Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing — TEI-tagged view

Peining LipersName, Martin LewinpersName, Andrey V. KretininpersName, Joshua D. CaldwellpersName, Kostya S. NovoselovpersName, Takashi TaniguchipersName, Kenji WatanabepersName, Fabian GaussmannpersName, Thomas TaubnerpersName (2015date). “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing.” Nature Communicationstitle·j.

Object of study — hyperbolic phonon polaritonsterm·key in a flat hexagonal boron nitrideterm·dom slab used for near-field imagingterm·key and focusingterm·key

Research question — how the two natural hyperbolic regimes of one homogeneous material affect nanoimaging and focusingterm·key

Contribution — demonstration of enlarged imaging and sub-diffractionalterm·key focusingterm·key through hBNterm·dom in both Type I and Type II bands

Full text — tagged

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Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusingterm·key Abstract Hyperbolic materials exhibit sub-diffractionalterm·key, highly directional, volume-confined polariton modes. Here we report that hyperbolic phonon polaritonsterm·key allow for a flat slab of hexagonal boron nitrideterm·dom to enable exciting near-field optical applications, including unusual imaging phenomenon (such as an enlarged reconstruction of investigated objects) and sub-diffractionalterm·key focusingterm·key. Both the enlarged imaging and the super-resolution focusingterm·key are explained based on the volume-confined, wavelength dependent propagation angleterm·var of hyperbolic phonon polaritonsterm·key. With advanced infrared nanoimaging techniques and state-of-art mid-infraredterm·key laser sources, we have succeeded in demonstrating and visualizing these unexpected phenomena in both Type I and Type II hyperbolic conditions, with both occurring naturally within hexagonal boron nitrideterm·dom. These efforts have provided a full and intuitive physical picture for the understanding of the role of hyperbolic phonon polaritonsterm·key in near-field optical imaging, guiding, and focusingterm·key applications.

The propagation of sub-diffractionalterm·key waves in hyperbolic media 1 enables many unusual optical possibilities such as hyperlensingterm·key 2 3 4 , negative refraction 5 6 , enhanced quantum radiation 7 , nanolithography 8 and sub-diffractionalterm·key resonators 9 10 . Very recently, it was demonstrated that the highly directional propagation of volume-confined, hyperbolic polaritonsterm·dom (HPsterm·dom) is key for these sub-diffractionalterm·key phenomena 8 10 11 . Their directionality derives from the sign and magnitude of the two principal (in- and out-of-plane) components of the dielectric-permittivity tensor ( ), which have opposite signs in hyperbolic materials. The propagation angleterm·var θ (for example, the angle between the Poynting vector and the z axis) of the HPsterm·dom in hyperbolic media can be roughly approximated as 10 , where ɛ t = ɛ xx = ɛ yy and ɛ z = ɛ zz are the in- and out-of-plane dielectric permittivities of the hyperbolic medium, respectively. Therefore, by controlling the ratio of the two principal dielectric components, the propagation direction of the HPsterm·dom can be tuned.

Until very recently, hyperbolic media have been explored through man-made hyperbolic metamaterialterm·dom (HMMterm·dom) structures, such as metal-dielectric multilayers 4 5 , nanowire 6 12 or nanopyramid arrays 9 embedded within a dielectric medium. In HMMsterm·dom, the effective dielectric permittivities are determined by the geometric parameters of their subwavelength unit cells 1 . As such, the maximum wavevector k that can be induced to propagate through the material is limited by the size of the artificial unit cell. This in turn limits the degree of optical confinement and spatial resolution that can be realized. Furthermore, the high lossesterm·dom associated with noble metals 13 14 15 used in man-made HMMterm·dom structures result in short propagation lengthsterm·dom, quite broad resonance linewidths and in terms of hyperlens designs, low transmission efficiency.

During the search for better plasmonic materials 14 15 , polar dielectrics capable of supporting phonon-polaritons such as silicon carbide 16 17 18 19 20 and hexagonal boron nitrideterm·dom (hBNterm·dom) 10 11 21 have been demonstrated as superior alternatives to metals at mid-infraredterm·key to THz frequencies. Interestingly, many phonon-resonant materials such as quartz 22 , zinc oxide 23 , calcite 24 and hBNterm·dom 10 11 21 are natural hyperbolic materials 25 26 27 . These natural hyperbolic materials support hyperbolic phonon-polariton modes within homogeneous crystals with atomic-scale unit cells, thus the upper limit on the highest propagating wavevectors k associated with artificial metal-dielectric HMMsterm·dom is no longer an issue. Instead, photonic confinement within tiny volumes in the few nanometre range becomes possible. This was recently demonstrated by Dai et al. 11 where surface phonon polariton propagation within a three monolayer (<1 nm) thin flake of hBNterm·dom was reported. It is the propagation of such high- k fields that are scattered off or launched from deeply sub-diffractionalterm·key objects that is at the heart of super-resolution imaging. These benefits are also coupled with a drastic reduction in the optical losses compared with HMMsterm·dom, which results in improved performance, that is, higher field confinement 10 11 and improved image resolution.

In contrast to HMMsterm·dom reported to date, hBNterm·dom offers the additional functionality of sub-wavelength imaging in different spectral regions through the presence of two separate spectral bands ( Supplementary Fig. 1 ) that exhibit inverted hyperbolic response, making this an ideal material for exploring the basic phenomenon of HPsterm·dom. These two regimes are referred to as the lower and upper Reststrahlen bandsterm·dom 10 11 , where this term refers to the spectral range between the longitudinal and transverse optic phonons of a polar crystal where a negative real part of the dielectric function is observed. The presence of two bands results from the highly anisotropic crystal structure of hBNterm·dom, where a , b and c axis oriented optic phonons are supported and are widely separated in frequency 28 . These two bands not only exhibit hyperbolic behaviour, but the crystal axis featuring negative real permittivity is inverted, thus the lower and upper bands offer Type-I (Re( ɛ t ) > 0 and Re( ɛ z ) < 0 in ∼760 < ω < 825 cm −1 ) and Type-II (Re( ɛ t ) < 0 and Re( ɛ z ) > 0 in ∼1,360 < ω < 1,610 cm −1 ) hyperbolic response, respectively. The inversion of the signs of the dielectric function results in unusual behaviour, such as a negative (positive) z-component of the group velocity in the upper (lower) Reststrahlen bandsterm·dom. This results in unique phenomenon such as higher order resonance modes occurring at lower (higher) frequencies. Until now, due to a lack of a homogeneous material exhibiting both types of hyperbolicity, a comprehensive study of the impact of these two unique regimes for nanoimaging and super-resolution focusingterm·key have not been experimentally probed, with CaldwellpersName et al. 10 providing the only prior study comparing the unique behaviours of these two regimes, albeit within the context of three-dimensionally confined cavities. In addition to providing a homogeneous medium exhibiting both Type I and II hyperbolicity, hBNterm·dom also exhibits much lower losses (higher efficiencies) than plasmonic materials, with the imaginary part of the dielectric function, Im( ɛ t ) ∼ 0.1 for Re( ɛ t )=−1 at ω =1573, cm −1 and Im( ɛ z ) ∼ 0.1 for Re( ɛ z )=−1 at ω =809 cm −1 , which is crucial for realizing extended propagation and detection of high- k polariton modes (deeply sub-diffractionalterm·key confinement) 10 11 17 .

The dielectric permittivities are also highly dispersive in these two regions, giving rise to a frequency-dependent ratio between ɛ t and ɛ z . Thus, because of the presence of both Type I and II hyperbolicity, from equation (1) we can predict that the propagation angleterm·var θ will be an increasing (decreasing) function of the frequency in the lower (upper) Reststrahlen bandsterm·dom. As shown in Fig. 1a,b , as the frequency is increased, θ increases from about 16° to 87° (Δ θ ≈71°) within the Type I lower Reststrahlen bandterm·dom, while it decreases from θ ≈83° to θ ≈2°(Δ θ ≈ 81°) in the Type II upper Reststrahlen bandterm·dom.

Here we experimentally verify this inversion of the propagation angleterm·var within the two spectral bands, providing near-field imagingterm·key of sub-diffractionalterm·key objects under a thin slab of hBNterm·dom. This investigation also enabled the experimental demonstration of the unusual imaging properties of both Type I and II hyperbolic media, thereby providing the physical description necessary to realize and optimize near-field imagingterm·key using natural hyperbolic media.

Results Theory and simulations This frequency-dependent tuning of the angular HP propagation in hBNterm·dom and the suitability of this material for near-field imagingterm·key can be easily quantified and visualized via two-dimensional (2D) numerical calculations. For this, we consider a 0.3 μm wide gold stripe on a Si substrate with an hBNterm·dom cover layer (the thickness h =1 μm) illuminated by a p -polarized plane wave incident from the top. Simulated electric-field distributions (| E z |) at six typical operation frequencies are presented in Fig. 1c–h , and demonstrate the directional nature of the HPsterm·dom. Here the high- k fields scattered from the edges of the embedded gold stripe are induced to propagate within the hBNterm·dom flake (as marked in Fig. 1d ), with the angle of propagation being directly dependent upon the frequency of operation. As stated previously 1 2 3 4 , in the absence of the hyperbolic dispersion, such high- k modes would be evanescent (that is, decay rapidly) within the medium. Each edge of the Au stripe excites two sub-diffractionalterm·key HPsterm·dom that propagate at the angles ± θ . This frequency dependent propagation angleterm·var quantitatively agrees with the analytical predictions based on equation (1) (see Fig. 1a,b ), therefore the propagation angleterm·var can be predicted via the simple ratio of the extraordinary ( z axis) and ordinary ( x – y plane) components of the anisotropic dielectric function of hBNterm·dom.

The anticipated super-resolution imaging performance of the hBNterm·dom slab is directly tied to the propagation angleterm·var, as demonstrated in Fig. 1c-h , which as noted above is directly dependent on the type of hyperbolicity. For instance, at wavelengths with very low propagation anglesterm·var ( Fig. 1c,f ), the image of the sub-diffraction Au stripe is nearly perfectly restored on the top surface of the hBNterm·dom, similar to near-field superlensing 29 30 31 . Namely, the restored width d ′ is nearly identical to the actual width d of the investigated stripe (for example, d ′≈309 nm, around λ /40-resolution at ω =778.2 cm −1 or λ =12.85 μm). However, as the angle is increased ( Fig. 1d,e for the lower and Fig. 1g,h for the upper Reststrahlen bandsterm·dom), an enlarged outline of the object image is obtained with the width D ( ω )= d +2 h tan θ ( ω ). Note that due to the inversion of the dependence of θ on ω between the two spectral bands, superlensing-type response is observed at low and high frequencies within the lower and upper Reststrahlen bandsterm·dom, respectively, while the enlarged imaging behaviour is observed at high and low frequencies.

This unusual enlargement can be clearly observed in the more practical three-dimensional (3D) cases. As shown in Fig. 2a , the 0.6-μm-diameter gold disc is once again perfectly restored at very shallow angles; however, at larger propagation anglesterm·var a double concentric ring-like field distribution is recorded in the near-field ( Fig. 2b ), rather than a direct replication of the original field distribution of the object. This enlarged pattern results from the frequency-dependent propagation angleterm·var of the HPsterm·dom (cone-like shape for 3D case, see the sketch in Fig. 2c ). This unexpected phenomenon is also found for other shapes (like a Au square and stripe) as shown in Fig. 2d–i . Intriguingly, the trace of the HP cones reconstructs the enlarged and slightly distorted pattern that is still able to identify the outline (shape) information of the object. Quantitatively, through recording the HP-reconstructed outline ( D ( ω )), we can extract the geometric size and shape from the strict relationship of D ( ω )= d +2 h tan θ ( ω ). These results suggest an interesting HP-based imaging scenario, which will be verified and visualized by our experimentsterm·mth below.

Experimental results in Type I hyperbolic band The predicted imaging mechanism is verified by our experimentsterm·mth first in the Type I hyperbolic band, as presented in Fig. 3 . A schematic of the experimental setup is provided in Fig. 3a where the images restored by the hBNterm·dom layer are recorded using a scattering-type scanning near-field optical microscope (s-SNOMterm·key). We use a 0.15-μm-thick exfoliated hBNterm·dom flake to image the underlying, 30 nm tall, gold nanodiscs with 0.3-μm diameter and 1.3-μm centre-to-centre separation. The metallic tip of the s-SNOMterm·key is illuminated by a home-built, tunable broadband infrared laser 32 33 with the peak position of the laser spectrum (inset in Fig. 3a ) matched to the lower, Type-I hyperbolic region of hBNterm·dom (760 cm −1 < ω <825 cm −1 ). Both the optical and topographic information at the top surface of the hBNterm·dom layer are collected simultaneously (details in Methods). In the obtained topographic image ( Fig. 3b ), the gold discs are masked by the covering hBNterm·dom layer, while in the broadband-SNOM image ( Fig. 3c ), all three nanodiscs are clearly resolved with bright contrast (that is, high signal-to-background ratio). To ensure that the imaging is indeed due to the hyperbolic nature of the hBNterm·dom slab, a control image was also collected at a frequency outside of the lower Reststrahlen bandterm·dom using a CO 2 laser at ω =952 cm −1 , where both components of the dielectric function are positive (Re( ɛ t )=8.8 and Re( ɛ z )=2). As shown in Fig. 3e , in contrast to the hyperbolic case, only weak features of the discs are observed through the thin hBNterm·dom layer in the control experimentterm·mth. This is further demonstrated by the line profiles taken across the two discs for both cases presented in Fig. 3f , with a marked enhancement in the imaging efficiency observed in the hyperbolic regime. Such an effect would be further amplified within thicker hBNterm·dom slabs, whereby any structural morphology would be totally lost, but the near-field imagingterm·key properties retained. The hyperbolic images also provided a narrower FWHM (full width at half maximum) of about 0.5 μm in addition to the markedly improved contrast (signal-to-background ratio). Considering the resolved deeply subwavelength optical FWHM (∼ λ /24), this comparison clearly confirms the improved near-field imagingterm·key by the hBNterm·dom layer.

Although the broadband s-SNOMterm·key image shown in Fig. 3c is able to resolve the discs, it does not reflect the actual field distribution of the image due to its detection scheme 33 . Because of the broadband light source used, the detection is not monochromatic as in the simulations presented in Figs 1 and 2 . Instead, the collected images are the superposition of all the different frequency components of the broadband laser and therefore the concentric-ring field distributions are not directly observed. Further, depending on the chosen interference phase difference (constructive or destructive phases, involving the position of a reference mirror in our setup, see Methods), it can also show reversed imaging contrasts (see ref. 33 ). Therefore, the broadband s-SNOMterm·key image alone cannot directly reveal the actual image of the field distributions of the discs and the frequency dependence of the hBNterm·dom layer. For this, monochromatic s-SNOMterm·key images would be required; however, currently such sources are not readily available within this spectral range.

To determine the actual imaging response through the hBNterm·dom layer at each individual wavelength, we performed Fourier transform infrared nanospectroscopy (nano-FTIR) 11 33 along a line scan (dashed line in Fig. 3c ) across two discs. At each pixel, nano-FTIR delivers a full infrared spectrum recorded at the spatial resolution of the probing tip (∼50 nm). Thus we obtain s-SNOMterm·key signals s 2 ( ω , x ) as a function of the frequency ω and the spatial position x 11 16 33 . This hyperspectral imaging allows the extraction of detailed spatial line profiles at various frequencies as shown in Fig. 3g . For frequencies within the lower Reststrahlenterm·key but ω > 780 cm −1 , two peaks are observed for each disc (see the typical case at ω =783 cm −1 ). These peaks (with the width d ′ ∼ 0.3 μm, Supplementary Figs 2 and 3 ) correspond to the edge-excited HPsterm·dom. The distance D between the two edge-launched peaks increases from about 0.4 to ∼1.25 μm (for the right disc) when changing the frequency from 780 to 807 cm −1 , with this distance being directly related to the frequency-dependent HP propagation angleterm·var. At frequencies ω <780 cm −1 , the two edge-launched peaks are not resolved by the hBNterm·dom layer due to the very small directional angle of HPsterm·dom, leading to one single broad peak observed for each disc. On the basis of the smallest peak-to-peak separation in our results being ∼0.4 μm at ω =780 cm −1 ( λ =12.8 μm), this corresponds to a sub-diffractionalterm·key resolution of about λ /32 (also see Supplementary Fig. 3 ).

For the comparison of the theoretically predicted propagation anglesterm·var ( Fig. 1a ) and those experimentally derived from the s-SNOMterm·key measurements, we plot the experimentally determined D (blue curve and data) and corresponding directional angles θ (red curve and data) of the HPsterm·dom as functions of ω in Fig. 3h . The theoretical result (from D ( ω )= d +2 h tan θ ( ω )) is also shown for comparison. Good quantitative agreement is found between the experimentsterm·mth and theory. This verifies the predicted tuning range of the propagation angleterm·var of the HPsterm·dom to be about 35°−70° and the tunable ratio ( D / d ) to range from 1.39 to 4.2. However, certain discrepancies are still found in this comparison, and we do not observe multiple peaks originating from the multireflection of the HPsterm·dom within the hBNterm·dom slab.

Experimental results in Type II hyperbolic band To extract the near-field frequency-dependent imaging and HP propagation anglesterm·var, near-field imagingterm·key experimentsterm·mth were also performed in the Type II hyperbolic band by using a line-tunable quantum cascade laser (spanning from 1,310 to 1,430 cm −1 ). This monochromatic laser allows us to present the HP-reconstructed imaging phenomenon in a more intuitive way compared to the case with the broadband laser. First, we performed the s-SNOMterm·key measurements to image a Au stripe (about 1-μm long, 100-nm wide, as sketched in Fig. 4a ) that is covered by the 0.15-μm hBNterm·dom layer (atomic force microscopy (AFM) topography in Fig. 4b ). In comparison to the circular discs, this rectangular object can avoid the potential confusion caused by the HP cones (circular cross section) for understanding the imaging results. Because the deeply sub-diffractionalterm·key width (< λ /70) of the stripe, optical information cannot be recorded at frequencies outside the hyperbolic band, as shown in Fig. 4c . In contrast, we clearly observe enlarged optical patterns formed by the HPsterm·dom ( Fig. 4d–f ). Qualitatively, these elliptical, rectangular patterns carry and reflect the shape information of the original object. Quantitatively, from the measured width and length of the patterns, in conjunction with the known HP propagation angleterm·var, we can extract the geometric size of the investigated object. Using this approach, we estimate the width of the stripe is about 0.12 μm, and the estimated length is about 1.1 μm, which is consistent with SEM measurements of the stripe prior to hBNterm·dom exfoliation. We note that for frequencies where HPsterm·dom have smaller diffractional angles (namely, the HP cone with the very small diameter), the reconstructed image will be similar to the one-to-one near-field superlensing 29 30 31 . Therefore, in such HP-based imaging phenomenon, it has two frequency-dependent operation modes: the enlarged reconstruction and the one-to-one superlensing.

As previously discussed, we also experimentally demonstrated that the diameter of the HP cone increases with decreasing frequency, which is inverted with respect to the Type I band. These two distinct frequency dependences, found in two spectral regimes through imaging of the sub-diffractionalterm·key objects, verify again that the two types of hyperbolic dispersion exist in the hBNterm·dom crystal, without the need for fabricating HMMterm·dom structures.

In addition to the isolated structures, we also investigated periodic arrays of nanostructures. We imaged the arrays of the Au nanodiscs (5 × 5 array, sketched in Fig. 5a ) with different separations. The diameter of the discs was fixed at 0.3 μm. The gap separation between two discs varied from g =0.1 μm to g =1 μm. The experimental results are shown in Fig. 5d–f . We observed the complicated overlapping of the HP cone launched by each disc. However, with these sub-diffractionalterm·key HPsterm·dom, we have the opportunity to distinguish the deeply sub-diffractionalterm·key structures that are not readily seen in either AFM topography or near-field imagingterm·key at frequencies outside of the hyperbolic regime (see the comparison of Fig. 5b–d ).

HPsterm·dom for sub-diffractionalterm·key focusingterm·key and selective waveguiding In addition to the already proven high-resolution imaging with tunable enlargement of the outline of sub-diffractionalterm·key objects using only a simple slab of hBNterm·dom, the highly directional nature of HPsterm·dom can also result in sub-diffractionalterm·key focusingterm·key behaviour. When imaging the nanodiscs with a large diameter of 0.75 μm, we observe the focusingterm·key spot with the width of about 0.175 μm (∼ λ /40) at ω =1,420 cm −1 ( Supplementary Fig. 4 ). This is because all the HP cones launched by the nanodisc superimpose into the centre point, leading to the concentration of the light. We also investigate this focusingterm·key effect with the broadband laser in the Type I hyperbolic band. However, the obtained results are also the superposition of all the frequency components, which are not intuitive. We also note that this super-focusing effect is independently shown and discussed in ref. 34 , which was performed concurrently with the work discussed here.

Both the enlarged imaging and the super-focusing are based on the volume-confined, frequency-dependent propagation angleterm·var of HPsterm·dom in hBNterm·dom. We can envision other potential disruptive technologies based on the great potential of the highly directional HPsterm·dom. First, this frequency-selective waveguiding could be useful for photonic switching or computing, infrared filtering, or various other nanophotonic applications ( Supplementary Fig. 5a, b ). Another potential application is realized in the form of an ultracompact subwavelength spectrometer ( Supplementary Fig. 5c,d ). A natural hBNterm·dom layer should allow for the spatial separation or filtering of incoming broadband light into different wavelength channels, much like a grating, which could then be detected by subwavelength infrared detector pixels. This particular spectrometer configuration could also be used for chemical and biological detection schemes, in the form of spatially resolved infrared spectroscopy. Under broadband mid-infraredterm·key illumination the HPsterm·dom could carry the vibration (or absorption) information of molecules in contact with the surface, dispersing the spectral information at different angles, enabling them to be spatially resolved by a near-field intensity detector (like the s-SNOMterm·key tip) without the need of spectrometers.

Discussion Our work along with that of ref. 34 , demonstrate the complete hyperbolic imaging response of hBNterm·dom and its potential for improving the near-field imagingterm·key of deeply embedded objects 35 36 in both the Type I lower and Type II upper Reststrahlen bandsterm·dom, respectively. More specifically, we reveal the hyperbolic nature of the hBNterm·dom layer for near-field waveguiding, imaging, focusingterm·key and its dependence on the operational frequency. Although all our results are restricted in the near field, we also expect that these intriguing findings will benefit far-field imaging by introducing specific geometric designs, such as circular or wedge-shaped hyperlenses 2 3 . Furthermore, as a van der Waal's crystal 37 , hBNterm·dom lends itself to incorporation on non-planar and flexible substrates more amenable to true hyperlensingterm·key methodologies 4 . The realization of a naturally occurring, Type I and II hyperbolic media enable various opportunities for nanophotonics that go beyond sub-diffractionalterm·key near-field imagingterm·key and potential hyperlensingterm·key. Due to the similar material anisotropy present in other polar dielectric van der Waals crystals 37 , such as MoS 2 or WS 2 , the natural hyperbolic response of hBNterm·dom may be general to the entire class of polar 2D crystals, thus expanding the potential spectral range of this behaviour from the mid-infraredterm·key into the single-digit terahertz spectral region 17 24 .

Methods Sample preparation The gold nanostructures used for the near-field experimentsterm·mth were fabricated on a 1-μm-thick intrinsic silicon substrate using electron beam lithography into a bilayer PMMA (poly(methylmethacrylate)) resist. The nanostructures varied in size from 0.2–1 μm in diameter and in arrays with 0.1–1 μm edge-to-edge gaps. A standard liftoff procedure was used following the thermal evaporation of Cr (5 nm)/Au (30 nm) metallization.

hBNterm·dom crystals were grown using the high-pressure/high-temperature method 38 39 . The standard exfoliation process was used to randomly deposit hBNterm·dom flakes of various thicknesses onto a PMMA/PMGI (polydimethyl glutarimide) bilayer spun on a separate silicon substrate. Here the PMMA layer played the role of the flake carrier membrane and the PMGI served as a sacrificial lift-off layer later dissolved by tetramethyl ammonium hydroxide (TMAH) solution (MICROPOSIT MF-319). AFM was utilized to select specific flakes with both sufficient thickness and lateral size for the imaging experimentsterm·mth. The PMMA carrier membrane with an appropriate hBNterm·dom flake was lifted-off from the substrate and put onto the supportive metal ring held by a home-made micromanipulator. With the help of the micromanipulator, the hBNterm·dom flake was aligned and transferred face down onto the predefined gold nanostructure by releasing the carrier membrane from the metal ring. Following the transfer, the sample with the carrier membrane on was heated to 130 °C for about 10 min to soften the PMMA membrane and improve the adhesion of hBNterm·dom to the underlying nanostructures and silicon substrate. After that the carrier membrane was dissolved in acetone leaving the hBNterm·dom flake covering the entire array of nanostructures. To improve the adhesion, an ultrasonic clean in acetone and isopropyl alcohol with subsequent oxygen plasma clean was performed on the silicon substrate before the hBNterm·dom transfer. More details of this transfer technique are given in ref. 40 .

Infrared s-SNOMterm·key measurements An s-SNOMterm·key (commercially available, Neaspec GmbH) system was used to simultaneously measure the optical near fields and topography. The laser system used in Type I hyperbolic band was developed by the Fraunhofer ILT 32 33 . It consists of a commercially available picosecond-laser as the pump source and two subsequent nonlinear converter steps to cover the mid-infraredterm·key range. The peak wavelength is continuously tunable from ω =625 cm −1 (∼16 μm) to ω =1,100 cm −1 (∼9 μm) with bandwidths of some tens to more than hundred wavenumbers. At a repetition rate of 20 MHz and pulse duration of 10 ps, the system provides an average power of up to 10 mW. To address the lower Type-I hyperbolic region of the hBNterm·dom, the peak position of the laser spectrum in our measurements was set to be at around ω = 790 cm −1 (12.7 μm) with a FWHM of about 90 cm −1 . To suppress the far-field background contribution and solely measure the near-field contribution, the optical signal was demodulated at higher harmonics ( n Ω) of the oscillation frequency (Ω ∼ 270 kHz) of the cantilever (in our cases, n =2 for the broadband s-SNOMterm·key). Nano-FTIR spectra were obtained by constantly moving the mirror in the reference arm of the Michelson interferometer, recording the resulting interferograms and their corresponding complex Fourier transformation 11 33 . In contrast to conventional far-field FTIR, this setup allows to record spectral information with a spatial resolution of down to several tens nm. For 2D imaging, the position of the reference mirror was fixed to be at the position about λ /8 away from the maximum of the interference signals. This allows for a visualization of even small spectral changes 31 . The extracted line profiles shown in Fig. 3g were numerically smoothed by using a fast Fourier transform smoothing with three adjacent pixels. This smoothing does not improve the resolution, but rather leads to a conservative estimation of resolution (details in Supplementary Figs 2 and 3 ). The monochromatic quantum cascade laser used in the Type II band ( Figs 4 and 5 ) is commercially available from Daylight Solutions. The demodulation order n = 3 is chosen for the monochromatic s-SNOMterm·key imaging. Near-field optical amplitude ( s n ) and phase ( ϕ n ) are separated with an interferometric setup 11 19 .

Numerical simulations 2D simulations ( Fig. 1 ) were carried out by the finite-element software COMSOL Multiphysics. A plane-wave illumination was set by using scattering boundary condition. The surrounding boundaries used perfectly matched layer absorbing boundary conditions. 3D simulations ( Fig. 2 ) were done by using CST Microwave Studio. Open boundary conditions were used. We also checked different mesh sizes to make sure that all the simulations reach proper convergence. The dielectric data of hBNterm·dom used in all the simulations are extracted from far-field FTIR measurements 10 .

Additional information How to cite this article: Li, P. et al. Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusingterm·key. Nat. Commun. 6:7507 doi: 10.1038/ncomms8507 (2015).

Supplementary Material Supplementary Figures 1-5.