilon^{2} + 1}}\,,\,b = 4\frac{{\gamma_{d}^{4} q^{2} }}{{\Delta^{2} }}\,,\,\Delta = \pm \frac{{c^{2} (\omega_{d}^{2} - \omega_{s}^{2} )\Gamma_{s} }}{{2\omega_{d}^{2} ((\omega_{d}^{2} - \omega_{s}^{2} )^{2} + \Gamma_{s}^{2} )}}$$
(4)

where b is the damping parameter that arises when losses exist, and Δ is a form of resonant line width where c is also a coupling coefficient in heterogeneous systems. Notice that the corner marks d and s refer to the dark mode and bright mode (i.e. the nonradiative and radiative mode), and γd is the nonradiative loss. Figure 3 shows the schematic of a plasmonic resonator with loss γd and radiated by a flat wide-band wave (Fig. 3a–c, Direct excitation of the continuum medium and excitation of the dark mode through its coupling to the continuum) and a wave with frequency ωs (Fig. 3d–f, the continuum of radiative wave construction by bright modes in plasmonic nanostructures). While revealing the effect on the line shape introduced by damping parameter b, the analysis also showed two ways of generating the Fano effect in wave-structure interaction: the direct excitation of the continuum and the excitation of the dark mode through its coupling to the continuum.

Fig. 3
figure 3

Mechanism of Fano effect take place in a lossy plasmonic resonator in two different way a-c Resonant dark mode with complex resonance frequency ωd + iγd and a flat wide-band radiative wave producing the direct excitation of dark mode to the continuum, d-f Interference between a resonant dark mode and a bright mode with frequency ωs and spectral width Ws. And there is a frequency-dependent phase difference between the two pathways leads to both a destructive and a constructive interference. Reproduced with permission: Copyright 2011, ACS Publishing [76]

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Through these approaches, the quality of the resonant line shape and the coupling principles of the system can be further controlled. A better understanding of resonance through the Fano effects analysis indeed assists in the optimization of structures, such as the size, dielectric environment, coupling setups, etc., to achieve the certain response one requires for any application. Hence Fano resonance is involved in the designing and production of highly sensitive biosensors, medical examination instruments, filters, switches, detectors, and many other sophisticated devices that require high-quality factor (Q-factor), significantly.

3 Fano resonance based on various materials

By describing the principle of Fano resonance above, we know the principle of Fano resonance. At present, many terahertz Fano metasurfaces have been realized and applied. In this section, we will introduce types of terahertz Fano resonance achieved by the composition of different materials.

3.1 Common and noble metals

Since the start of the metasurface, most researchers employed noble metal or plasmonic [77,78,79,80] structures for resonant metasurface as well as for Fano resonance designing. The Fano resonance of these metal structures can realize many functions, such as magnetic field enhancement [81, 82] and modulation [83].

The first observation of Fano resonance in copper's asymmetric split-ring(ASR) array structure was made by Fedotov's group [84], as shown in Fig. 4a. On the ultrathin substrate, Fano resonance is more sensitive than quadrupole mode [85], and the ASR structure determines the strength of Fano resonance. Similarly, in the structure using aluminum broken the symmetry of split ring resonators(SRRs), the conductivity plays an important role in the Fano resonance, and the Q factor can be up to 50 in the case of weak asymmetry [86, 87]. These structures can have a wide range of applications, such as notch filters and narrowband terahertz emitters. The ASR metasurface of Germanium metal supporting Fano resonance can achieve ultra-sensitive resonant terahertz sensing and can sense analytes up to 7 nm thick [88]. The structurally reconfigurable metasurface micro-nano electromechanical systems (MEMS/NEMS) have the unique advantage of actively manipulating the sensitive field in space. Therefore, breaking the symmetry of the out-of-plane structure of the metasurface is also a way to achieve electrically tunable Fano resonance [89], as shown in Fig. 4c.

Fig. 4
figure 4

Terahertz metal-based metasurfaces and graphene metasurfaces a The quality factor of the open ring is a function of the degree of asymmetry in both lossy and lossless substrates. The inset showsthe evolution of narrow resonance at different asymmetry calculated for the lossy case [84], b Dynamically tunable graphene-based metasurface unit structure and electric field transport amplitude spectrum [103] Dynamically tunable graphene-based metasurface unit structure and electric field transport amplitude spectrum c Active tuning in MEMS metasurface. Terahertz spectra are described experimentally and numerically by varying the driving voltage and structural asymmetry [89], d–f The elementary unit cell of symmetric metasurface. The transmission spectrum shows a very wide stop band split by sharp asymmetric resonance features[91], g–h A metasurface consisting of symmetrical circular nanoclusters that can excite Fano resonance and its images of electric and magnetic fields [96], i Graphene-gold hybrid structure of biperiodic array under normal incidence [106]

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In particular, not only the asymmetric structure can realize the Fano resonance, but also the partially symmetric structure [90]. The Fano resonator composed of an array of concentric rings of copper has the characteristic of polarization insensitivity [91], as shown in Fig. 4d–f. For example, shu et al. demonstrated experimentally that Fano resonance could be tuned by changing the geometry and size of the structure [92,93,94].

Array metasurface composed of metal nanospheres can also support Fano resonance [95]. For the first time, Campione's team proposed that magnetic Fano resonance could be achieved on the surface composed of symmetric circular nanoclusters (CNCs) under the oblique incidence of TE polarized plane waves [96], as shown in Fig. 4g, h. Consistent results from full-wave simulations and single dipole approximation evaluations of the metasurface show that the array mode is narrower than the resonance induced by a single CNC, thereby enhancing the electric and magnetic fields, where the magnetic field is distributed over a large area of the nanocluster, while the electric field is mainly concentrated in the gaps between nanoparticles.

3.2 Two dimensional materials

Currently, two-dimensional materials can also be a good solution for achieving Fano resonance due to their unique electrical and optical properties. Terahertz graphene metasurfaces can be used for applications such as biosensing due to their large specific surface area and good adsorption properties [97, 98]. In previous studies, most graphene metasurfaces can be actively tuned to Fano resonance by adjusting the Fermi energy level or gate voltage and doping [99] or achieve higher sensitivity by exhibiting dynamic slow-light behavior through EIT effects [100,101,102]. As shown in Fig. 4b, Tang et al. [103] investigated a graphene split resonator, achieving tunable frequencies and amplitudes by varying the Fermi energy level of the graphene. The sensitivity of the Fano resonance measurement film can reach 2.12139THz/RIU. Similarly, Li's team [104] works on asymmetrically structured graphene terahertz metasurfaces on silicon substrates to achieve active modulation of terahertz with low-power and continuous wave excitation. The effect of Fano resonance is more pronounced at negative bias voltage.

In addition to individual graphene structures, hybrid structures of two-dimensional materials have been [102]applied to achieve Fano resonances [105]. A hybrid graphene-gold symmetric structure to excite Fano resonances at terahertz frequencies was first reported [106] in 2013, as shown in Fig. 4i. The design uses square graphene cells in the center of a square gold frame, and by exploiting the fact that the dipole surface plasmon polaritons(SPP) induced on the graphene dipole SPP is much narrower than that induced on gold to induce asymmetric Fano resonance line shape in the spectrum. Moreover, Ruan et al. [107] used a hybrid graphene/waveguide structure that enabled coupling between the wide resonance of the monolayer graphene and the narrow resonance of the waveguide structural mode to achieve a sharp Fano resonance. By varying the Fermi energy level of graphene, the asymmetric line shape of the Fano resonance can be controlled, measuring the sensitivity in solution water. Overall, the hybrid structure of graphene leads to the emergence of single or multiple Fano resonances that play an important role in the realization of tunable terahertz sensors.

3.3 Liquid crystals

The traditional Fano modulation with two-dimensional functional materials, external bias, and optical pump has a small modulation depth and narrow modulation range. Therefore, it is necessary to develop Fano resonance with a wide band and large modulation depth. Liquid crystal is a phase between liquid and crystal. Therefore, the combination of metasurfaces and liquid crystals has great potential in actively regulating electromagnetic waves [108,109,110,111,112]. The arrangement becomes orderly when energized and chaotic when not, thus exhibiting different physical properties. The large modulation of Fano resonance can be realized by integrating liquid crystal with metasurface[104]. In 2019, Shen's team [113] proposed a terahertz dynamic stealth metasurface integrated by liquid crystals, whose Farno resonance is highly dependent on incident polarization. As shown in Fig. 5a, the Fano resonance is excited when the terahertz wave is incident perpendicular to the gap; when it is polarised parallel, the Fano resonance disappears. Li's group has proposed a tunable sensor based on tunable liquid crystal permeable Fano resonators that can achieve dual tuning of the operating frequency band and sensing range. The purpose of the metasurface can of tuning the tilt angle of the liquid crystal molecules is achieved by adjusting the external bias voltage [104], and realizing a reconfigurable sensor with first-order resonant frequencies of the Fano resonator that can be shifted by 57 GHz and 140 GHz, respectively, as shown in Fig. 5d.

Fig. 5
figure 5

The liquid crystal and hybrid materials achieve terahertz Fano resonance a Liquid crystal realizes Fano dynamic cloaking [113], b–c Transmission spectrum and electric field distribution of terahertz metasurface composed of vanadium dioxide/gold [114], d The transmission spectrum of Fano resonator is realized by liquid crystal with an annular groove structure [104], e–f Cell lattice of metasurface composed of perovskite under terahertz pulse and light pump and its experimental transmission spectra [116], g–h Metasurface array structure and spectral hybridized and experimental transmission spectroscopy by vanadium dioxide/aluminum [115]

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3.4 Hybrid materials

Hybrid materials exhibit reconfigurable responses to external stimuli such as electric and light fields. The unique phase transition characteristics of vanadium dioxide, such as hysteresis and ultrafast dynamics, provide a huge possibility for the study of the terahertz band. The combination of vanadium dioxide and metasurface can provide a new attractive method for the dynamic regulation of terahertz waves. Most scholars combine metals of asymmetric structure with vanadium dioxide. These hybrid systems can support relatively high-quality factor Fano resonance and achieve the modulation of terahertz waves by changing the dielectric constant and conductivity of vanadium dioxide. Wang [114] used an asymmetric vanadium dioxide/gold structure to design a dynamic tuning of the Fano resonance metasurface over a wide range. Figure 5b, c shows the spectrum of vanadium dioxide when the conductivity changes. The excited Fano resonance forms a non-radiative magnetic resonance to enhance the magnetic field between the rods. Zhu and colleagues [115] achieved a frequency-dependent terahertz modulation by combining a metasurface of misaligned Fano structures with a heat-induced insulator–metal transition in vanadium dioxide, as shown in Fig. 5g, h.

Combining inorganic materials with metasurfaces shows excellent performance and is expected to be applied to controllable slow light and other nonlinear terahertz devices. Manjappa et al. [116] also proposed a way to achieve regulated Fano resonance by covering the metasurface with solution-treated perovskite film, as shown in Fig. 5e, f.

In addition to the material structures mentioned above that can achieve Fano resonance, there are a number of other ways in which Fano resonance can also be excited. For example, the use of semi-coated metasurfaces to achieve thin film analysis of various substances in DNA [117]. The 3D Dirac semimetal mode is used to achieve terahertz adjustment [118].

4 Application

There are different operating mechanisms in metasurface-based sensing [119]. In plasmonic structures [77,78,79,80], the resonance linewidth is mainly determined by radiative and nonradiative damping. By suppressing interband damping, the dephasing of plasmon can be reduced and the Q factor can be increased. BIC [120, 121]can also provide a high-quality factor based on the principle of destructive interference of multimode radiation [122,123,124,125]. By breaking the symmetric structure of the cell, the difference in resonance displacement or phase is realized to sense the change in the local environment [126]. EIT enables a narrow band of transparent windows to appear in an opaque spectrum, thus leading to enhanced slow-light and nonlinear effects [68]. EIT realized in metasurfaces systems, is called EIT-like. Usually, EIT-like is realized by the interference of two intrinsic modes, the bright mode and the dark mode [127, 128]. Most implementations of EIT modulation are accomplished through optically or electrically tunable [129,130,131,132,133]. The toroidal dipolar resonator can realize the strongly enhanced electromagnetic field in a small dielectric region [134,135,136]. The toroidal dipolar resonantors [137,138,139,140] can support high-quality Q-factors that can be used in metasurfaces devices [141]. Compared to these sensings, the Fano resonance-based sensing is characterized by a slight refractive index changing that induces sharp changing in scattering from peak to dip, allowing more efficient modulation in sensing applications. Therefore, based on the Fano resonance produced by different structural materials in the terahertz band [142, 143], this section presents some applications and recent trends in Fano resonance, including chemical sensors, biosensors, and optical switches, which have been summarised for comparison in Table 1.

Table 1 Summarize the performance of different kinds of sensors
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4.1 Chemical concentration sensor applications

Because Fano resonance is generated by the interference between multiple oscillators, it has a strong sensitivity to geometric structure or local changes in the outside world. The slight disturbance will cause intense resonance or migration, so it can provide a high-quality factor, and get a clear transmission spectrum. This feature makes Fano resonant metasurfaces a promising material for detecting concentration chemicals [144,145,146].

Recently, Srivastava's team [147] proposed a flexible Fano resonance terahertz sensor in Fig. 6c, d. An ultra-thin, low refractive index polyimide was used as a substrate for the sensor, sensing the analyte from the bottom and top of the metasurface. The edge electric field of the Fano resonance excited by a low index 25 mm thick polyimide metasurface can reach the spatial distribution, and the analyte can be measured from the bottom, thus enabling dual surface sensing. This ultra-thin and low-index sensor design scheme can be extended to different sensing fields according to the application needs.

Fig. 6
figure 6

Realization of terahertz biological and chemical sensors based on Fano resonance a–b Integrated terahertz biosensor schematic and transmission curve [176], c–d Array structure, microscopic image, and Fano resonance shift of double-sided flexible Fano resonance sensor [147], e–g Schematic diagram of a terahertz biosensor for a graphene/Bragg reflector [148]

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The sensor based on the graphene metasurface structure has a broad application prospect in the matter sensing and detection of micro and nano thickness. Highly sensitive terahertz sensors composed of graphene/Bragg reflector composites can simultaneously enable liquid biosensing and gas biosensing. The Tamm plasmons (TPs) mode generated by the graphene and Bragg reflector and the defect mode generated by the symmetric Bragg reflector can excite sharp Fano resonances and can achieve high refractive index sensitivity of over 1000°/RIU[148], as shown in Fig. 6e–g.

All of the above demonstrates the power and excellence of Fano resonant metasurfaces in terahertz spectroscopy for the chemical monitoring of molecules, as well as the avoidance of damage to the molecules being detected.

In addition to the above ways to realize ultra-sensitive sensors, the BIC in the metasurface also plays an essential role in enhancing Fano resonance, thus achieving high sensor sensitivity. Under the study of Chen's team [149], the sensitivity and Q-factor can reach 775.7 GHz/RIU and 1016, respectively. In addition, wang et al. also proposed a sensor based on BIC electric Fano resonant metasurface, which consists of three periodic arranged gold microbars. The Cen team [150] used an asymmetric structure to achieve a high sensitivity of 465.74 GHz/RIU.

4.2 Biomacromolecule sensing applications

Terahertz waves are widely used in biochemical sensing due to their rich material spectrum information as well as their low photon energy. As a result, researchers have proposed a number of Fano-based biochemical sensors.

In 2017, Geng et al. [148] implemented biosensing for the detection of two liver cancer markers using asymmetric open loop stimulated Fano resonance, and the results showed that they matched the simulated values, as shown in Fig. 6a, b. In 2019, Yan and his teammates [151] proposed a sensitive biosensor for the detection of cancer cells in the terahertz band. The EIT-like Fano resonance of this structure only depends on the inherent Drude model loss of metal materials, as shown in Fig. 7a, b, where changes in the refractive index of the extracted analyte result in a redshift of the transparency peak. Therefore, any environmental change in the external medium will lead to changes in spectrum. As a result, the sensor is sensitive to different concentrations of cancer cells. It also offers new ideas for achieving rapid and low-cost cell detection.

Fig. 7
figure 7

Other applications are realized according to Fano resonance a–b Fano resonance unit structure model for monitoring cancer cells and frequency shift curve of the analyte's refractive index [177], c–d Micrograph of terahertz biosensor for detection of glioma cells and micrograph of adhesion of glioma cells to the superstructure surface at different concentrations [132], e–f Schematic diagram of tunable terahertz metasurface structure [144], g–h Schematic of the phototunable THz metasurfaces for discriminating colorectal cells between normal, adenoma and cancer states [151], i Reconfigurable Fano resonance metasurface with dual voltage drive [89]

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EIT is the coupling of light–dark mode resonant states. As a special case of Fano resonance, it can also provide extremely strong sensing capability due to the local enhanced electromagnetic field or modes interference. Eigenmodes that interact weakly with the surroundings become dark modes and can exhibit high-quality factors [152, 153]. Excitation of LC resonances in dark resonant cavities is usually associated with a magnetic dipole response [154, 155]. In contrast, bright-bright modes are based on frequency loss and spacing hybridization, which can also enable biosensing [156]. The improvement of the detection ability of biomacromolecules will help people make great progress in the field of biomedicine. Du group studied the sensing properties of silicon-metal hybrid structures in the terahertz band, In the absence of pump excitation, the THz time-domain signal directly furnishes a high-sensitivity platform for analyzing tiny analytes withoutextra Fourier data transformation, originating from thesensitivity-difference between Lorentz and lattice modes. Once adding an optical pump, the established EIT resonance naturally supports another sensing function due to electric field enhancement, and successfully identified colorectal cells between normal cells and cancer cell states in experiments, as shown in Fig. 7g, h [151], showing the structure of the sensor and the time delay of the experimental transmission spectrum with the pumped probe. Colorectal cells were used as characteristic cells before cancer lesions. In addition, a label-free biosensing method for glioma cell molecular classification has been proposed, which achieves polarization-independent crystal at terahertz frequencies, as shown in Fig. 7c, d. The sensing function is realized using an ultra-material consisting of cut wires and split-ring resonators by strong enhance local field interact with the analytes. The sensor is theoretically sensitive to 496.01 GHz/RIU [132]. Two types of mutant glioma cells and wild-type glioma cells can be directly distinguished experimentally. This technology provides a new way to detect biological substances with greater sensitivity, flexibility, and practicality using terahertz waves. It advances the development of terahertz metasurfaces for detecting large biological molecules by tracking changes in the sensor's transmission spectrum as the analyte's refractive index changes.

4.3 Other applications

The integration of Fano resonant structures with non-linear and phase change materials offers many opportunities for switching [157,158,159] and electro-optical applications. Reconfigurable metasurfaces are a type of metasurface that can be modified using external excitation techniques to alter their properties without changing their geometry. This enables a single device to perform multiple modulation functions and broadens its potential applications [160,161,162,163].

Most metasurfaces are implemented in single input and output states, and general resonance is accomplished by breaking the in-plane symmetries of the structure. However, in 2018, the Manjappa group [89] achieved a multi-input–output (MIO) reconfigurable MEMS Fano resonant metasurface by breaking the symmetry of the out-of-plane structure, as shown in Fig. 7i, demonstrating the MIO state of the asymmetry value controlled Fano metasurface. This MIO state can be observed in the Fano resonance excitation. The far-field characteristics of Fano resonance are expressed as XOR and XNOR operations, while the near-field resonance makes NAND operations possible. Digital logic gates are achieved by using independently controllable electrical inputs and optics in the incoming coupling of the resonant cavity. The introduction of reconfigurable Fano metasurfaces lays the foundation for the realization of programmable and random-access metasurfaces that enhance electro-optical properties across terahertz, infrared, and optical frequencies.

An effective optical switch can also be realized by changing the position of the metal frame of the resonator. In 2021, Wen et al. [164] proposed two tunable terahertz metasurface structures based on the Fano resonance principle, as shown in Fig. 7e, f, which can control the tuning range of the device by moving the metal frame vertically or horizontally. Thus tunable terahertz devices exhibit a strong terahertz switching characteristic dependent on the position of the metal frame.

5 Prospective and conclusion

This paper presents metasurface structures and some typical applications for the realization of terahertz Fano resonance. Among these, terahertz sensors have become a key research direction. Fano resonance can reduce or even completely suppress radiation loss in plasma nanostructures, so it is easy to obtain a high Q factor in this system. In addition, according to the characteristics of different biomolecules, the terahertz metasurfaces are designed to achieve Fano resonance so as to achieve ultra-sensitive biosensing [165,166,167,168]. This has important implications for energy, information, medicine, the environment, and many other fields.

Fano resonance has unique properties that enable the implementation of filters [169, 170], modulators, and waveguides to realize low-loss optical fibers and large-area lasers [171], in addition to the typical applications such as biological and chemical sensors and optical switches described above, as well as a number of other applications. Applications combining Fano resonance and metasurface to broaden the bandwidth have already been realized in the Gigahertz band [172], so Fano resonance may also be used in the terahertz band to achieve high efficiency and ultra-broadband extension of the metasurface. The development of Fano metasurfaces in combination with other materials could provide ideas for achieving some special properties. In addition, by studying the relationship between Fano resonance metasurface and lattice, it is of great significance to realize the terahertz multifunctional resonant device to control the characteristics of electromagnetic waves. In the optical band, Fano resonances can be continuously tuned, abruptly switched, and dynamically modulated and have been observed experimentally [173,174,175]. All of these have the potential to be combined with terahertz waves, and although these functions are challenging in the terahertz band, it promises to be the next generation of terahertz devices offering solutions [50]. The main challenges in Fano resonance-based practical applications include: (i) the narrow bandwidth of Fano resonance, which means Fano resonance can only sense liquid and thin film in a specific narrow frequency band; (ii) the excessive losses, which are currently too high for metals and some substrate materials, resulting in relative low values of Q, which leads to limited sensing. To address these two limitations, we believe the performance can be improved by constructing reconfigurable metasurfaces or active metasurfaces, and the development of high dielectric constant low-loss dielectrics to diminish the impact on the Q-value. By changing the pumping or voltage of active metasurfaces, some semiconductors or graphene are made to generate gain to compensate for the loss of the original substrate, thus achieving the compensation of the Q value. The realization of multi-functional integrated biosensors with high sensitivity is of significant importance for clinical diagnosis and biomolecular detection. It opens the windows for high-efficiency resonators in terahertz filters, sensors, switches, polarizers, and imaging applications.