1. Introduction

Recent research has revealed the excellent abilities of PhPs including the high optic field confinement (large momentum) [1,2], ultraslow group velocities [3,4], long lifetimes (low propagation loss) [5,6] and extreme polariton anisotropy (hyperbolic dispersion) [7,8]. These characteristics make PhPs ideal for super-resolution imaging [9–12], field-enhanced molecular sensing [13,14], sub-diffraction waveguiding [10,15], infrared metasurfaces [7,16,17], thermal energy transfer [18] and many others [19,20]. In recent years, α-MoO₃ has been proven to be a natural biaxial van der Waals (vdW) crystal supporting hyperbolic PhPs in the mid-infrared region [21–28], which can achieve a stronger confinement than isotropic PhPs and show great potential to directional control of light. At the same time, by precisely adjusting the thickness of polar vdW layers, e.g., via mechanical exfoliation technique, the PhPs modes are controlled by the number of vdW layers and the field could be further confined when scaling down the thickness to atomic scale. The highly confined in-plane isotropic PhPs in atomically thin layers or even monolayer [5,29] is demonstrated and their real-space propagation are presented. Additionally, the PhPs achieved in atomically thin slabs also lays the foundation for highly-confined acoustic modes, as has been theoretically demonstrated [30,31]. However, the picture of in-plane anisotropic PhPs when approaching thickness limit is still unrevealed.

Here we present the optical nanoimaging of highly-confined phonon polaritons in α-MoO₃ nanoribbons with atomically thin thicknesses (6.5–7 nm: 5 atomic layers). The high-quality nanoribbon structure of α-MoO₃ strongly squeezes the electromagnetic field of PhPs into a nanoscale cavity between the two long edges of nanoribbon. Consequently, we are able to detect enhanced intensity of the electromagnetic field on the α-MoO₃ nanoribbon and observe significant PhP dispersion, particularly in the elliptical band.

2. Result and discussion

To explore the polaritonic response of ultrathin α-MoO₃ nanoribbons, we performed nanoimaging measurement using scattering-type scanning near-field optical microscopy (s-SNOM, Fig. 1(a)). In such a system, the metallic atomic force microscope (AFM) tip of s-SNOM in the vicinity of the sample is illuminated by a p-polarized infrared light of frequency ω. Acting as an infrared antenna, the tip focuses the incident field precisely at its apex, creating a nanoscale infrared spot locally probing material properties and exciting polaritons. Simultaneously, the electromagnetic radiation scattered by the tip is captured along with the topography of α-MoO₃ nanoribbons, resulting in near-field images with nanoscale resolution.

 

Fig. 1. Ultra-confined PhPs in ultrathin α-MoO₃ nanoribbons on SiO₂ (300 nm)/Si substrate. (a) Schematic of real-space nanoimaging of PhPs launched in α-MoO₃ nanoribbons with s-SNOM. (b) Calculated momentum dispersion of PhPs in the elliptic (top panel) and hyperbolic (bottom panel) regimes along [100] (x-direction) with different thicknesses (grey: 50 nm and red: 6.5 nm) of α-MoO₃. Yellow triangles show the experimental data points extracted from s-SNOM measurements. (c) Calculated thickness-dependence of k_x/k₀ (k_x: PhP complex wavevector, k₀: free-space wavevector) in the elliptic (red line, ω = 1000 cm⁻¹) and hyperbolic (black line, ω = 870 cm⁻¹) regimes. (d) Near-field amplitude image S₃ of α-MoO₃ nanoribbons measured at ω = 870 cm⁻¹ (top panel) and AFM image (bottom panel). The black line in AFM image shows the height profile of an ultrathin α-MoO₃ nanoribbon which is about 6.5 nm, corresponding to five atomic layers.

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α-MoO₃ has a layered structure in which covalent-bonded ac planes (in-plane) are arranged along the b-axis (out-of-plane) direction through vdW forces. Note that the b lattice constant of an α-MoO₃ unit cell is 1.4 nm [32], therefore, our AFM result indicates that the 6.5-nm α-MoO₃ has 5 layers. The rectangular shape of α-MoO₃ crystals is predominantly determined by their anisotropic crystal structure, with the long axis corresponding to the [001] direction [21]. Previous works have indicated that ribbon-type α-MoO₃ flakes oriented along the [001] direction as favored upon exfoliation because the energy release along the [001] direction is much greater than that along the [100] direction [33,34].

It is noted that the confinement of PhPs in α-MoO₃ increases with decreased thickness, allowing for significant modifications to the dispersion properties via the thickness tailoring. We calculated the momentum dispersion relation in the [100] direction for 50-nm and 6.5-nm thick α-MoO₃ (Fig. 1(b)). The dark stripes represent the allowed fundamental modes in the upper (elliptic regime) and the lower (hyperbolic regime) Reststrahlen bands. The dispersions show that the PhP wavelength can be easily varied by the excitation frequency and scales significantly with the thickness of α-MoO₃. It is noted that when the thickness of α-MoO₃ is at atomic scale (5 layers), the confinement factor could reach beyond 133, the experimental results are indicated as triangles which will be discussed later. Figure 1(c) shows the thickness dependence of the confinement factor. When the thickness is larger than 10 nm, the confinement factor changes slowly with thickness. However, when the thickness drops below 10 nm, the confinement factor increases sharply as the thickness decreases. Figure 1(d) presents an overall view of α-MoO₃ nanoribbons’ near-field amplitude images measured at 870 cm⁻¹ in hyperbolic bands of α-MoO_3. There are only two bright fringes occur at the boundaries of ribbons parallel to the [100] direction and some slight fringes in the interior of the ribbons (more clearly seen by the line profiles in Fig. 3). This suggests an in-plane anisotropic interference pattern of PhPs in the atomically-thin α-MoO₃, demonstrating the unique in-plane hyperbolic polaritons that propagate in one direction while being cut off in the perpendicular direction near the thickness limit.

To analyze the anisotropic PhPs in α-MoO₃ nanoribbons in more detail, we further conducted frequency-dependent near-field nanoimaging experiments on the sample. When the free-space light field is initially coupled onto the α-MoO₃ via a metallic tip, the excited PhP waves propagate in the ultra-thin nanostructure until reaching a physical boundary where strong reflection occurs. The reflected and incident waves then interfere with each other, resulting in the formation of characteristic interference fringes (Fig. 2(a)). More complex interference patterns can be generated by increasing the number of boundaries, which enables the back-and-forth reflections of the PhP waves in all different directions (Fig. 2(b)). Thus, the interference patterns can be modulated by the wavelength of PhP which is related to the frequency of excitation light, or by precisely modifying the geometry of nanostructures. The PhP waves within the α-MoO₃ nanostructures were the sum of the tip-launched PhP waves and those reflected from the boundaries [35]:

 

Fig. 2. Sketches of the reflection and interference of PhP waves in α-MoO₃ with one (a) or two boundaries (b). (c, d) Elliptical-band PhPs in ultrathin α-MoO₃ nanoribbon. (c) Near-field amplitude images S₃ of α-MoO₃ nanoribbon measured at ω = 997 cm⁻¹, 1000 cm⁻¹, 1002 cm⁻¹, 1004 cm⁻¹ and 1005 cm⁻¹, respectively, normalized to the amplitude of the surrounding SiO₂. (d) Extracted experimental amplitude profiles (black lines) compared with calculation (red dashed lines) along the blue dashed line marked in image (c).

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Figure 2(c, d) displays the optical near-field images of an ultrathin α-MoO₃ nanoribbon in the elliptical band using s-SNOM. The frequency-dependent variation of interference fringes in the cavity of the nanoribbon is clearly observed. Note that the α-MoO₃ nanoribbon is nearly transparent at 1005 cm⁻¹ since the third-order demodulated signal S₃ was almost equal inside and outside the cavity, which indicates the fading of PhPs. Simultaneously, owing to the high confinement of PhPs inside the cavity from 997 cm⁻¹ to 1004 cm⁻¹, we observed an intracavity signal intensity S₃ far above the SiO₂ background. To extract the polariton wavevector k_p from measured interference fringes, we use Eq. (1) to fit the extracted line profiles, which have been used in previous investigations [35]. The subtle differences between the fitting and experiment data come from the oblique illumination [36]. Our fitting results (see enlarged image at 1000 cm⁻¹ in Fig. S3) indicate that the wavelength of PhPs in the 5-layer α-MoO₃ is as small as 75 nm at 10 µm (1000 cm⁻¹), implying a high confinement factor 133 that is consistent with the calculated dispersion relation (Fig. 1(b)). In addition, the positions of peaks and valleys near the two boundaries can be seen shifting from 1002 cm⁻¹ to 997 cm⁻¹ in Fig. 2 due to the decreasing λ_p, pointing at a higher confinement at the smaller frequency. A small deviation is observed between the theoretical dispersion and the experiment data (obtained from Fig. 2) for 6.5-nm thick α-MoO₃ nanoribbon. The reason might be that the optical and electronic properties gradually deviate from the bulk response when the thickness of material is reduced below 4–6 vdW layers which are commonly found in MoS₂ [37,38].

The experimental near-field images in the elliptical band provide an indication that the ultrathin α-MoO₃ nanoribbon support a high confinement of PhPs, consistent with the calculated dispersion. We further investigated the PhPs of ultrathin α-MoO₃ nanoribbons in the hyperbolic band (Fig. 3). In this frequency range (860 cm⁻¹ to 890 cm⁻¹), the in-plane polariton wavelength λ_p becomes much smaller (see also Fig. 1(b)) and one observes an expansion of low-intensity near-field signals in the center of nanoribbon cavity, similar to the darker regions found in near-field images from 1002 cm⁻¹ to 997 cm⁻¹ in Fig. 2(c, d). In addition, a rather faint bright line in the center of the cavity can be observed at 860 cm⁻¹ and 870 cm⁻¹, corresponding to the small bump at 250 nm in the amplitude profile, see Fig. 3(b). The phenomenon in the hyperbolic band is far less pronounced than that in the elliptical band. This can be understood by considering that the fast group velocity of hyperbolic band leads to less drastic dispersion changes compared to elliptic band with slow group velocities, and the PhP modes of α-MoO₃ supported in the hyperbolic band was reported to have a relatively weak E_z component than that in the elliptical band [27].

 

Fig. 3. Hyperbolic-band PhPs in ultrathin α-MoO₃ nanoribbon. (a) Near-field amplitude images S₃ of the same α-MoO₃ nanoribbon as in Fig. 2, measured at ω = 890 cm⁻¹, 882 cm⁻¹, 870 cm⁻¹, 860 cm⁻¹. (b) Extracted experimental amplitude profiles along the blue dashed line marked in image (a).

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We next proceed to study the cavity-width tailored PhPs in two wedge-shaped α-MoO₃ nanoribbons (Fig. 4(a)). We investigated the orientation-dependent dispersion of PhPs, considering that α-MoO₃ is a typical anisotropic vdW material and PhPs propagate anisotropically along the surface. Under the approximation of high momentum where k_p/k₀ ≫ 1, the in-plane dispersion relation of the PhP propagating as a function of frequency ω can be resolved [23]:

 

Fig. 4. Elliptical-band PhPs of wedge-shaped α-MoO₃ nanoribbons (thickness: 7 nm). (a) Near-field amplitude images S₃ of two wedge-shaped nanoribbons at measured at 1002 cm⁻¹. (b) Calculated momentum dispersion. The isofrequency contour at 1002 cm⁻¹ is highlighted with red line. (c) Projection of the calculated momentum dispersion on the k_x-k_y plane. Gray dashed lines: isofrequency contours at different frequencies from 1000 cm⁻¹ (outside) to 1005 cm⁻¹ (inside) with 1 cm⁻¹ step size. Red line: isofrequency contour at 1002 cm⁻¹. Red dotted line: a circle for comparison. (d) Extracted amplitude profiles (solid lines) along the corresponding dashed lines marked in (a), in comparison with calculation (red dashed lines).

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Here, $\psi = i\sqrt {{\varepsilon _z}/({{\varepsilon_x}\textrm{co}{\textrm{s}^2}\theta + {\varepsilon_y}\textrm{si}{\textrm{n}^2}\theta } )} $, ε_x,y,z is the dielectric permittivity of α-MoO₃ along the corresponding crystallographic axis, d is the α-MoO₃ flake thickness, ε_a and ε_s are the dielectric permittivities of the surrounding air and the substrate, θ is the angle between the x axis ([100]) and the in-plane component vector, respectively.

In Fig. 4(b, c), we plot the isofrequency curves for the fundamental modes in 7-nm thick α-MoO₃. When k₀ increases, for instance at 1002 cm⁻¹, the isofrequency contour (red line) becomes more circular (indicated by the red dotted line) instead of being elliptical. Under this condition, the angle between the optical axis and the edge has less impact on the anisotropy of PhP propagation. We extracted three amplitude profiles at three different positions from the near-field optical image in Fig. 4(a) and the results are shown in Fig. 4(d). Here, when the cavity width expands (the nanoribbon widths for L1, L2 and L3 positions extracted from AFM images are 297 nm, 205 nm and 128 nm, respectively), an increase in the number of peaks can be determined, in good agreement with the calculated results (red dashed lines). In addition, there was no indication of a strong decay in the intensity of interference fringes when the cavity width, i.e., the propagation distance, is varied.

3. Conclusions

In summary, we have successfully demonstrated that the atomically-thin layers of α-MoO₃ nanoribbons enable a high electric field confinement and the active control over the polariton propagation properties by changing the illumination frequency. Especially, the interference fringe patterns can be significantly changed in the elliptical band. The nanoribbons naturally provide a physical boundary for the strong interference of phonon polaritons and the atomically thin thickness of α-MoO₃ offers a desired field confinement for strong light−matter interactions. The observation and analysis of in-pane anisotropic PhPs propagation in atomically thin layers may provide an empirical reference point for lattice dynamics models of vdW few-layers and lay the foundation for the atomically integrated design of different vdW materials.