Towards Mirror-Less Graphene-Based Perfect Absorbers

Abstract

Owing to its exceptional electronic and optical properties, graphene has attracted extensive attention among researchers in the development of high-performance optoelectronic devices. However, the light absorption of pure graphene is very poor, limiting its development in practical application. In this review, as a solution for this issue, various types of graphene-based perfect absorbers are addressed in terms of their operation principles and design requirements. Their recent progress and potential applications such as photodetectors and modulators are also discussed. In particular, we emphasize the importance of mirror-less (in particular, one-port mimicking) perfect absorber design due to simplified fabrication processes or enhanced tolerance for fabrication error.

1. Introduction

Enhancing the light–matter interaction of various materials is of great importance in many optoelectronic device applications. A perfect absorber (PA) is a device in which the incident light wave at operating wavelengths can be perfectly absorbed via efficient light–matter interaction and then transformed into ohmic heat or other forms of energy [1,2,3,4,5,6,7,8,9,10]. It is not so difficult for thick absorbing materials to achieve highly enhanced absorption because the optical path length is proportional to thickness of absorbing medium. However, in ultrathin absorbing materials such as two-dimensional (2D) materials with atomic-layer thickness, high absorption cannot be obtained without proper engineering of the geometry of the structured elements. For example, pure monolayer graphene (with an atomically ultrathin thickness of ~0.34 nm), which is basically a semimetal with linear dispersion of two-dimensional Dirac fermions, has an optical absorption of ~2.3% under normal incidence in the near-IR to visible regime [6,7,8,9,10,11]. Here, pure graphene means that it is intrinsic or undoped. In addition, it does not include impurities such as oxygen, and it has a flat surface without any patterns. Thus, despite of its excellent carrier mobility, the weak light–matter interaction with graphene limits its development towards practical applications such as high-efficiency photodetection and modulation [12,13,14,15,16].

Here, we will address graphene perfect absorbers (GPAs). Over the past decade, to construct GPAs, various configurations have been proposed, such as asymmetric cavities using multiple layers [16,17,18,19,20], gratings or photonic crystals [21,22,23,24,25,26,27,28,29,30,31,32,33], metamaterials [34,35,36,37,38,39,40], and prism couplers [41,42,43,44]. Previous reviews on GPAs have mainly focused on categorization in terms of absorption bandwidth (for example, narrowband, dual-band, broadband) or their operating wavelength ranges (for example, Visible to THz band) [7,8,9,10]. In this topical review, these GPAs are classified into two types according to the presence or absence of 100% reflective external mirrors. As a typical external mirror, metal reflectors inevitably induce ohmic loss, and the distributed Bragg reflector (DBR) requires a sophisticated growth technique limited to certain material systems or the use of a complicated fabrication process, which are undesirable in applications such as modulators and photodetectors [14,15,16]. For example, in the asymmetric Fabry–Perot microcavity described in ref. [16] (which will also be addressed in the applications section), the bottom DBR, consisting of 25 pairs of alternating AlAs and AlGaAs layers, can be grown via molecular beam epitaxy (MBE) on an n-doped GaAs substrate. Owing to the low difference between the refractive indexes of AlAs and AlGaAs, the use of so many deposition processes is inevitable. Compared to conventional GPAs utilizing these external mirrors [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44], mirror-less GPAs are desirable due to their simpler fabrication process, although their somewhat strict design requirements are inevitable [45,46,47,48,49]. In the case of the former, substantial progress has been made with respect to their development, but for the latter, development remains immature. We review the basic theory behind the two main types of GPAs in Section 2 and Section 3, and then we discuss the performance of relevant potential applications in Section 4. Finally, the conclusions and future perspectives are provided in Section 5.

2. Graphene Perfect Absorbers with External Mirror

Before we get started the main issue, the optical properties of graphene need to be addressed. In the mid-IR to THz regime (strictly, hf < 2E_f, where h, f, and E_f are the Plank constant, the frequency of incident light, and the Fermi level of graphene, respectively), the optical conductivity of graphene is dominated by the intraband transition, and thus, it can be treated as a metallic material [6,7,8,9,10]. This indicates that doped graphene supports plasmon resonances, which are collective oscillations of free electrons. Unlike noble metals, free carriers in doped graphene can easily be tuned by electrostatic gating or chemical doping. Additionally, graphene plasmons have lower loss and stronger field confinement compared to plasmons in noble metals in the mid-IR to THz regime [7]. On the other hand, in the near-IR to visible regime (strictly, hf > 2E_f), absorption is nearly wavelength independent because its optical conductivity is dominated by the interband transition [6,7,8,9,10]. In particular, undoped monolayer graphene is treated as a lossy dielectric material that has an absorption efficiency of ~2.3% over a wideband wavelength range.

Under single-sided illumination, the most straightforward approach for achieving perfect absorption is to use a one-port resonant system that has a 100% reflective external mirror on the backside, as shown in Figure 1. In general, DBRs (distributed Bragg reflectors) and noble metals can be used as typical external mirrors for achieving zero transmission. According to the coupled mode theory (CMT), absorption efficiency in a lossy one-port resonant system can be described using the following equation [24,33,49]

$$A(\omega )=\frac{4{\gamma }_{leak}{\gamma }_{loss}}{{(\omega -{\omega }_o)}^2+{({\gamma }_{leak}+{\gamma }_{loss})}^2}$$

(1)

where ω_o, γ_leak, and γ_loss are the resonant frequency, leakage rate, and loss rate, respectively. When γ_leak = γ_loss, A = 1 at resonance (ω = ω_o). This means that perfect absorption is achieved by balancing the internal loss rate and the external leakage (or coupling) rate of the resonator, commonly referred to as the ‘critical coupling’ condition. While γ_leak is controlled by the quality factor (Q-factor) of the resonator, γ_loss is controlled by the absorption coefficient and the electric field intensity in the graphene layer. The graphene absorption coefficient is determined by the doping level and the quality of the graphene, which can be generally described by the Kubo formula [6,7,8,9,10]. In this review, we mainly consider a CVD-grown graphene because it has moderate carrier mobility [50,51].

Due to the straightforward critical coupling concept, most previous perfect absorbers, including GPAs, have employed an external mirror [1,2,3,4,5,6,7,8,9,10]. When these GPAs support only single-resonance at wavelength range of interest, as shown in Figure 1 or Equation (1), they are dubbed as the ‘single-resonance/mirror absorber’. In the case of dual-band [52,53,54,55,56] or multi-band [57,58,59,60,61,62] absorption, the absorption efficiency can be described through the superposition of absorption in single-resonance/mirror absorbers with different resonances. In particular, ultra-broadband absorption [63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78] can be attributed to the overlapping of multiple resonance absorption bands which exhibit a significantly wider bandwidth. An alternative approach for implementing a one-port resonant system is ‘Prism-coupling absorber’ scheme [41,42,43,44], which utilizes total internal reflection (TIR) to achieve zero transmission. This implies that the prism functions as an external mirror at above critical incident angles. While the prism-coupling scheme can provide a wide absorption bandwidth owing to its relatively weak resonance feature, its drawback is that it works only for an oblique incidence angle and has a bulky absorber system due to introduction of prism.

2.1. ‘Single-Resonance/Mirror Absorber’ Scheme

As previously mentioned, perfect absorption in this absorption scheme can be attained when critical coupling condition is satisfied at resonance wavelength. Key parameters in Equation (1) (that is, leakage rate, loss rate, and resonance wavelength) are controlled by incident angle [18,19,41,42,43,44] or periodically patterned structures [21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40], as well as graphene doping level.

2.1.1. Absorption Control by Oblique Incidence

In 2017, Fan et al. [18] experimentally showed angle-selective giant light absorption by placing large-area unpatterned graphene on a structure consisting of a dielectric layer atop a gold mirror (Figure 2a). The doped graphene has metallic property due to hf < 2E_f. Such a simple structure supports a resonance mode with light trapped in the dielectric layer owing to the reflections at its top and bottom surfaces. The loss rate is insensitive to incident angle, whereas the leakage rate reaches zero at 90 degrees. Thus, the critical coupling condition can be always satisfied by adjusting the incident angle, even though the critical angle is a considerably high value. In ref. [19], the proposed structure can lead to perfect THz absorption because of strong light localization in the defect layer of the heterostructure using two Si/SiO₂ DBR (Figure 2b). When the incident angle increases, the resonant peak shifts toward higher frequencies due to the correlation between the resonance frequency and the incident angle. In 2016, Zhao et al. [20] proposed a multi-layer photonic configuration, which consists of an ultrathin metal film coated on a DBR and a graphene sheet in a silica spacer. The monolayer graphene exhibits an impressive absolute absorption of light, which can reach up to 80% (34.8-fold enhancement compared to the intrinsic value of 2.3%), due to the strong field confinement of Tamm plasmon in the silica spacer. The Tamm plasmon originates from the appropriate combination of a metal film (not a dielectric graphene) and a DBR. Changing the incident angle is a straightforward method to efficiently adjust the operating wavelength of graphene absorption. In detail, the absorption peak wavelength experiences a blueshift as the incident angle increases.

In 2013, Pirruccio et al. [41] proposed a prism-coupling absorber in which a gap layer of an intermediate index value was embedded, and graphene was located at the interface between the gap layer and the substrate. They demonstrated broadband enhanced absorption with practically available materials by using five or ten layers of graphene. However, it is difficult to achieve perfect absorption for monolayer graphene due to the limitation on material index choice. In 2017, Kim et al. [42] proposed a modified absorber structure in which monolayer graphene is embedded in the middle of the gap layer, enabling practical perfect absorption in monolayer graphene with naturally available materials. The perfect absorption is attributed to enhanced light–graphene interaction through the creation of a cavity mode within the gap layer when a proper gap thickness and a graphene position are chosen. In 2019, the excellent performance of the proposed absorber was also experimentally demonstrated [43] (Figure 2c). The absorption peak is enhanced up to ~86% at λ = 650 nm with bandwidth of 314 nm (from 542 nm to 856 nm); this absorption performance is the best experimental result for monolayer graphene in the visible range, to the best of our knowledge.

2.1.2. Absorption Control by Patterned Structures

In the mid-IR to THz regime (strictly, hf < 2E_f), due to the metallic property of doped graphene, tunable graphene plasmons can be utilized by periodically patterning graphene itself. In 2012, Abajo et al. [21] reported that 100% light absorption can take place in the graphene disk arrays supported on a dielectric-coated gold surface, provided that the critical coupling condition is satisfied by properly choosing the dielectric coating layer thickness. Liu et al. [22] incorporated an air nano-slit into a similar structure, positioned at a specific displacement distance from its center, as illustrated in Figure 3a. The air nano-slit can not only exhibit an efficient asymmetrical characteristic for the graphene disk but also proposes a viable approach for realizing a high-Q resonant spectrum. Also, there have been many reports based on different metamaterials, such as graphene ribbon arrays [34,35], square metal patches [36], cross-shaped resonators [36,37], and split-ring resonators [36,38], as shown in Figure 3b–d. Most importantly, plasmon resonances in patterned graphene also exhibit good absorption stability over a wide-angle range [34,35], as shown in Figure 3b, similarly to plasmon resonance in noble metals [31].

In near-IR to visible regime (strictly, hf > 2E_f), there is no plasmonic response in undoped graphene, so the critical coupling is entirely controlled by the resonance properties of the patterned structures excluding the graphene layer. To greatly enhance graphene absorption, a quite low γ_leak resonant structure is required to be balanced with quite low γ_loss. In many reports, unpatterned graphene is coupled with periodically patterned dielectric resonant structures of a high-Q. Fan et al. [24] and Qin et al. [25] numerically demonstrated that by using guided resonance in a photonic crystal slab backed by a DBR or a metal reflector, the absorption of monolayer graphene located on the top of a photonic crystal slab can reach perfect absorption (Figure 4a). By properly adjusting structural parameters such as period, thickness, and hole radius of photonic crystal slab, the system is critically coupled (γ_leak = γ_loss). Valentine et al. [26] and Zhou et al. [27] demonstrated experimentally close to total absorption in monolayer graphene absorbers based on critical coupling with guided resonances in transfer printed photonic crystal Fano resonance filters at near-IR.

In 2018, Lin et al. [39] introduced an asymmetric metasurface for an ultra-narrowband GPA. In the proposed absorber, in which monolayer graphene is on top of the dielectric metasurface backed by a silver substrate, the high angle tolerance and Q (~2600) are due to the magnetic dipole resonance based on two asymmetric silicon rings placed over a silica slab. Qin et al. [29] reported that peak absorptions over 99% with FWHM about 20 nm in the near-IR were measured for monolayer graphene coupled with subwavelength gratings on top of a back gold mirror (Figure 4b). The absorption structures shown are highly compact with a total thickness of less than 1μm. In 2019, Kim et al. [33] proposed the narrowband GPAs with an exceptional fabrication tolerance, which consists of a low-contrast grating (LCG) and a finite DBR layer with monolayer graphene (Figure 4c). It is numerically shown that the proposed GPA outperforms the previously proposed schemes in terms of fabrication tolerance. In addition, without degrading the fabrication tolerance, the bandwidth of the proposed absorber can be controlled by the DBR thickness (the number of pairs). For example, by stacking 8.5 Si/SiO₂ pairs in the DBR, a narrow absorption bandwidth of sub-nanometer can be attained.

2.2. Performance Improvement of Absorbers

2.2.1. Angle-Insensitive Absorption

For certain graphene-based optoelectronic devices, achieving broadband graphene absorption with incident angle independence is highly desirable. In particular, GPAs designed by coupling the graphene with metal nanocavity can effectively provide angle-insensitive absorption due to the magnetic dipole resonance based on plasmon in metals [23,31]. In 2015, Kim et al. [23] proposed an electrically tunable absorber based on epsilon-near-zero (ENZ) effect of graphene embedded in a nanocavity, which is composed of metal grating and metal reflector (Figure 5a). When hf is close to 2E_f, graphene can be an ENZ material with vanishingly small permittivity [23,79] at certain wavelengths under the proper contributions of interband and intraband transitions. Due to the strong surface-normal electric field confined in ENZ graphene, greatly enhanced absorption is achieved. Moreover, owing to the ENZ effect and the magnetic dipole resonance, it has a unique feature of incident angle insensitiveness. In 2018, Qin et al. [31] also demonstrated the GPA based on a deep subwavelength 2D square plate, where graphene has a dielectric property because undoped graphene is applied (Figure 5b). Similarly to the structure described in ref. [23], the electric field is mostly concentrated around the bottom corners of the silver plates, and the magnetic field is highly confined in the dielectric layer between the silver plates and silver reflection mirror. The direction of the magnetic field of the TM incident wave remains unchanged with varying incident angles, which can effectively drive a current loop circulating the cavity, and thus, the angle dependence of its resonant wavelength is significantly weak. Compared to GPAs using the patterned dielectric structures of Figure 4, a wider absorption bandwidth is obtained at the cost of high ohmic loss in noble metals.

2.2.2. Ultra-Broadband Absorption

In general, a fundamental trade-off exists between the bandwidth and amplitude of attainable absorption. To achieve both broadband and high absorption, it is crucial to employ multiple resonances. In this subsection, we focus on ultra-broadband absorber structures, wherein various resonant modes are superimposed upon one another. The graphene-based ultra-broadband absorbers are highly desirable for some applications such as photovoltaics, photodetectors, and thermal emitters.

Firstly, monolayer graphene-based ultra-broadband absorbers are reviewed. One effective method is to use unpatterned monolayer graphene sandwiched between a periodic structure consisting of dielectric or metal (for example, 1D gratings with isosceles trapezoid cross section [63], bricks arrays [64], elliptic cylinder arrays [65], and muti-circular gold patches of different radii [66], snowflake Koch Fractal (SKF) [67]) and a dielectric spacer on top of a metal reflector. In particular, in ref. [63] (Figure 6a), due to the coupling between Mie resonances with graphene plasmon resonance, a flat-top absorption spectrum (in detail, above 99% absorption covers the frequency ranges of 0.66–1.21 THz, and the fractional bandwidth reaches about 60%) is demonstrated. In 2019, Basiri et al. [67] introduced an ultra-wideband THz metamaterial absorber based on SKF dielectric loaded on a graphene sheet. For both TE and TM polarizations, ~160% fractional bandwidth is achieved while attaining over 90% absorption. Another alternative method to accomplish broadband absorption could be the utilization of multi-resonances of patterned monolayer graphene. For example, by applying the graphene concentric double rings [68], graphene ribbons with gradient width [69], sinusoidal-patterned graphene [70] (Figure 6b), complementary cross-oval-shaped graphene [71], and slotted-square graphene meta-rings [72], several or continuous graphene plasmon resonances can be excited over a broadband wavelength range. In 2023, Massoud et al. [72] proposed the polarization-insensitive, broadband THz absorber comprising a simple meta-square ring of graphene, which possesses different slots in its structure to induce multiple plasmonic resonances. Above 95% absorption covers the frequency ranges of 2.2–4.6 THz, and thus, the fractional bandwidth reaches ~70%.

Secondly, mutli-layer graphene can be used to obtain ultra-broadband absorption. In 2019, Jia et al. [73] experimentally demonstrated a 90 nm thick graphene metamaterial with grating, which consists of alternating graphene and dielectric layers (Figure 6c). The grating couples the light sideways into waveguide modes that propagate along the surface, leading to large absorption in the metamaterial. The absorber has broad-bandwidth absorption of well over 80% of non-polarized light over almost the entire solar spectrum (300–2500 nm). Yao et al. [74] showed that the absorption efficiency of the proposed absorber can be as high as more than 90% over 2.10 THz (from 6.98 to 9.10 THz). From top to bottom, the structure consists of a periodical graphene pattern and a double-layer graphene sheet (the two layers of graphene sheets are unpatterned graphene planes) sandwiched with a silicon dioxide layer and the gold ground plane, tightly stacked to form the unit cell. In 2018, Abdolali et al. [75] demonstrated that the proposed absorber exhibits an absorption of >90% in an ultra-broad range of 0.55–3.12 THz. The proposed absorber is a compact, three-layer structure, comprising square-, cross-, and circular-shaped graphene metasurfaces embedded between three separator dielectrics, and all of them are backed by a metal reflector (Figure 6d). Chen et al. [76] introduced a broadband THz absorber with an array of graphene-dielectric multilayered pyramids on a metal reflector. High absorption with an ultra-broad bandwidth from 8 THz to over 100 THz is achieved due to squeezing graphene plasmons at different levels of the gradually tapered pyramid stack, similarly to sawtooth anisotropic hyperbolic metamaterial absorbers in ref. [77].

Thirdly, the prism-coupling absorber scheme can be also utilized for ultra-broadband absorption. Kim et al. [44] proposed GPAs of ultra-wide bandwidths based on prism coupling with wavelength-insensitive phase matching, which consists of three dielectric layers (prism–cavity–air) with monolayer graphene embedded in the cavity layer (Figure 6e). Due to inherent material dispersion of the dielectric layers in near-IR regime, with the proper choice of the incidence angle and the cavity thickness, the proposed perfect absorbers can satisfy the phase matching condition over a wide wavelength range, inducing enormous enhancement of the absorption bandwidth. According to theoretical investigation, 99% absorption bandwidth of ~300 nm with perfect absorption at λ = 1.51 μm can be achieved, which is ~7 times wider than the conceptual design based on the non-dispersive materials.

3. Graphene Perfect Absorbers without External Mirror

As mentioned in the previous section, back-reflection mirrors are often either lossy (e.g., metallic mirrors) or require additional fabrication efforts (e.g., DBR). Therefore, under single-sided illumination, the possibility of achieving perfect absorption without the aid of backing mirrors is highly attractive and could open up many engineering possibilities [45]. Over the past decade, three types of GPAs schemes without external mirror have been proposed: ‘Degenerate critical coupling absorber’, ‘All-pass filter-based absorber’, and ‘One-port mimicking absorber’.

3.1. ‘Degenerate Critical Coupling Absorber’ Scheme

If a mirror-symmetric two-port resonator supports a single resonance, then at most 50% of the incident power can be absorbed when the system is illuminated from a single side. In 2014, however, Fan et al. [80] theoretically demonstrated that the perfect absorption can be achieved through degenerate critical coupling with two resonant modes of opposite symmetry, which are each responsible for 50% absorption (Figure 7a). The proposed resonator consists of a graphene layer placed on top of a photonic crystal slab. When we assume that the loss of graphene does not change the underlying symmetry of the resonator, according to CMT, the total absorption in the system is given by

$$A(\omega )={\displaystyle \sum _{j=1}^2\frac{2{\gamma }_{leak,j}{\gamma }_{loss,j}}{{(\omega -{\omega }_j)}^2+{({\gamma }_{leak,j}+{\gamma }_{loss,j})}^2}}$$

(2)

where the loss of each mode remains independent and total absorption is the sum of the contribution of each mode. Each of the two terms of in Equation (2) will attain a maximum of 50% when the leakage rate of the mode exactly matches the loss rate of graphene at each resonance (ω = ω_j, γ_leak,j = γ_loss,j). If the two modes are degenerate (ω₁ = ω₂), the entire system reaches the so-called degenerate critical coupling, and 100% absorption will be achieved. As shown in Figure 7a, at the point of the mode crossing, the conditions for degenerate critical coupling can be fulfilled, giving rise to the perfect absorption of the structure, thus breaking the limit of 50% absorption. But in reality, it is very difficult to simultaneously satisfy the frequency degeneracy and the critical coupling conditions of dual modes.

Recently, ultrathin all-dielectric Huygens’ metasurfaces have also been proposed for perfect absorption based on degenerate critical coupling [81,82,83,84,85,86,87], although graphene is not used as an absorbing medium. By overlapping two orthogonal Mie resonance (such as one electric dipole (ED) and one magnetic dipole (MD) resonance), perfect absorption can be achieved. In 2018, Qiu et al. [83] verified the principle of perfect absorption for all-dielectric metasurfaces based on Ge disks (Figure 7b): the destructive interference between simultaneously excited electric and magnetic dipoles inside each element in the backward direction (known as Kerker condition) in combination with the destructive interference between the scattered field and the incident field in the forward direction. In comparison to photonic crystal slab or grating configurations [80], metasurfaces are more useful for individual tuning of the leakage rates of resonant modes by adjusting the geometrical parameters of each element. In particular, to address the issue of only a moderate quality factor (Q ~ 10) resulting from the high radiative loss of Mie resonance, Qiu et al. also adopted the quasi-bound states in the continuum (quasi-BIC) resonance, thereby achieving high-Q (~640) near-unity absorption in the near-infrared regime [84]. These all-dielectric Huygens’ metasurfaces would offer a new route for mirror-less GPA.

Figure 7. Perfect absorbers based on degenerate critical coupling. (a) Top: schematic of a GPA consisting of monolayer graphene placed on top of a photonic crystal slab. Bottom: absorption spectra as a function of slab thickness [80]. (b) Top: schematic of a PA consisting of Ge disks. Bottom: absorption spectra as a function of disk diameter [83]. Reproduced with permission from [80,83], © 2023 AIP Publishing LLC; © 2023 WILEY-VCH.

Figure 7. Perfect absorbers based on degenerate critical coupling. (a) Top: schematic of a GPA consisting of monolayer graphene placed on top of a photonic crystal slab. Bottom: absorption spectra as a function of slab thickness [80]. (b) Top: schematic of a PA consisting of Ge disks. Bottom: absorption spectra as a function of disk diameter [83]. Reproduced with permission from [80,83], © 2023 AIP Publishing LLC; © 2023 WILEY-VCH.

3.2. ‘All-Pass Filter-Based Absorber’ Scheme

Most of the THz PAs that have been proposed thus far are of the reflection type. As a result, the relevant modulators are also of the reflection type, meaning that only the reflected wave can be modulated. In 2019, Kim et al. [88] proposed a GPA scheme employing an all-pass filter such that it functions as a highly efficient transmissive modulator in the THz range (Figure 8). All-pass filter generates a very rapid change from 0 to 360 degree in the vicinity of the resonance while maintaining a unity transmission efficiency, and in general, it is necessary to use at least two resonances (or resonators) [89,90,91,92]. In ref. [88], the proposed absorber is composed of two coupled grating resonators with mirror inversion-symmetry as a pure all-pass filter, and the graphene layers are added to introduce loss (Figure 8a). They also theoretically analyzed the proposed scheme using the temporal coupled mode theory. The two resonators are coupled both indirectly, through the propagation channel with a phase retardation of θ, and directly, through evanescent coupling with a coupling coefficient of μ (Figure 8b). The perfect absorption is obtained when θ = π/2, μ = 2/τ, and τ_L1 = τ_L2 = τ/2, which is completely different from degenerate critical coupling condition [80] because the suggested absorber scheme considers the coupling of two identical resonators. At the optimal structure, a considerably high modulation depth (~70 dB) is achieved via graphene chemical potential variation of ~0.15 eV because the proposed transmissive modulator scheme is based on the low transmission state of the near perfect absorption (~99.8%) (Figure 8c,d). In ref. [45], there is another type of PA scheme with a similar inversion symmetry, in which a two-resonance, four-port model is required. Two opposite-direction propagation modes with nonzero in-plane momentum were considered. However, the design and fabrication of the structure will be rather complicated because the scheme works only for an oblique incident angle.

3.3. ‘One-Port Mimicking Absorber’ Scheme

As aforementioned, the mirror-less GPA is extremely desirable for circumventing numerous limitations associated with the use of the external mirror such as DBR or metal reflector. As an alternative, one-port mimicking absorber scheme is conceptually to mimic a single-mode/mirror system by introducing the internal (or virtual) mirror in a two-port system, and thus the relevant absorption efficiency can be approximately described as Equation (1). In 2017, Kim et al. [46] proposed a novel device structure for the perfect absorption of single-sided illumination, which consists of a high-contrast grating (HCG) with a broadband reflection spectrum, a slab separated by a gap region, and monolayer graphene placed just below the slab (Figure 9). In the CMT analysis, the authors treated the HCG as a lossless resonator with two nondegenerate resonance modes with high leakage rates γ₁ and γ₂ and resonance frequencies ω₁ and ω₂, respectively, while the slab with a graphene layer is treated as a lossy single-mode resonator with a low leakage rate γ₃, a loss rate γ_loss, and a resonance frequency ω₃ (Figure 9b). The proposed scheme can be dubbed triple-mode absorber’. The perfect absorption is obtained through proper direct and indirect coupling between the HCG and slab, by which the HCG (as a 100% internal mirror) and slab (as a single-mode resonator) act as single-mode/mirror system, that is, one-port mimicking. Regardless of the existence of graphene layer, transmission becomes zero. The proposed absorber provides excellent tolerance to structural parameters and graphene quality due to the strong field enhancement in the slab region (Figure 9d). Also, absorption spectrum tuning over a wider wavelength range of ~300 nm is possible, keeping significantly high maximum absorption (>95%). These results mean that the proposed scheme significantly relieve the complexity of absorber design compared to the degenerate critical coupling absorber (or dual-mode absorber) [80] because the frequency degeneracy condition is no longer required.

Recently, Kim et al. [47] proposed one-port mimicking scheme in an asymmetric single resonator supporting two degenerate resonant modes (Figure 10). Although the two coupled resonator-based PA scheme mimicking the one-port system has many advantages [46], in general, a single resonator-based structure is preferred in terms of fabrication simplicity if no specific structural symmetry is required [47,48,49]. In the designed GPA with undoped monolayer graphene placed on a slab–waveguide grating (SWG), only one of the guided-mode resonance modes (GMR₂₁) is responsible for absorption, while the other (GMR₁₃) plays as an internal 100% mirror in conjunction with the Fabry–Perot-like background scattering. The operation concept was confirmed through CMT analysis (Figure 10b). Almost perfect absorption (A > 99.95%) was achieved at the resonant wavelength of the high-Q GMR₂₁ mode. Unlike the degenerate critical coupling absorber [80], the proposed SWG structure is vertically asymmetric, and thus, two degenerate resonant modes (that is, GMR₁₃ and GMR₂₁) are indirectly (not directly) coupled due to partial reflection in the internal wave propagation channel (Figure 10c). The designed device also showed enhanced fabrication error tolerance, which was approximately an order of magnitude larger compared to the scheme based on degenerate critical coupling [80]. Since the proposed GPA structure does not require any structural symmetry, its design is straightforward, and its fabrication will be easier.

In the GPA design, the critical coupling condition is a common and essential requirement. Mostly, the leakage rate of any resonant mode can hardly be adjusted after device fabrication because it is determined by structural parameters. On the other hand, due to the difficulty of the precise control of the quality of synthesized graphene and unwanted doping in graphene transferred to the substrate, the loss rate of graphene is rather unpredictable, so that the perfect absorption is quite difficult to achieve in practice. To solve this problem, in 2021, Kim et al. [49] proposed the GPA with a loss-adaptive Q-factor control function enabled by quasi-BIC, in which its leakage rate is adapted to the loss rate by a proper choice of the incident angle (Figure 11). The proposed absorber consisting of monolayer graphene placed on an SWG that supports both quasi-BIC and GMR. Similarly to the one-port mimicking scheme in asymmetric resonators of [47,48], the quasi-BIC (in detail, BIC2nd) is responsible for absorption, while the GMR (in detail, GMR1st) works as an internal mirror. Another outstanding feature of the proposed PA is remarkably uncomplicated manufacturing process since absorbing medium (including graphene) is placed on the ridge side of the SWG. Moreover, the proposed device scheme can have an arbitrarily small leakage rate via adaptive control of the incident angle, and thus, it can be used to implement a PA for any kind of ultrathin absorbing media.

4. Applications

Until now, practical applications of GPAs have yet to reach a state of maturity. In this section, we briefly introduce a few optoelectronic applications of GPA structures using external mirrors. Figure 12a indicates the schematic depiction of the possible applications, such as high-efficiency modulators [14,15,36,93,94,95], photodetectors [12,13,16], tunable polarizers [96,97,98], switches [99,100,101,102,103], and sensors [104,105,106].

To create the optical modulator based on an electrically tunable GPA, in 2014, Capasso et al. [14] proposed a widely tunable metasurface composed of optical antennas on graphene, which is incorporated into an ultrathin (<λ₀/10) optical cavity (Figure 12b). By switching the GPA in and out of the critical coupling condition via the gate voltage applied on graphene, a maximum modulation depth over 95% and modulation speed up to 20 GHz over a mid-IR range can be achieved. The operation wavelength can be scaled from the near-IR to THz ranges due to the great flexibility in tailoring the response of metasurfaces combined with the broadband optical response of graphene.

In 2012, Mueller et al. [16] reported that by monolithically integrating graphene with a Fabry–Perot microcavity with a high finesse, compared to the ~2.3% absorption of free-standing graphene, the optical absorption is 26-fold enhanced at ~850 nm wavelength, as shown in Figure 12c. The absorbing graphene layer is sandwiched between two DBR mirrors. A buffer layer ensures that the maximum of the field amplitude occurs right at the position where the graphene sheet is placed. In particular, for bilayer graphene, a maximum responsivity of 21 mA/W is achieved.

In 2020, Zhang et al. [96] experimentally demonstrated an electrically tunable perfect absorber at 0.43 THz by integrating a metallic grating into a graphene-based Salisbury screen structure (Figure 12d). In particular, polarization-dependent reflection of the hybrid absorber was investigated. The measured results reveal that the reflection remains nearly 1 under different gate voltages when the polarization of the incident THz field is parallel to the gate grating, while the reflection can be electrically tuned from 0.5 to nearly 0 for the crossing polarization. Therefore, the proposed graphene–grating hybrid metasurface is highly anisotropic and able to function as an electrically tunable THz polarizer with an extinction ratio up to 23 dB.

In particular, the GPAs based on dielectric resonant structures have the potential for sensing or switching applications because they can minimize the undesired ohmic loss in metals, and even ultra-narrow (Q > 10,000) graphene perfect absorption can be achieved [28,33,102,103]. For example, in 2020, Tang et al. [103] numerically demonstrated a GPA structure with a record-breaking Q-factor (up to 10⁵), which is one or two orders of magnitude larger than that of the conventional GPAs. An unpatterned monolayer graphene is placed between the periodic dielectric nanowires and DBR layers. The ultra-low leakage rate of the quasi-BIC resonator and the ultra-low loss rate in the graphene layer are the main contributions for the ultra-high Q perfect absorption. The sensitivity (S) of a spectral wavelength shift for the refractive index change in the resonator is up to 915 nm/RIU, and the figure of merit (FOM = S/FWHM) is ~5 × 10⁴, providing the possibility for applications in all-optical switches when a Kerr nonlinear medium is introduced.

5. Conclusions and Perspectives

In this topical review, we briefly summarized the recent advancements of the GPAs with external mirror and without external mirror, focusing mainly on their operation principle and design requirement. Graphene is a very attractive material for optoelectronic devices due to its remarkable carrier mobility and broad absorption band. However, because its potential use is limited by low absorption of graphene, GPA is the first step to approach practical application. Until now, numerous studies for enhancing graphene absorption have been reported, but there is still considerable room to develop the perfect graphene absorbers based on the different schemes investigated in this review paper.

Table 1. Summary of the key absorption performance parameters of representative GPAs.

Structure	Wavelength or Frequency	Absorption Efficiency (%)	FWHM	Fractional Bandwidth (%)	Sim. or Exp.	Ref.
with external mirror	~1500 nm	99.6	~5.5 nm	—	Sim.	[24]
	1306 nm	99.4	~0.5 nm	—	Sim.	[39]
	1586 nm	95.52	~35 nm	—	Sim.	[54]
	~1606 nm	~95.8	~0.018 nm	—	Sim.	[103]
	~7 μm	~100	~1.5 μm	—	Exp.	[14]
	~13 μm	77.6	~1 μm	—	Exp.	[18]
	1526.5 nm	99	~18 nm	—	Exp.	[25]
	1507 nm	96	~3 nm	—	Exp.	[26]
	~1545 nm	85	~3.5 nm	—	Exp.	[27]
	1483.5 nm	~99	~20 nm	—	Exp.	[29]
	650 nm	86.1	~314 nm	—	Exp.	[43]
	~3150 nm	84	~44 nm	—	Exp.	[107]
	~850 nm	~60	~15 nm	—	Exp.	[108]
	~8.5 μm	94	~2 μm	—	Exp.	[109]
	1370–1670 nm	>99	—	~20	Sim.	[44]
	0.66–1.21 THz	>99	—	~60	Sim.	[63]
	2.20–4.60 THz	>95	—	~70	Sim.	[72]
	6.98–9.10 THz	>90	—	~26	Sim.	[74]
	2.50–3.80 THz	>90	—	~43	Sim.	[69]
	0.55–3.12 THz	>90	—	~140	Sim.	[75]
	0.88–8.12 THz	>90	—	~160	Sim.	[67]
	300–2500 nm	>85	—	~157	Exp.	[73]
without external mirror	1320 nm	~98	~6 nm	—	Sim.	[80]
	~50 μm	99.8	~40 nm	—	Sim.	[88]
	~1281 nm	~100	~16 nm	—	Sim.	[46]
	~1535 nm	99.95	~1.52 nm	—	Sim.	[47]
	~1547 nm	~100	~4.5 nm	—	Sim.	[49]

presents a comprehensive summary of the key parameters governing the absorption performance of representative GPAs, including the state-of-the-art technology GPAs. Actually, experimental achievements have been limited to the GPAs with an external mirror. For example, as shown in Figure 4b, for monolayer graphene coupled with subwavelength PMMA gratings on top of a back gold mirror, peak absorptions over 99% at a wavelength of ~1500 nm with FWHM about 20 nm were measured, which are in excellent quantitative agreement with the simulation results [29]. In 2021, Grilli et al. [107] demonstrated experimentally for the first time a great enhancement in absorption in large-area (1 in diameter) monolayer CVD graphene by exploiting the electric field inside an asymmetric Fabry–Perot resonator fabricated by RF sputtering. The measured absorption of 84% that peaked at 3150 nm with a bandwidth of 44 nm is in very good agreement with COMSOL Multiphysics calculations. In 2023, Chen et al. [108] proposed the photodetector structure using Tamm plasmon by combining a metal film and a DBR, where graphene was transferred onto the DBR, and a metal film was fabricated on the graphene layer. A strong localized field is generated by the structure and detected by graphene, which converted to the photocurrent response. So, the responsivity of the photodetector can be affected by the absorption of the structure. In detail, a maximum absorption of ~60% and responsivity of ~330 μA/W are measured at an incident angle of 50 degrees and a wavelength of ~850 nm. The difference in reflectance (or absorption) between the experiment and simulation can be observed, which is caused by the error in the thickness of the metal film in the fabrication process.

Among various absorbers discussed in this review, the mirror-less GPAs are expected to be very promising due to their having two key advantages over the conventional absorbers using an external mirror. Firstly, they simplify the design and fabrication of absorber structure due to the absence of DBR, which requires a sophisticated growth technique. Secondly, they improve net absorption in the graphene layer because the parasitic absorption such as ohmic loss in metal mirror is minimized. In particular, it is noteworthy that the mirror-less absorbers based on one-port mimicking scheme do not require strict structural symmetry, and thus, the limitation on material index choice is greatly relieved. Adopting a novel all-dielectric Huygens’ metasurface, which offers easy individual tuning of the relevant resonant modes by adjusting geometrical parameters of each element, would offer a new route for mirror-less GPAs. Another prospective research direction is to introduce mechanical flexibility in GPAs by utilizing flexible substrate. Graphene produced via CVD can be transferred to different polymers, such as polyethylene terephthalate (PET), polyimide (PI), and polydimethylsiloxane (PDMS), which are the most commonly used flexible substrates because these have unique flexibility, high mechanical stability, and high chemical stability [110,111]. For example, in 2019, by using a graphene FSS (frequency-selective surface) combined with an oxide-metal-oxide film fabricated on a PET substrate, Jiang et al. [112] showed that the graphene absorber structure with good flexibility can provide a wideband absorption in microwave regime.