Infrared hyperbolic metasurface based on nanostructured van der Waals materials

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Science  23 Feb 2018:
Vol. 359, Issue 6378, pp. 892-896
DOI: 10.1126/science.aaq1704

Patterning a hyperbolic metasurface


Science, this issue p. 892



Optical metasurfaces are thin layers with engineered optical properties (described by the effective permittivities in the two lateral directions), which are obtained by lateral structuring of the layers (13). Applications include flat lenses, high-efficiency holograms, generation of optical vortex beams, and manipulation of the polarization state of light (15). With metallic metasurfaces, one can also control the properties of surface plasmon polaritons (SPPs, electromagnetic waves arising from the coupling of light with charge oscillations in the metasurface) propagating along the metasurface. The near-field enhancement and confinement provided by SPPs are other effective means for controlling the phase and polarization of transmitted light, or the thermal radiation emitted from the metasurface (2, 3). Metasurfaces can also be used to control the properties of SPPs in nanophotonic circuits and devices for applications such as unidirectional excitation of SPPs, modulation of SPPs, or two-dimensional (2D) spin optics (2, 6, 7).

Recently, hyperbolic metasurfaces (HMSs) were predicted, which are uniaxial metasurfaces where the two effective in-plane permittivities εeff,x and εeff,y have opposite signs (2, 6). In such materials, the SPPs exhibit a hyperbolic in-plane dispersion, i.e., the isofrequency surface in wave vector space describes open hyperboloids (2, 6, 813). Consequently, the polaritons on HMSs possess an extremely anisotropic in-plane propagation (i.e., different wave vectors in different lateral directions). This behavior leads to remarkable photonic phenomena. For example, the wavefronts of a diverging polariton beam emitted by a pointlike source can exhibit a concave curvature (6, 8), in stark contrast to the convex wavefronts in isotropic materials. Further, the large wave vectors (limited only by the inverse of the structure size) yield a diverging, anomalously large photonic density of states, which can be appreciably larger than that of isotropic SPPs (2, 8). Such polariton properties promise intriguing applications, including planar hyperlenses (2, 8), diffraction-free polariton propagation (6, 13), engineering of polariton wavefronts (6), 2D topological transitions (8), and super-Coulombic optical interactions (10).

HMSs could be created artificially by lateral structuring of thin layers of an isotropic material (2, 6, 13). Alternatively, 2D materials with natural in-plane anisotropy, e.g., black phosphorous, could represent a natural class of HMSs (1416). However, only a few experimental studies at microwave (11, 12) and visible frequencies (13) have been reported so far, demonstrating only weakly confined SPPs on structured metal surfaces. Artificial HMSs at mid-infrared and terahertz frequencies (corresponding to energies of molecular vibrations and thermal emission and absorption) have not been realized yet, and visualization of the diverging concave wavefronts of deeply subwavelength-scale confined in-plane hyperbolic polaritons on either artificial or natural HMSs has been elusive.

Here we propose, design, and fabricate a mid-infrared HMS by lateral structuring of thin layers of the polar van der Waals (vdW) material hexagonal boron nitride (hBN). In contrast to metal layers, they support strongly volume-confined phonon polaritons (quasiparticles formed by the coupling of light with lattice vibrations) with notably low losses, thus representing a suitable basis for mid-infrared HMSs.

The material hBN is a polar vdW (layered) crystal, thus possessing a uniaxial permittivity (1723). It has a mid-infrared Reststrahlen band from 1395 to 1630 cm−1 (24), where the in-plane permittivity is negative and isotropic, εhBN,x = εhBN,y = εhBN,⊥ < 0, and the out-of-plane permittivity is positive, εhBN,z = εhBN,|| > 0. As a result, the phonon polaritons in natural hBN exhibit an out-of-plane hyperbolic dispersion, whereas the in-plane dispersion is isotropic (1723). The isotropic (radial) propagation of the conventional hyperbolic phonon polaritons (HPhPs) in a natural hBN layer is illustrated with numerical simulations (Fig. 1, A to D), where a dipole above the hBN layer essentially launches the fundamental slab mode M0 (1719). To turn the hBN layer into an in-plane HMS, a grating structure is patterned, consisting of hBN ribbons of width w that are separated by air gaps of width g (Fig. 1E). Because of the anisotropic permittivity of hBN, however, the hBN grating represents a biaxial layer exhibiting three different effective permittivities (εeff,x ≠ εeff,y ≠ εeff,z), in contrast to uniaxial metal gratings where εeff,x ≠ εeff,y = εeff,z (which can be considered as canonical HMS structures at visible frequencies). These designed biaxial layers can support highly confined polaritons with in-plane hyperbolic dispersion. They could be considered as Dyakonov polaritons (25), which are similar to Dyakonov waves on biaxial dielectric materials (26).

Fig. 1 Dipole-launching of hBN phonon polaritons.

(A) Schematic of dipole launching of phonon polaritons on a 20-nm-thick hBN flake. h, height. (B) Simulated magnitude of the near-field distribution above the hBN flake, |E|. (C) Simulated real part of the near-field distribution above the hBN flake, Re(Ez). (D) Absolute value of the Fourier transform (FT) of panel (C). kx and ky are normalized to the photon wave vector k0. (E) Schematic of dipole launching of phonon polaritons on a 20-nm-thick hBN HMS (ribbon width w = 70 nm; gap width g = 30 nm). (F) Simulated magnitude of the near-field distribution above the hBN HMS, |E|. (G) Simulated real part of the near-field distribution above the hBN HMS, Re(Ez). (H) Absolute value of the FT of panel (G). The features revealed by the FT of the dipole-launched polaritons can be well fitted by a hyperbolic curve (white dashed lines). (I to L) Simulated magnitude of the near-field distributions for HMSs with different gap sizes and operation frequencies. The grating period w + g is fixed to 100 nm in all simulations. The white arrows in (B) and (F) display the simulated power flow.

We first applied effective medium theory (25) to determine the parameters required for the grating to function as an HMS. The effective permittivities were calculated as a function of ribbon and gap widths, w and g (figs. S1 and S2), according toEmbedded Image(1)Embedded Image(2)Embedded Image(3)where ξ = g/(w + g) is the so-called filling factor. We find that the condition for well-pronounced in-plane hyperbolic dispersion, –10 < Re(εeff,y)/Re(εeff,x) < 0, can be fulfilled in the frequency range 1400 to 1500 cm−1 for filling factors in the order of ξ = 0.5. For example, at a frequency ω = 1425 cm−1hBN,⊥ = –22.2 + 0.9i and εhBN,|| = 2.6), we obtain εeff,x = 3.7, εeff,y = −15.2 + 0.6i, and εeff,z = 2.1 for w = 70 nm and g = 30 nm, which corresponds to a grating structure that can be fabricated by electron beam lithography and etching. Note that the same effective in-plane permittivities for a metal grating [Re(εmetal) < –1000 at mid-infrared frequencies] would require 100-nm-wide ribbons separated by less than 1-nm-wide gaps (fig. S1), thus strongly challenging their fabrication. Alternatively, one could use doped semiconductors and (isotropic) polar crystals, where the permittivities in the mid-infrared and terahertz spectral range are similar to that of hBN (27, 28). However, the losses in doped semiconductors are typically larger than those in hBN. Phonon polaritons in polar crystals such as SiC exhibit low losses similar to hBN, but thin layers are difficult to grow without defects, which increase losses (27, 28). Thus, hBN represents a promising material for the experimental realization of grating-based HMSs, owing to the easy preparation of high-quality single-crystalline thin layers.

To verify the HMS design parameters, we carried out numerical simulations (see supplementary materials, note S3) of dipole-launched polaritons on a 20-nm-thick hBN grating, using w = 70 nm, g = 30 nm, and bulk hBN permittivities at ω = 1425 cm−1 (Fig. 1, F and G). The typical hyperbolic polariton rays can be seen in the intensity image (Fig. 1F), whereas the real part of the electric field distribution reveals the concave polariton wavefronts (Fig. 1G). The formation of these wavefronts arises from an interference phenomenon of polaritons that propagate with a direction-dependent wavelength (determined by the hyperbolic isofrequency curves) at a given frequency. Fourier transform (FT) of Fig. 1G corroborates the polaritons’ in-plane hyperbolic dispersion and large wave vectors (deep subwavelength-scale confinement) thus showing that the biaxial grating structure functions as a HMS (Fig. 1H). We repeated the numerical simulation of dipole-launched polaritons on a 20-nm-thick biaxial layer with the corresponding effective permittivities (fig. S3). Excellent quantitative agreement is found with the simulated near-field distribution above the grating structure.

The numerical simulations also show that the wave vector (and thus the confinement) of the hyperbolic metasurface phonon polaritons (HMS-PhPs) is increased compared to that of the conventional HPhPs on the natural hBN layer (compare Fig. 1H with 1D). They further demonstrate that the HMS-PhP propagation depends on frequency (Fig. 1, J to L) and that it can be tuned by varying the structure size (Fig. 1, F, I, and J).

For an experimental demonstration of our proposed metasurface, we etched a 5 μm–by–5 μm grating (schematic in Fig. 2A and topography image in Fig. 2B) into a 20-nm-thick exfoliated flake of isotopically enriched (2931) low-loss hBN (see supplementary materials, note S1). The ribbon and slit widths are 75 and 25 nm, respectively (fig. S4). Near-field polariton interferometry was used to show that the grating supports polaritons (17, 18). The metallic tip of a scattering-type near-field scanning optical microscope (s-NSOM), acting as an infrared antenna, concentrates an illuminating infrared beam to a nanoscale spot at the tip apex, which serves as a point source to launch polaritons on the sample (Fig. 2A). The tip-launched polaritons reflect at sample discontinuities (such as edges and defects), propagate back to the tip, and interfere with the local field below the tip. Recording the tip-scattered field (amplitude signal s in our case; see supplementary materials, note S2) as a function of the tip position yields images that exhibit interference fringes of λp/2 spacing, where λp is the polariton wavelength (17, 18).

Fig. 2 Polariton-interferometry imaging of phonon polaritons on a 20-nm-thick hBN HMS.

(A) Schematic of the near-field polariton interferometry experiment. IR, infrared. (B) Topography image of the hBN HMS (nominal grating parameters are w ≈ 75 nm and g ≈ 25 nm; see also fig. S4). (C) Near-field images (amplitude signal s) recorded at four different frequencies. a.u., arbitrary units. (D) s-NSOM amplitude profiles along the solid (vertical) and dashed (horizontal) white lines in (C). (E) Illustration of the polariton interferometry contrast mechanism. The tip launches phonon polaritons on the HMS (indicated by simulated near fields). The polaritons with wave vector parallel to the grating reflect at the lower horizontal boundary (indicated by the black arrow) and interfere with the local field underneath the tip. Tip-launched polaritons propagating in other directions cannot be probed by the tip. The orange dashed lines mark the boundaries of the HMS. (F and G) Experimental (squares) and numerically calculated (solid lines) wave vectors of phonon polaritons on the unpatterned flake and the HMS, respectively. The line colors indicate the frequency ω according to (D).

Figure 2C shows the polariton interferometry images of our sample measured at four different frequencies. On both the grating (HMS) and the surrounding (unpatterned) hBN flake, polariton fringes are observed. On the grating, we see fringes only parallel to the horizontal HMS boundary, which could be explained by a close-to-zero reflection at the left and right boundaries of the grating, or, more interestingly, by the absence of polariton propagation in the x direction (horizontal), the latter being consistent with hyperbolic polariton dispersion. We further observe a nearly twofold-reduced fringe spacing on the grating, dHMS, compared to that of the unpatterned flake, dhBN (see line profiles in Fig. 2D), indicating superior polaritonic-field confinement on the grating. For further analysis (see also fig. S5), we compare in Fig. 2, F and G, the experimental polariton wave vectors k = 2π/λp = π/d (squares) with isofrequency curves of the calculated polariton wave vectors (solid lines). The calculation predicts a hyperbolic isofrequency curve for the grating polaritons, where the wave vector in the y direction is increased by nearly a factor of two, which quantitatively matches our experimental observation well. Although the polariton confinement increases on the HMS, the calculated relative propagation length [often used as figure of merit (FOM) = k/γ, with k and γ being the real and imaginary parts of the complex wave vector K (17, 31)] and polariton lifetime remain nearly the same (fig. S6). Experimentally, however, the FOM and lifetime on the metasurface are reduced by more than 35% as compared to that of polaritons on the unpatterned flake, which we attribute to polariton losses caused by fabrication imperfections leading, for example, to polariton scattering (figs. S7 and S8).

The near-field images provide experimental indication that the hBN grating functions as an in-plane HMS. However, they do not reveal anomalous (concave) wavefronts such as the ones observed in Fig. 1. This can be understood by considering that only the polaritons propagating perpendicular to the metasurface boundary are back-reflected to the tip and thus recorded (Fig. 2E). The anomalous wavefronts are the result of interference of hyperbolic polaritons propagating in all allowed directions. To obtain real-space images of the anomalous wavefronts, we performed near-field imaging of HMS polaritons emerging from a nanoscale confined source located directly on the sample.

For nanoimaging of the polariton wavefronts, we used antenna-based polariton launching (32). A gold rod acting as an infrared antenna was fabricated on top of the sample studied in Fig. 2 (schematic in Fig. 3A and topography image in Fig. 3B). Illumination with p-polarized infrared light excites the antenna, yielding nanoscale concentrated fields at the rod extremities, which launch polaritons on either the metasurface or the unpatterned flake (upper and bottom parts of Fig. 3, B and C, respectively). The polariton field propagating away from the antenna, Ep, interferes with the illuminating field, Ein, yielding interference fringes on the sample (illustrated by solid lines in Fig. 3B) (19). This pattern is mapped by recording the field scattered by the metal tip of the s-NSOM while the sample is scanned. Because Ein is constant (i.e., independent of sample position), the interference pattern observed in the amplitude image directly uncovers the spatial distribution of the polariton field Ep and thus the polariton wavefronts [note that retardation in first-order approximation can be neglected owing to the much shorter polariton wavelength compared to the illuminating photon wavelength (19)].

Fig. 3 Wavefront imaging of antenna-launched HMS-PhPs.

(A) Schematic of the experiment. (B) Topography image. The lines illustrate wavefronts of HMS-PhPs on the HMS (yellow and black) or phonon polaritons on the unpatterned flake (yellow and blue). (C) Near-field image recorded at ω = 1430 cm−1, clearly revealing concave wavefronts of HMS-PhPs emerging from the rod’s upper extremity.

Figure 3C shows a near-field image of the antenna on the hBN sample at ω = 1430 cm−1. In the lower part of the image, we clearly observe the conventional (convex) polariton fringes, which are caused by antenna-launched HPhPs on the unpatterned hBN layer (see also fig. S9). The upper part of the image, in notable contrast, exhibits anomalous polariton fringes emerging from the rod’s upper extremity. They clearly reveal the concave wavefronts of a diverging polariton beam on the hBN grating. The image thus provides clear experimental visualization of in-plane hyperbolic polaritons and thus verifies that the grating functions as a HMS. By varying the illumination frequency, the anomalous polariton wavefronts can be tuned (Fig. 4A) from smoothly concave [nearly diffraction-free polariton propagation (6)] at ω = 1435 cm−1 to a wedge-like shape at ω = 1415 cm−1. We corroborate the experimental near-field images with the numerical simulations shown in Fig. 4B, which indeed show an excellent agreement, particularly regarding the fringe spacing and curvatures.

Fig. 4 Frequency dependence of HMS-PhP wavefronts.

(A and B) Experimental and calculated near-field distribution of HMS-PhPs launched by the antenna at three different frequencies. Black arrows in (A) indicate the fringes of polaritons launched by the tip and reflected at the boundary between the HMS and the unpatterned flake. Black dashed lines indicate the extremity of the gold rod. (C) Absolute value of the FT of the images shown in (A). White dashed lines represent the numerically calculated isofrequency curves of antenna-launched HMS-PhPs. The features in the gap between the hyperbolic isofrequency curves correspond to the FT of the antenna fields that are not coupled to polaritons (32), analogous to the central circular feature in the FT of the dipole-launched HMS-PhPs (Fig. 1H). The light-blue circle at ω = 1425 cm−1 marks a pixel whose value is still above the noise floor. The largest polariton wave vectors thus amount to about k = (kx2 + ky2)0.5 = [(15k0)2 + (15k0)2]0.5 > 20k0.

For simplicity, we did not include the metallic tip into the calculations, which in the experiment launches polaritons simultaneously with the gold antenna. Analogous to Fig. 2, the tip-launched polaritons reflect at the boundary between the hBN grating and the unpatterned hBN flake, yielding horizontal fringes in the experimental near-field images (marked by arrows in Fig. 4A) that are not seen in the simulated images (Fig. 4B). Note that the tip-launched polaritons are weakly reflected at the gold antenna and thus are not producing disturbing interference with the antenna-launched polaritons. The weak polariton reflection at metal structures on top of hBN samples is consistent with former observations and could be explained by the hyperbolic polaritons propagating through the hBN underneath the metal structure (19). For further details on tip-launched versus antenna-launched polaritons, see also fig. S10.

To determine the in-plane HMS-PhP wave vectors, we performed a FT of the experimental near-field images of Fig. 4A (fig. S11). The FTs are shown in Fig. 4C (see also fig. S13), clearly revealing hyperbolic features. They exhibit an excellent agreement with the numerically calculated hyperbolic dispersions of HMS-PhPs (white dashed lines; see supplementary materials, note S3), thus further corroborating that the real-space images in Fig. 4A reveal the wavefronts of in-plane hyperbolic polaritons. Figure 4C also verifies the large polariton wave vectors k achieved with our HMS [for example, k = (kx2 + ky2)0.5 > 20k0 at ω = 1425 cm−1, with k0 being the photon wave vector], which are considerably larger than that of the SPPs on metal-based HMSs (k < 3k0) (12, 13). In principle, the wave vectors predicted theoretically (Fig. 1H) and observed experimentally (Fig. 4C) could be larger, amounting up to 70k0, which is their theoretical limit given by the grating period. We explain the nonvisibility of such large wave vectors by the wave vector distribution of the near fields of the 250-nm-wide antenna, which exhibits dominantly small wave vectors below 28k0. For that reason, large wave vector polaritons on the HMS are only weakly excited and masked by small wave vector polaritons. To increase the excitation and relative weight of large wave vector HMS-PhPs, we suggest fabricating launching structures of smaller dimensions. Indeed, in numerical calculations, we can observe larger polariton wave vectors (and thus more pronounced polariton rays) by simply placing the polariton-launching dipole closer to the HMS surface (see fig. S12). We can also see a second (much weaker) hyperbolic feature at larger k values. We assign it to tip-launched polaritons that weakly reflect at the gold rod (fig. S13). Because of their weak reflection, they are barely recognized in the real-space images of Fig. 4A. More interestingly, the FTs of the near-field images verify that the opening angle θ of the hyperboloids decreases with increasing frequency (fig. S14). This has been predicted in numerous previous theoretical and numerical studies (6, 8) and now can be directly observed in experimental data.

Considering that fabrication of nanoscale gratings by electron beam lithography and etching is a widely applicable technique, we envision HMSs based on other vdW materials (MoS2, Bi2Se3, etc.) or multilayer graphene samples, as well as on thin layers of polar crystals (SiC, quartz, etc.) or low-loss doped semiconductors (27, 28). Combinations of different materials could lead to HMSs covering the entire spectral range, from mid-infrared to terahertz frequencies. The combined advantage of strong polariton-field confinement, anisotropic polariton propagation, tunability by geometry and electric gating, as well as the possibility of developing vdW heterostructures (33), could open exciting new possibilities for flatland infrared, thermal, and optoelectronic applications, such as infrared chemical sensing, planar hyperlensing (8, 18, 21), exotic optical coupling (10), and manipulation of near-field heat transfer (2, 8). Real-space wavefront nanoimaging of in-plane hyperbolic polaritons, as demonstrated in our work, will be an indispensable tool for verifying new design principles and for quality control.

Supplementary Materials

Materials and Methods

Figs. S1 to S14

References (3436)

References and Notes

  1. See supplementary materials.
Acknowledgments: Funding: The authors acknowledge support from the European Commission under the Graphene Flagship (GrapheneCore1, grant no. 696656), the Marie Sklodowska-Curie individual fellowship (SGPCM-705960), the Spanish Ministry of Economy, Industry, and Competitiveness (national projects MAT2015-65525-R, MAT2015-65159-R, FIS2014-60195-JIN, MAT2014-53432-C5-4-R, FIS2016-80174-P, MAT2017-88358-C3-3-R and the project MDM-2016-0618 of the Maria de Maeztu Units of Excellence Programme), the Basque government (PhD fellowship PRE-2016-1-0150), the Regional Council of Gipuzkoa (project no. 100/16), and the Department of Industry of the Basque Government (ELKARTEK project MICRO4FA). Further, support from the Materials Engineering and Processing program of the NSF, award number CMMI 1538127, and the II−VI Foundation is greatly appreciated. Author contributions: P.L. and R.H. conceived the study. Sample fabrication was performed by I.D. and S.V., coordinated by S.V., and supervised by F.C. and L.E.H. P.L. performed the experiments and simulations. F.J.A.-M. and A.Y.N. contributed to the simulations. S.L. and J.H.E. grew the isotopically enriched boron nitride. R.H. coordinated and supervised the work. P.L. and R.H. wrote the manuscript with the input of all other co-authors. Competing interests: R.H. is cofounder of and on the scientific advisory board of Neaspec GmbH, a company producing scattering-type near-field scanning optical microscope systems, such as the one used in this study. The remaining authors declare no competing financial interests. Data and materials availability: All data are available in the manuscript or the supplementary materials.
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