Introduction

An acoustic plasmon mode supported by a system of two graphene sheets1, or by a single graphene sheet over a metal gate2, was experimentally detected recently3, and its unprecedented field confinement can benefit applications in the technologically important mid-infrared (MIR) and THz regimes4,5,6,7,8. This mode is supported by a structure comprising of a metal, a dielectric spacer, and a graphene layer, where the image charges in the metal effectively “mirror” the charge density oscillations in the doped graphene layer. The acoustic graphene plasmon (AGP) supported by the structure is mostly confined in the dielectric spacer and does not experience cutoff as the spacer thickness decreases8, thus resembling the fundamental plasmonic mode of a narrow metal gap. The AGP excited at the important MIR frequencies9,10 does not exhibit significant loss and is detectable even when the spacer is reduced to a single atomic layer of hexagonal boron nitride5. Inside such a narrow dielectric spacer, the AGP wavevector can be about two orders of magnitude larger than that of free space light, which grants access to quantum and non-local phenomena in graphene5,11,12, and allows for the AGP localization in nanostructures13 with a stunning mode volume confinement factor4 of ~1010. This ultimate capability to compress MIR light outperforms that of other polaritonic species in van der Waals materials9, including graphene surface plasmon (GSP)14,15, and is similar to the case of image phonon-polaritons in boron nitride16. For that reason, AGP is promising for applications that require strong light–matter interaction such as molecular sensing6,17,18,19,20, polaritonic dispersion engineering in van der Waals crystals21,22, and dynamic light manipulation by graphene-based active metasurfaces23,24,25,26.

The key advantage of the AGP is its confinement within the dielectric spacer, in contrast to the GSP bound to the graphene layer. Therefore, ohmic losses in graphene are expected to hinder the AGP propagation to a lesser extent compared to GSP. On the other hand, the larger AGP wavevector requires an intermediary structure to alleviate the momentum mismatch under the far-field excitation. So far, structures containing an array of metallic elements have been used to couple far-field radiation to the AGP mode4,5,6. However, the near-field optical probing of AGP, which provides detailed microscopic information about the mode, is yet to be demonstrated.

In this work, we employ a scattering-type scanning near-field optical microscope (s-SNOM) based on an atomic force microscope (AFM) for real-space mapping and analysis of MIR AGP. We directly measure the AGP dispersion, evaluate the mode propagation loss, and investigate its behavior in a periodic structure designed for the far-field coupling. Most importantly, our results reveal a relatively low propagation loss of infrared AGP even when unprotected, CVD-grown, large-area graphene is used at ambient conditions, suggesting a practical route to construct large-area graphene-based optoelectronic devices.

Results

Near-field coupling to AGP

Although the AGP fields are mainly confined inside the dielectric spacer, their evanescent components have non-zero amplitudes above the graphene layer (Fig. 1a). The vertical component of the mode’s electric field, Ez, penetrates into the free space above the structure, and hence, can couple to the AFM tip of the s-SNOM effectively acting as a z-oriented electric dipole27,28,29,30 (Fig. 1b). We define the Ez penetration depth above graphene, De, as corresponding to the 1/e attenuation of the field amplitude. By solving Maxwell’s equations in a multilayer configuration31, it is possible to find the unique solution for the AGP eigenmode supported by the structure of interest (see Supplementary Information section S-1). Then, De = 1/Im{kz}, where kz is the z-component of the AGP wavevector in the medium above graphene. At a given graphene Fermi level, EF, the wavevector depends on both the excitation frequency ω and the spacer thickness t, and so does the De. At the same time, the amplitude of the scattered near-field signal from the AFM tip is proportional to |Ez | at the position of the tip. Therefore, the performance of the s-SNOM method is expected to vary significantly depending on the experimental conditions.

In order to estimate the optimal experimental conditions for the near-field AGP probing by s-SNOM, it is instructive to calculate De(ω,t) for the structure of interest. Figure 1c shows De(ω,t) calculated for the range of MIR frequencies and spacer thicknesses, assuming EF = –0.5 eV. Considering that the average tip height above the sample is 40–80 nm, which is approximately equal to the tapping amplitude of the tip29,32, the most favorable experimental conditions are expected in the frequency window of 1000–1300 cm–1 (where Al2O3 absorption stays sufficiently low), while t > 10 nm.

Substrates with gold and Al2O3 films were fabricated using the template-stripping method33,34, allowing a sub-nm roughness of substrate surface even when the gold film is patterned6 (see Supplementary Information section S-2). The large-area monocrystalline graphene35 was grown by chemical vapor deposition (CVD), wet-transferred on top of the alumina-coated gold substrates, and chemically doped (see Methods section for details).

Dispersion and loss analysis

Near-field imaging of doped graphene on the Au/Al2O3 substrate reveals an abundance of μm-long edges of monocrystalline areas with AGP interference fringes formed due to its reflection from the graphene termination (Fig. 2a). Figure 2b demonstrates a close-up scan of such an edge for a sample with t = 18 nm at ω = 1150 cm–1. The near-field signal intensity s(x,y) is proportional to the amplitude of the z-component of the electric field under the tip30, s |Ez |, thus it can be numerically calculated by full-wave simulations in a quasi-static approximation29,36 (see Supplementary Information section S-3). As shown in Fig. 2c, the full-wave simulations by finite element method (FEM) with AFM tip modeled as a point dipole source provide a perfect fit to the interference pattern, where numerical and experimental data normalized by that from the graphene-free area. The fitted value of the optical conductivity of graphene (given by the random phase approximation in local limit37,38,39) corresponds to EF = –0.51 eV and carrier mobility μ = 2000 cm2/V s, consistent with a high-quality CVD graphene7. The roughness-mediated scattering of AGP is neglected in the full-wave simulations. Additional simulations support this assumption, considering the measured root-mean-square (RMS) roughness of 0.5 nm at gold and alumina surfaces (Supplementary Information section S-2).

The AGP interference fringes allow for the direct measurement of the plasmonic wavelength30,40 λAGP ≈ 222 nm (Fig. 2c, d); note that this is not the case for graphene patches of finite size where multiple reflections contribute to near-field signal30. Additionally, we observe AGP interference in a sample with t = 8 nm (inset in Fig. 2d). As expected, the AGP mode in the thinner 8 nm spacer is more tightly confined in the gap, hence the shorter λAGP ≈ 156 nm and the weaker amplitude of the near-field signal above graphene, despite the similar doping level EF = –0.49 eV. We note that the probed structure with t λAGP does not support propagating GSP due to the proximity of graphene to the gold layer. For the MIR frequencies of interest and EF ≈ –0.5 eV, it has been analytically demonstrated8 that the AGP dispersion approaches that of the GSP when t 100 nm.

By plugging the recovered graphene conductivity into the semi-analytic eigenmode solver, the parameters of the detected AGP can be obtained. For the sample with t = 18 nm (8 nm), the effective index of the AGP is qAGP = kAGP/k0 = 39.06 + 2.92i (55.96 + 4.17i), where kAGP is the propagation constant of the AGP, and k0 = 2π/λ0 is that of free space light. To quantify the dissipation of plasmonic modes, we use the figure of merit (FOM) defined as the ratio of the plasmon propagation length Lp to its wavelength λp: Lp/λp = lp = Re{kp}/(2πIm{kp}), where lp is the normalized plasmon propagation length in optical cycles. It can be noted that the FOM of AGP lAGP = 2.12 (in both samples) is almost twice larger than the reported value for MIR GSP in exfoliated graphene on an SiO2 substrate41 lGSP = 1.18. An analytical solution for GSP in the same graphene on a thick Al2O3 substrate provides qGSP = 23.41 + 2.47i (24.43 + 2.62i), and thus, an expected lGSP ≈ 1.5 in both cases. Therefore, our near-field measurements indicate that, while the observed AGP is ×1.7 (×2.3) times more compressed in terms of the wavenumber, its FOM is 1.4 times higher than that of the GSP in the same graphene sheet. The better FOM of AGP has been predicted8 due to the larger compression factor of the plasmonic wavelength compared to the decrease in the propagation distance. However, dispersion analysis also indicates that the AGP is in general less sensitive to the loss in graphene if considered in local limit42 (see Supplementary Information section S-1). Nonetheless, the experimental observation of the low-loss AGP with unprotected CVD graphene at ambient conditions is encouraging for the development of large-area polaritonic devices operating in the MIR9.

The AGP dispersion can be directly measured from the near-field images at different frequencies. The AGP dispersion measured in a sample with t = 21 nm (circles) is shown in Fig. 3a, along with the fitted analytical dispersion for EF = –0.46 eV. The near-field data are obtained from a series of measurements over the same sample area, which makes it possible to compare the spectral dependency of the near-field contrast29,32 $$\eta (x,y) = (s(x,y)/s_{{\mathrm{ref}}}){e}^{{i}(\varphi (x,y) - \varphi _{{\mathrm{ref}}})}$$, where sref and φref are the amplitude and phase of the near-field signal over the graphene-free area, respectively. Figure 3b demonstrates mapping of $$\left| {\eta (x,y)} \right| = s(x,y)/s_{{\mathrm{ref}}}$$ and corresponding AGP interference fringes at different frequencies, indicating the effective mode index increasing from 34 at 1080 cm–1 to 46 at 1260 cm–1. Furthermore, the spectral dependency of $$\left| \eta \right|$$ above graphene (averaged across the area far from the edge) generally follows the calculated value of De (Fig. 3c), in agreement with the tighter mode confinement inside the spacer. According to Fig. 3c, $$\left| \eta \right|$$ approaches unity when De ≈ 25 nm. Therefore, based on the calculations for De shown in Fig. 1c, we predict that the s-SNOM technique would be feasible for AGP probing even when the spacer thickness is reduced down to a few nanometers if ω is sufficiently low.

AGPs in periodic structures

Due to the significant momentum mismatch, the efficient AGP coupling to a far-field requires a mediator—an array of metallic elements (e.g. gold nanoribbons), which can provide coupling efficiency exceeding 90% when combined with an optical cavity6. We fabricated AGP resonators similar to those used in Ref. 6, where gold nanoribbons are embedded in the alumina layer (Fig. 4a). Due to the periodicity and finite width of the nanoribbons, their interaction with AGP may produce non-trivial near-field patterns depending on the ratio between the AGP wavelength, array period P, and ribbon width w. We investigate samples with different w, while the gap size is 30 nm and t = 18 nm in all devices; the effect of the underlying cavity is not considered in this study.

The near-field signal from a non-uniform structure bears information from multiple scattering sources. Therefore, the AGP propagation loss cannot be extracted from the interference fringes. At the same time, λAGP does not depend on the geometry of the structure, thus EF in graphene can be fitted using the AGP dispersion obtained from the near-field imaging (see Supplementary Information section S-4). Figure 4b demonstrates the spatial distribution of $$\left| \eta \right|$$ at different frequencies, measured over the same area of graphene deposited on alumina with embedded gold nanoribbons (w = 240 nm). Dispersion fit to λAGP at different frequencies (Fig. 4c) provides EF = –0.58 eV, while the qAGP increases from 32 at 1080 cm–1 to 44 at 1280 cm–1. The correlation between $$\left| \eta \right|$$ and De (Fig. 4d) is very similar to that observed in the uniform structure, indicating a stronger AGP confinement at higher frequencies, while $$\left| \eta \right|$$ approaches unity at De ≈ 30 nm.

In our experiments, the plane of incidence of the TM-polarized excitation beam is always orthogonal to the nanoribbons in order to maximize the scattering at the metal edges (as indicated by the red arrow in the first panel of Fig. 4b). While the AFM tip is able to excite AGP with an arbitrary direction and magnitude of the wavevector, the excitation beam is expected to couple only to the mode propagating in the periodic structure across the ribbons, with maximum coupling efficiency reached at the phase-matching condition between the AGP and the array6 kAGP = 2π/P. One might expect that the near-field signal can be enhanced at the phase-matching condition. However, the near-field contrast over the nanoribbons (measured far from the graphene edge; Fig. 4d) does not show any noticeable feature around the phase-matching frequency of 1105 cm–1. To understand this and gain an insight into the near-field excitation of AGP in the array, we calculate the dispersion of AGP propagating in a periodic array of nanoribbons.

The AGP dispersion in the x-direction (across the nanoribbons) is calculated using a simple model of a planar AGP waveguide with an infinite array of nanogaps, treated as partially reflective “mirrors” with complex transmission and reflection coefficients. Then, the dispersion solution is reduced to the eigenvalue problem for a lossy Bloch state in a 1D periodic medium43. The periodicity of the structure does not lead to the opening of a bandgap or flattening of bands at the center or edges of the Brillouin zone, possibly due to the lossy nature of plasmonic modes (see Supplementary Information section S-5). As a result, the density of optical states has similar value throughout the measured spectral range. Therefore, our measurements of the near-field contrast (Fig. 4) do not show stronger near-field signal at the frequency of the phase matching.

We proceed with analysis of the several instances of near-field images. We first analyze the case of phase matching between the array and the AGP. Figure 5a shows the spatial distribution of near-field signal intensity s(x,y) and phase φ(x,y) obtained at ω = 1200 cm–1 in the sample with P = 230 nm and EF = –0.62 eV; λAGP ≈ 228 nm, so that βAGP = 2π/P. The measured and the numerically calculated profiles of s |Ez | and φ arg{Ez} across the nanoribbons (Fig. 5b) both show a periodic variation with the period P equal to the plasmonic wavelength, as demonstrated by the identical red scale bars on the left panel of Fig. 5a. Furthermore, the electric field amplitude (phase) has its maxima (minima) over the center of the nanoribbons, while the minima (maxima) are aligned with the nanogaps (Fig. 5b). When the AGP momentum starts to exceed that of the array, the near-field patterns of both amplitude and phase drastically change, as demonstrated in Fig. 5c, d for the sample with P = 260 nm, ω = 1150 cm–1, graphene EF = –0.52 eV, and λAGP ≈ 225 nm, so that kAGP = 1.15 × 2π/P. Now, the field maxima are recorded over the gaps, while the minima are at the centers of the nanoribbons. The difference in the near-field distribution can be attributed to the excitation of different eigenmodes in the periodic structure (see Supplementary Section S-6 for detailed analysis of eigenmodes in the structure).

The near-field data in Fig. 5b, d is collected far from the graphene edge where the contribution of the edge-reflected AGP is minimized, which allows for employing a simplified model for 2D full-wave simulations using an infinitely long line dipole instead of a point dipole; without a far-field excitation source. Yet the simulation results show a qualitative agreement with the measurements. At higher frequencies, when the AGP wavelength is significantly smaller than P and w, the near-field mapping reveals the AGP reflection and scattering at nanoribbon edges and nanogaps. Even then, the simple numerical model successfully renders the near-field distributions (see Supplementary Information section S-6).

Discussion

In conclusion, we employ the near-field coupling for the excitation and direct optical probing of AGP at MIR frequencies. Since the AGP field is tightly confined in the dielectric region underneath graphene, direct near-field optical imaging of the AGP fields has been considered very challenging. Nevertheless, with a highly sensitive s-SNOM system and a high-quality CVD graphene sample, we are able to directly probe the relatively weaker evanescent tail of AGP above the graphene layer. Furthermore, near-field imaging reveals a lower propagation loss of MIR AGP compared to the reported earlier FOM of GSP in exfoliated graphene, even with unprotected CVD graphene at room temperature. The probed AGP mode is up to 2.3 times more confined than the GSP under similar conditions yet exhibits a 1.4 times larger FOM. These results highlight the promise of the AGP platform for investigating strong light–matter interactions and building graphene-based optoelectronic devices.

Methods

Device fabrication

The gold/alumina layers on a Si substrate were prepared with template stripping as described in Ref. 6. Large-area monocrystalline graphene was chemically grown on a single-crystal Cu foil. First, a commercial Cu foil (Nilaco Corporation, Japan) of 30 μm thickness was cut into ribbons and placed inside a CVD quartz tube, stretching between the hottest and the coldest zones inside the tube. Then, cycle annealing was introduced with a thermal gradient along the ribbons. The Cu foil was annealed at 1040 °C for two hours in an atmosphere of 40 sccm hydrogen and 1000 sccm argon gases. Then temperature was decreased to 700 °C during 30 min, and then increased up to 1040 °C during the same time. This process was repeated for four cycles in total, after which we opened the chamber to cool naturally.

For growing the high-quality graphene, we used low-concentration methane (0.1% in argon) in four stages: ramping, annealing, growth, and cooling. First, the temperature was increased up to 1060 °C during one hour and then kept stable for one hour for annealing, which is necessary for removing organic molecules and enlarging the Cu grain size. Then, we used a mix of three gases (CH4, H2, Ar) for graphene synthesis. The graphene flake size is controlled by growth conditions such as the ratio between CH4 and H2 concentrations, the total amount of CH4, and the growth time. Here, we purged 5 sccm of CH4, 30 sccm of H2, and 1000 sccm of Ar for a full coverage of Cu by graphene. Then, Cu ribbons were cut and graphene was wet-transferred from Cu onto the prepared samples, and chemically doped by vapors of HNO3 acid by placing the devices over the acid for 4 min at room temperature in a fume hood.

Device characterization

The near-field scans were obtained by commercial s-SNOM (Neaspec GmbH) coupled with a tunable quantum cascade laser (Daylight Solutions, MIRcat), which illuminates the Pt-coated AFM tip (Nano World, ARROW-NCPt). The background-free interferometric signal44, demodulated at third harmonic 3Ω (where Ω is the tapping frequency of the AFM tip), was used for near-field imaging. s-SNOM in AFM tapping mode was used to perform surface scans with 5 nm step and tip oscillation amplitude of ≈70 nm.

Numerical simulations

Commercial finite element method software (COMSOL Multiphysics) was used for full-wave simulations. In our 2D simulations, graphene is implemented as a thin film of finite thickness α = 0.2 nm, having the effective relative dielectric permittivity $$\varepsilon = \varepsilon _{\mathrm{r}} + {\rm{i}}\sigma /\left( {\omega \varepsilon _0\alpha } \right)$$, where εr is the background relative permittivity and σ is the optical conductivity of graphene. Dielectric permittivity of gold was taken from Ref. 45, and that of thin film Al2O3 was taken from Ref. 46. See Supplementary Information for details on full-wave simulations.