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Peining Li, Martin Lewin, Andrey V. Kretinin, Joshua D. Caldwell, Kostya S. Novoselov, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Fabian Gaussmann, Thomas Taubner

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[Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing](https://mdr.nims.go.jp/datasets/e7a64ed9-0e7b-4e5a-a67a-6078c2d994da)

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Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusingARTICLEReceived 24 Dec 2014 | Accepted 14 May 2015 | Published 26 Jun 2015Hyperbolic phonon-polaritons in boron nitridefor near-field optical imaging and focusingPeining Li1, Martin Lewin1,2, Andrey V. Kretinin3, Joshua D. Caldwell4, Kostya S. Novoselov3, Takashi Taniguchi5,Kenji Watanabe5, Fabian Gaussmann2 & Thomas Taubner1,2Hyperbolic materials exhibit sub-diffractional, highly directional, volume-confined polaritonmodes. Here we report that hyperbolic phonon polaritons allow for a flat slab of hexagonalboron nitride to enable exciting near-field optical applications, including unusual imagingphenomenon (such as an enlarged reconstruction of investigated objects) andsub-diffractional focusing. Both the enlarged imaging and the super-resolution focusingare explained based on the volume-confined, wavelength dependent propagation angleof hyperbolic phonon polaritons. With advanced infrared nanoimaging techniques andstate-of-art mid-infrared laser sources, we have succeeded in demonstrating and visualizingthese unexpected phenomena in both Type I and Type II hyperbolic conditions, with bothoccurring naturally within hexagonal boron nitride. These efforts have provided a full andintuitive physical picture for the understanding of the role of hyperbolic phonon polaritons innear-field optical imaging, guiding, and focusing applications.DOI: 10.1038/ncomms8507 OPEN1 Institute of Physics (IA), RWTH Aachen University, Aachen 52056, Germany. 2 Fraunhofer Institute for Laser Technology ILT, Aachen 52074, Germany.3 School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK. 4 US Naval Research Laboratory, 4555 OverlookAvenue, S.W., Washington, D.C. 20375, USA. 5 National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan. Correspondence andrequests for materials should be addressed to J.D.C (email: joshua.caldwell@nrl.navy.mil) or to Th.T. (taubner@physik.rwth-aachen.de).NATURE COMMUNICATIONS | 6:7507 | DOI: 10.1038/ncomms8507 | www.nature.com/naturecommunications 1& 2015 Macmillan Publishers Limited. All rights reserved.mailto:joshua.caldwell@nrl.navy.milmailto:taubner@physik.rwth-aachen.dehttp://www.nature.com/naturecommunicationsThe propagation of sub-diffractional waves in hyperbolicmedia1 enables many unusual optical possibilities such ashyperlensing2–4, negative refraction5,6, enhanced quantumradiation7, nanolithography8 and sub-diffractional resonators9,10.Very recently, it was demonstrated that the highly directionalpropagation of volume-confined, hyperbolic polaritons (HPs) iskey for these sub-diffractional phenomena8,10,11. Theirdirectionality derives from the sign and magnitude of the twoprincipal (in- and out-of-plane) components of the dielectric-permittivity tensor (~e ¼ diag exx; eyy; ezz� �), which have oppositesigns in hyperbolic materials. The propagation angle y (forexample, the angle between the Poynting vector and the z axis) ofthe HPs in hyperbolic media can be roughly approximated as10,y ¼ p=2� arctanffiffiffiffiffiffiffiffiffiffiffiezðoÞp=iffiffiffiffiffiffiffiffiffiffiffietðoÞp� �ð1Þwhere et¼ exx¼ eyy and ez¼ ezz are the in- and out-of-planedielectric permittivities of the hyperbolic medium, respectively.Therefore, by controlling the ratio of the two principaldielectric components, the propagation direction of the HPscan be tuned.Until very recently, hyperbolic media have been exploredthrough man-made hyperbolic metamaterial (HMM) structures,such as metal-dielectric multilayers4,5, nanowire6,12 ornanopyramid arrays9 embedded within a dielectric medium. InHMMs, the effective dielectric permittivities are determined bythe geometric parameters of their subwavelength unit cells1. Assuch, the maximum wavevector k that can be induced topropagate through the material is limited by the size of theartificial unit cell. This in turn limits the degree of opticalconfinement and spatial resolution that can be realized.Furthermore, the high losses associated with noble metals13–15used in man-made HMM structures result in short propagationlengths, quite broad resonance linewidths and in terms ofhyperlens designs, low transmission efficiency.During the search for better plasmonic materials14,15, polardielectrics capable of supporting phonon-polaritons such assilicon carbide16–20 and hexagonal boron nitride (hBN)10,11,21have been demonstrated as superior alternatives to metals atmid-infrared to THz frequencies. Interestingly, many phonon-resonant materials such as quartz22, zinc oxide23, calcite24 andhBN10,11,21 are natural hyperbolic materials25–27. These naturalhyperbolic materials support hyperbolic phonon-polariton modeswithin homogeneous crystals with atomic-scale unit cells, thus theupper limit on the highest propagating wavevectors k associatedwith artificial metal-dielectric HMMs is no longer an issue.Instead, photonic confinement within tiny volumes in the fewnanometre range becomes possible. This was recentlydemonstrated by Dai et al.11 where surface phonon polaritonpropagation within a three monolayer (o1 nm) thin flake of hBNwas reported. It is the propagation of such high-k fields that arescattered off or launched from deeply sub-diffractional objectsthat is at the heart of super-resolution imaging. These benefits arealso coupled with a drastic reduction in the optical lossescompared with HMMs, which results in improved performance,that is, higher field confinement10,11 and improved imageresolution.In contrast to HMMs reported to date, hBN offers theadditional functionality of sub-wavelength imaging in differentspectral regions through the presence of two separate spectralbands (Supplementary Fig. 1) that exhibit inverted hyperbolicresponse, making this an ideal material for exploring the basicphenomenon of HPs. These two regimes are referred to as thelower and upper Reststrahlen bands10,11, where this term refers tothe spectral range between the longitudinal and transverse opticphonons of a polar crystal where a negative real part of thedielectric function is observed. The presence of two bands resultsfrom the highly anisotropic crystal structure of hBN, where a, band c axis oriented optic phonons are supported and are widelyseparated in frequency28. These two bands not only exhibithyperbolic behaviour, but the crystal axis featuring negative realpermittivity is inverted, thus the lower and upper bands offerType-I (Re(et) 4 0 and Re(ez) o 0 in B760 o oo 825 cm� 1)and Type-II (Re(et) o 0 and Re(ez) 4 0 in B1,360 o oo1,610 cm� 1) hyperbolic response, respectively. The inversion ofthe signs of the dielectric function results in unusual behaviour,such as a negative (positive) z-component of the group velocity inthe upper (lower) Reststrahlen bands. This results in uniquephenomenon such as higher order resonance modes occurring atlower (higher) frequencies. Until now, due to a lack of ahomogeneous material exhibiting both types of hyperbolicity, acomprehensive study of the impact of these two unique regimesfor nanoimaging and super-resolution focusing have not beenexperimentally probed, with Caldwell et al.10 providing the onlyprior study comparing the unique behaviours of these tworegimes, albeit within the context of three-dimensionally confinedcavities. In addition to providing a homogeneous mediumexhibiting both Type I and II hyperbolicity, hBN also exhibitsmuch lower losses (higher efficiencies) than plasmonic materials,with the imaginary part of the dielectric function, Im(et) B 0.1for Re(et)¼ � 1 at o¼ 1573 cm� 1 and Im(ez) B 0.1 forRe(ez)¼ � 1 at o¼ 809 cm� 1, which is crucial for realizingextended propagation and detection of high-k polariton modes(deeply sub-diffractional confinement)10,11,17.The dielectric permittivities are also highly dispersive in thesetwo regions, giving rise to a frequency-dependent ratio between etand ez. Thus, because of the presence of both Type I and IIhyperbolicity, from equation (1) we can predict that thepropagation angle y will be an increasing (decreasing) functionof the frequency in the lower (upper) Reststrahlen bands. Asshown in Fig. 1a,b, as the frequency is increased, y increases fromabout 16� to 87� (DyE71�) within the Type I lower Reststrahlenband, while it decreases from yE83� to yE2�(Dy E 81�) in theType II upper Reststrahlen band.Here we experimentally verify this inversion of the propagationangle within the two spectral bands, providing near-field imagingof sub-diffractional objects under a thin slab of hBN. Thisinvestigation also enabled the experimental demonstration of theunusual imaging properties of both Type I and II hyperbolicmedia, thereby providing the physical description necessary torealize and optimize near-field imaging using natural hyperbolicmedia.ResultsTheory and simulations. This frequency-dependent tuning of theangular HP propagation in hBN and the suitability of thismaterial for near-field imaging can be easily quantified andvisualized via two-dimensional (2D) numerical calculations. Forthis, we consider a 0.3 mm wide gold stripe on a Si substrate withan hBN cover layer (the thickness h¼ 1 mm) illuminated bya p-polarized plane wave incident from the top. Simulatedelectric-field distributions (|Ez|) at six typical operation fre-quencies are presented in Fig. 1c–h, and demonstrate the direc-tional nature of the HPs. Here the high-k fields scattered from theedges of the embedded gold stripe are induced to propagatewithin the hBN flake (as marked in Fig. 1d), with the angle ofpropagation being directly dependent upon the frequency ofoperation. As stated previously1–4, in the absence of thehyperbolic dispersion, such high-k modes would be evanescent(that is, decay rapidly) within the medium. Each edge of the Austripe excites two sub-diffractional HPs that propagate at theARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms85072 NATURE COMMUNICATIONS | 6:7507 | DOI: 10.1038/ncomms8507 | www.nature.com/naturecommunications& 2015 Macmillan Publishers Limited. All rights reserved.http://www.nature.com/naturecommunicationsangles ±y. This frequency dependent propagation anglequantitatively agrees with the analytical predictions based onequation (1) (see Fig. 1a,b), therefore the propagation angle canbe predicted via the simple ratio of the extraordinary (z axis) andordinary (x–y plane) components of the anisotropic dielectricfunction of hBN.The anticipated super-resolution imaging performance of thehBN slab is directly tied to the propagation angle, as demon-strated in Fig. 1c-h, which as noted above is directly dependent onthe type of hyperbolicity. For instance, at wavelengths with verylow propagation angles (Fig. 1c,f), the image of the sub-diffractionAu stripe is nearly perfectly restored on the top surface of thehBN, similar to near-field superlensing29–31. Namely, the restoredwidth d 0 is nearly identical to the actual width d of theinvestigated stripe (for example, d0E309 nm, around l/40-resolution at o¼ 778.2 cm� 1 or l¼ 12.85 mm). However, asthe angle is increased (Fig. 1d,e for the lower and Fig. 1g,h for theupper Reststrahlen bands), an enlarged outline of the objectimage is obtained with the width D(o)¼ dþ 2h tany(o). Notethat due to the inversion of the dependence of y on o between thetwo spectral bands, superlensing-type response is observed at lowand high frequencies within the lower and upper Reststrahlenbands, respectively, while the enlarged imaging behaviour isobserved at high and low frequencies.This unusual enlargement can be clearly observed in the morepractical three-dimensional (3D) cases. As shown in Fig. 2a, the0.6-mm-diameter gold disc is once again perfectly restored at veryshallow angles; however, at larger propagation angles a doubleconcentric ring-like field distribution is recorded in the near-field(Fig. 2b), rather than a direct replication of the original fielddistribution of the object. This enlarged pattern results from thefrequency-dependent propagation angle of the HPs (cone-likeshape for 3D case, see the sketch in Fig. 2c). This unexpectedphenomenon is also found for other shapes (like a Au square andstripe) as shown in Fig. 2d–i. Intriguingly, the trace of the HPcones reconstructs the enlarged and slightly distorted patternthat is still able to identify the outline (shape) informationof the object. Quantitatively, through recording the HP-reconstructed outline (D(o)), we can extract the geometric sizeand shape from the strict relationship of D(o)¼ dþ 2h tany(o).These results suggest an interesting HP-based imagingscenario, which will be verified and visualized by our experimentsbelow.Experimental results in Type I hyperbolic band. The predictedimaging mechanism is verified by our experiments first in theType I hyperbolic band, as presented in Fig. 3. A schematic of theexperimental setup is provided in Fig. 3a where the imagesrestored by the hBN layer are recorded using a scattering-typescanning near-field optical microscope (s-SNOM). We use a0.15-mm-thick exfoliated hBN flake to image the underlying,30 nm tall, gold nanodiscs with 0.3-mm diameter and 1.3-mmcentre-to-centre separation. The metallic tip of the s-SNOM isilluminated by a home-built, tunable broadband infraredlaser32,33 with the peak position of the laser spectrum (inset inFig. 3a) matched to the lower, Type-I hyperbolic region of hBN(760 cm� 1 ooo825 cm� 1). Both the optical and topographicinformation at the top surface of the hBN layer are collectedsimultaneously (details in Methods). In the obtained topographicimage (Fig. 3b), the gold discs are masked by the covering hBNlayer, while in the broadband-SNOM image (Fig. 3c), all threenanodiscs are clearly resolved with bright contrast (that is, highsignal-to-background ratio). To ensure that the imaging is indeeddue to the hyperbolic nature of the hBN slab, a control image wasalso collected at a frequency outside of the lower Reststrahlenband using a CO2 laser at o¼ 952 cm� 1, where bothcomponents of the dielectric function are positive (Re(et)¼ 8.8and Re(ez)¼ 2). As shown in Fig. 3e, in contrast to the hyperboliccase, only weak features of the discs are observed through the thinhBN layer in the control experiment. This is furtherdemonstrated by the line profiles taken across the two discs forboth cases presented in Fig. 3f, with a marked enhancement in theimaging efficiency observed in the hyperbolic regime. Such aneffect would be further amplified within thicker hBN slabs,whereby any structural morphology would be totally lost, but thenear-field imaging properties retained. The hyperbolic imagesalso provided a narrower FWHM (full width at half maximum) ofabout 0.5 mm in addition to the markedly improved contrast(signal-to-background ratio). Considering the resolved deeplyabAirhBNSiAu dischc d ef g hDd' d'd''d'' dEkzx 1,613.8 cm–1 1,527 cm–11,459.6 cm–1795 cm–1778.2 cm–1761 cm–1arb. u.01,400 1,500 1,6000306090� (°)� (°)� (cm–1)� (cm–1)760 780 800 8200306090�Figure 1 | Frequency-dependent directional angles of the hyperbolic polaritons propagating inside the hBN. Solid lines in (a,b) the critical angle y of theHPs as a function of the frequency o in the Type-I (760ooo825 cm� 1, et40 and ezo0) and Type-II (1,360ooo1,610 cm� 1, eto0 and ez40)hyperbolic bands of the hBN. (c–h) Simulated electric-field distribution (|Ez|) at various frequencies. The directional angles evaluated from thesesimulations are plotted in a,b (colour dots) for comparison: y¼ 16� (c, at o¼ 761 cm� 1), y¼ 2� (f, at o¼ 1,613.8 cm� 1), y¼45� (d,g; at o¼ 778.2 cm� 1and o¼ 1,527 cm� 1) and y¼60� (e,h; at o¼ 795 cm� 1 and o¼ 1,459.6 cm� 1). Scale bar, 1mm (c).NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8507 ARTICLENATURE COMMUNICATIONS | 6:7507 | DOI: 10.1038/ncomms8507 | www.nature.com/naturecommunications 3& 2015 Macmillan Publishers Limited. All rights reserved.http://www.nature.com/naturecommunicationssubwavelength optical FWHM (Bl/24), this comparison clearlyconfirms the improved near-field imaging by the hBN layer.Although the broadband s-SNOM image shown in Fig. 3c isable to resolve the discs, it does not reflect the actualfield distribution of the image due to its detection scheme33.Because of the broadband light source used, the detection is notmonochromatic as in the simulations presented in Figs 1 and 2.Instead, the collected images are the superposition of allthe different frequency components of the broadband laserand therefore the concentric-ring field distributions are notdirectly observed. Further, depending on the chosen interferencephase difference (constructive or destructive phases, involvingthe position of a reference mirror in our setup, see Methods),it can also show reversed imaging contrasts (see ref. 33).Therefore, the broadband s-SNOM image alone cannot directlyreveal the actual image of the field distributions of the discsand the frequency dependence of the hBN layer. For this,monochromatic s-SNOM images would be required; however,currently such sources are not readily available within thisspectral range.To determine the actual imaging response through the hBNlayer at each individual wavelength, we performed Fouriertransform infrared nanospectroscopy (nano-FTIR)11,33 along aline scan (dashed line in Fig. 3c) across two discs. At each pixel,nano-FTIR delivers a full infrared spectrum recorded at thespatial resolution of the probing tip (B50 nm). Thus we obtains-SNOM signals s2(o, x) as a function of the frequency o and thespatial position x11,16,33. This hyperspectral imaging allows theextraction of detailed spatial line profiles at various frequencies asshown in Fig. 3g. For frequencies within the lower Reststrahlenbut o 4 780 cm� 1, two peaks are observed for each disc (see thetypical case at o¼ 783 cm� 1). These peaks (with the widthd0 B 0.3 mm, Supplementary Figs 2 and 3) correspond to theedge-excited HPs. The distance D between the two edge-launchedpeaks increases from about 0.4 to B1.25 mm (for the right disc)when changing the frequency from 780 to 807 cm� 1, with thisdistance being directly related to the frequency-dependent HPpropagation angle. At frequencies oo780 cm� 1, the two edge-launched peaks are not resolved by the hBN layer due to the verysmall directional angle of HPs, leading to one single broad peakxyzdd' d' Dd'dH Ek0arb.u.1-μm-thick hBNa b cd761 cm–1778.2 cm–1768 cm–1761 cm–1761 cm–1768 cm–1778.2 cm–1778.2 cm–1g hfeiFigure 2 | Three dimensional simulations of imaging different structures through the hBN layer. (a,b) 3D simulations of imaging a gold disc (0.6-mmdiameter) below the 1-mm-thick hBN layer (scale bars, 0.6mm). Simulated electric-field distributions (|Ez|) taken at top and bottom surface of the hBN layerfor imaging, a, at o¼ 761 cm� 1. b, at o¼ 778.2 cm� 1 show the frequency-dependent transition between perfect imaging and enlarged imaging. (c) Thesketch of the mechanism of the enlargement observed in b. (In this sketch we do not consider the influence of the illumination polarization). (d–f) |Ez|-distributions of imaging a gold square (1-mm length, 50-nm height). (g–i) |Ez|-distributions of imaging a gold bar (1-mm width, 2-mm length, 50-nm height).All these images show the frequency-dependent transition between perfect imaging and enlarged imaging of the geometric outline of the structures. Scalebars, 1.2mm (d–i). The z axis in all the images is not to scale for better visualization.ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms85074 NATURE COMMUNICATIONS | 6:7507 | DOI: 10.1038/ncomms8507 | www.nature.com/naturecommunications& 2015 Macmillan Publishers Limited. All rights reserved.http://www.nature.com/naturecommunicationsobserved for each disc. On the basis of the smallest peak-to-peakseparation in our results being B0.4 mm at o¼ 780 cm� 1(l¼ 12.8 mm), this corresponds to a sub-diffractional resolutionof about l/32 (also see Supplementary Fig. 3).For the comparison of the theoretically predicted propagationangles (Fig. 1a) and those experimentally derived from thes-SNOM measurements, we plot the experimentally determinedD (blue curve and data) and corresponding directional angles y(red curve and data) of the HPs as functions of o in Fig. 3h. Thetheoretical result (from D(o)¼ dþ 2h tany(o)) is also shown forcomparison. Good quantitative agreement is found between theexperiments and theory. This verifies the predicted tuning rangeof the propagation angle of the HPs to be about 35�� 70� and thetunable ratio (D/d) to range from 1.39 to 4.2. However, certaindiscrepancies are still found in this comparison, and we do notobserve multiple peaks originating from the multireflection of theHPs within the hBN slab.Experimental results in Type II hyperbolic band. To extract thenear-field frequency-dependent imaging and HP propagationangles, near-field imaging experiments were also performed in theType II hyperbolic band by using a line-tunable quantum cascadelaser (spanning from 1,310 to 1,430 cm� 1). This monochromaticlaser allows us to present the HP-reconstructed imaging phe-nomenon in a more intuitive way compared to the case with thebroadband laser. First, we performed the s-SNOM measurementsto image a Au stripe (about 1-mm long, 100-nm wide, as sketchedin Fig. 4a) that is covered by the 0.15-mm hBN layer (atomic forcemicroscopy (AFM) topography in Fig. 4b). In comparison to thecircular discs, this rectangular object can avoid the potentialconfusion caused by the HP cones (circular cross section) forunderstanding the imaging results. Because the deeply sub-dif-fractional width (ol/70) of the stripe, optical information cannotbe recorded at frequencies outside the hyperbolic band, as shownin Fig. 4c. In contrast, we clearly observe enlarged optical patternsformed by the HPs (Fig. 4d–f). Qualitatively, these elliptical,rectangular patterns carry and reflect the shape information ofthe original object. Quantitatively, from the measured width andlength of the patterns, in conjunction with the known HP pro-pagation angle, we can extract the geometric size of the investi-gated object. Using this approach, we estimate the width of thestripe is about 0.12 mm, and the estimated length is about 1.1 mm,which is consistent with SEM measurements of the stripe prior tohBN exfoliation. We note that for frequencies where HPs havesmaller diffractional angles (namely, the HP cone with the verysmall diameter), the reconstructed image will be similar to theone-to-one near-field superlensing29–31. Therefore, in such HP-based imaging phenomenon, it has two frequency-dependentoperation modes: the enlarged reconstruction and the one-to-onesuperlensing.As previously discussed, we also experimentally demonstratedthat the diameter of the HP cone increases with decreasingfrequency, which is inverted with respect to the Type I band.These two distinct frequency dependences, found in two spectralregimes through imaging of the sub-diffractional objects, verify0.40.81.21.6ExperimentTheoryExperimentTheoryOptical width D (μm)304560751.01.11.2Normalized s2 CO2 laserBroadbandSNOM singals s2 (a.u.) 773 777 780 783 787 790 793 797 800 803 807abcdeInfraredbroadband laser 13 nm02.11.110 nm0.550.480s2s2fgh0.00.51.0Laser intensity (a.u.)hBNDd'd' d' d'∼ 0.5 μm∼ 0.5 μm� (cm–1)� (cm–1)� (cm–1)700 800 9000.00.00.50.51.01.01.51.52.02.02.52.5 780 790 800 810� (°)x (μm)x (μm)Figure 3 | Experimental demonstration of super-resolution imaging with tunable hyperbolic polaritons in the Type I band. (a) Sketch of theexperimental setup. The right inset is the normalized laser spectrum of the used mid-infrared broadband laser. The gold nanodiscs are with 0.3-mmdiameter and 1.3-mm centre-to-centre separation. (b) The AFM topography taken at the top surface of the 0.15-mm-thick hBN flake. (c) The 2D infraredoptical amplitude (s2) images taken with the broadband laser. (e) The control infrared amplitude image taken with a CO2 laser at o¼ 952 cm� 1 that is outof the hyperbolic region of the hBN. The small black dots in the image are caused from topographic features (corresponding topographic image shown in(d). Scale bars, 0.5 mm. (f) Detailed profiles of the s-SNOM signals across two neighbouring discs (along the line marked in e, averaged over five scan lines)for the cases using the broadband laser (red line) and the CO2 laser (black line), respectively. Both profiles are normalized to their respective minimumvalues outside the discs. The broadband imaging shows much stronger contrasts for the discs. (g) Detailed Nano-FTIR line profiles at various frequencies.Dashed line marks the position variations of the peak of edge-launched hyperbolic polaritons. (h) Optical widths and corresponding directional angles ofthe hyperbolic polaritons evaluated from the experimental results (dots) in comparison with the calculated results (solid lines). The error bars result fromthe spatial pixel size (50 nm) in nano-FTIR measurements.NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8507 ARTICLENATURE COMMUNICATIONS | 6:7507 | DOI: 10.1038/ncomms8507 | www.nature.com/naturecommunications 5& 2015 Macmillan Publishers Limited. All rights reserved.http://www.nature.com/naturecommunicationsagain that the two types of hyperbolic dispersion exist in the hBNcrystal, without the need for fabricating HMM structures.In addition to the isolated structures, we also investigatedperiodic arrays of nanostructures. We imaged the arrays of the Aunanodiscs (5� 5 array, sketched in Fig. 5a) with differentseparations. The diameter of the discs was fixed at 0.3 mm.The gap separation between two discs varied from g¼ 0.1 mm tog¼ 1mm. The experimental results are shown in Fig. 5d–f. Weobserved the complicated overlapping of the HP cone launchedby each disc. However, with these sub-diffractional HPs, we havethe opportunity to distinguish the deeply sub-diffractionalstructures that are not readily seen in either AFM topographyor near-field imaging at frequencies outside of the hyperbolicregime (see the comparison of Fig. 5b–d).HPs for sub-diffractional focusing and selective waveguiding.In addition to the already proven high-resolution imaging withtunable enlargement of the outline of sub-diffractional objectsusing only a simple slab of hBN, the highly directional nature ofHPs can also result in sub-diffractional focusing behaviour. Whenimaging the nanodiscs with a large diameter of 0.75 mm, weobserve the focusing spot with the width of about 0.175 mm (Bl/40) at o¼ 1,420 cm� 1 (Supplementary Fig. 4). This is because allthe HP cones launched by the nanodisc superimpose into thecentre point, leading to the concentration of the light. We alsoinvestigate this focusing effect with the broadband laser in theType I hyperbolic band. However, the obtained results are alsothe superposition of all the frequency components, which are notintuitive. We also note that this super-focusing effect is inde-pendently shown and discussed in ref. 34, which was performedconcurrently with the work discussed here.Both the enlarged imaging and the super-focusing are based onthe volume-confined, frequency-dependent propagation angle ofHPs in hBN. We can envision other potential disruptivetechnologies based on the great potential of the highly directionalHPs. First, this frequency-selective waveguiding could be usefulfor photonic switching or computing, infrared filtering, or variousother nanophotonic applications (Supplementary Fig. 5a, b).Another potential application is realized in the form of anultracompact subwavelength spectrometer (SupplementaryFig. 5c,d). A natural hBN layer should allow for the spatialseparation or filtering of incoming broadband light into differentwavelength channels, much like a grating, which could then bedetected by subwavelength infrared detector pixels. This parti-cular spectrometer configuration could also be used for chemicaland biological detection schemes, in the form of spatially resolvedinfrared spectroscopy. Under broadband mid-infraredillumination the HPs could carry the vibration (or absorption)information of molecules in contact with the surface, dispersingthe spectral information at different angles, enabling them to bespatially resolved by a near-field intensity detector (like thes-SNOM tip) without the need of spectrometers.DiscussionOur work along with that of ref. 34, demonstrate the completehyperbolic imaging response of hBN and its potential forimproving the near-field imaging of deeply embeddedobjects35,36 in both the Type I lower and Type II upperReststrahlen bands, respectively. More specifically, we reveal thehyperbolic nature of the hBN layer for near-field waveguiding,imaging, focusing and its dependence on the operationalfrequency. Although all our results are restricted in the nearfield, we also expect that these intriguing findings will benefitfar-field imaging by introducing specific geometric designs, suchas circular or wedge-shaped hyperlenses2,3. Furthermore, as avan der Waal’s crystal37, hBN lends itself to incorporation onnon-planar and flexible substrates more amenable to truehyperlensing methodologies4. The realization of a naturallyoccurring, Type I and II hyperbolic media enable variousopportunities for nanophotonics that go beyond sub-diffractional near-field imaging and potential hyperlensing. Dueto the similar material anisotropy present in other polar dielectrica b cd952 cm−11,430 cm−11,410 cm−11,390 cm−1D (�)D (�)0 28 nm Min Maxe fFigure 4 | Experimental demonstration of enlarged imaging of a Au stripe with tunable HPs in the Type II band. (a) Sketch of the imaged object—a Austripe (not to scale), located below the 0.15mm thick hBN flake. The length l of the stripe is about 1 mm, and the width w is around 0.1 mm. The dashed ringsresult from launched HPs from the edges of the stripe. These HPs form an enlarged outline that reveals the object information. (b) AFM topography takenfrom the hBN top surface. (c) the s-SNOM amplitude image (s3) taken at o¼ 952 cm� 1 outside the hyperbolic band. No optical feature is observed fromthe underlying structure. (d–f) Spectroscopic imaging the stripe in the Type II hyperbolic band. The bright outlines found in the images (amplitude s3) areformed by the HP cones, which are enlarged compared to the original structure. From the measured D(o), we can estimate the width w of the stripe (usingthe relationship D(o)¼wþ 2h tany(o)) is about 0.12mm, and the estimated length is about 1.1mm. These results verify that from imaging the enlargedoutline, we are able to reveal the object information due to the frequency-dependent directivity of HPs. Scale bars, 1 mm.ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms85076 NATURE COMMUNICATIONS | 6:7507 | DOI: 10.1038/ncomms8507 | www.nature.com/naturecommunications& 2015 Macmillan Publishers Limited. All rights reserved.http://www.nature.com/naturecommunicationsvan der Waals crystals37, such as MoS2 or WS2, the naturalhyperbolic response of hBN may be general to the entire class ofpolar 2D crystals, thus expanding the potential spectral range ofthis behaviour from the mid-infrared into the single-digitterahertz spectral region17,24.MethodsSample preparation. The gold nanostructures used for the near-field experimentswere fabricated on a 1-mm-thick intrinsic silicon substrate using electron beamlithography into a bilayer PMMA (poly(methylmethacrylate)) resist. The nanos-tructures varied in size from 0.2–1 mm in diameter and in arrays with 0.1–1 mmedge-to-edge gaps. A standard liftoff procedure was used following the thermalevaporation of Cr (5 nm)/Au (30 nm) metallization.hBN crystals were grown using the high-pressure/high-temperature method38,39.The standard exfoliation process was used to randomly deposit hBN flakes of variousthicknesses onto a PMMA/PMGI (polydimethyl glutarimide) bilayer spun on aseparate silicon substrate. Here the PMMA layer played the role of the flake carriermembrane and the PMGI served as a sacrificial lift-off layer later dissolved bytetramethyl ammonium hydroxide (TMAH) solution (MICROPOSIT MF-319).AFM was utilized to select specific flakes with both sufficient thickness and lateralsize for the imaging experiments. The PMMA carrier membrane with an appropriatehBN flake was lifted-off from the substrate and put onto the supportive metal ringheld by a home-made micromanipulator. With the help of the micromanipulator,the hBN flake was aligned and transferred face down onto the predefined goldnanostructure by releasing the carrier membrane from the metal ring. Followingthe transfer, the sample with the carrier membrane on was heated to 130 �C forabout 10 min to soften the PMMA membrane and improve the adhesion of hBN tothe underlying nanostructures and silicon substrate. After that the carrier membranewas dissolved in acetone leaving the hBN flake covering the entire array ofnanostructures. To improve the adhesion, an ultrasonic clean in acetone andisopropyl alcohol with subsequent oxygen plasma clean was performed on thesilicon substrate before the hBN transfer. More details of this transfer techniqueare given in ref. 40.0a bdfD (�)g ceg = 0.1 μmg = 0.2 μmg = 1 μmAmplitude Phase Amplitude Phase� = 1,430 cm−1 � = 1,400 cm−150 nm Min MaxFigure 5 | Experiments of imaging the arrays of Au nanodiscs with hyperbolic polaritons in the Type II band. (a) Sketch of the arrays of the Aunanodiscs, located below the 0.15mm thick hBN flake. The diameter of the discs is fixed to be 300 nm. The gap separation between two discs varies fromg¼0.1mm to g¼ 1mm. The dashed rings indicate the launched hyperbolic polaritons. (b) the AFM topography of the array with g¼0.1mm, taken from thehBN top surface. (c) the s-SNOM image of the array with g ¼ 0.1mm taken at o ¼ 952 cm� 1 outside the hyperbolic band. No detailed optical feature isprobed for resolving the structure. (d–f) Near-field images (amplitude s3 and phase j3) of the arrays at two different frequencies of 1,430 and 1,400 cm� 1inside the Type II hyperbolic band. Obviously, the launched HPs help to reveal the arrays. In (e) colour spaces are added in the amplitude and phase imagestaken at 1,430 cm� 1, for keeping the square shape. Scale bars, 0.5 mm.NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8507 ARTICLENATURE COMMUNICATIONS | 6:7507 | DOI: 10.1038/ncomms8507 | www.nature.com/naturecommunications 7& 2015 Macmillan Publishers Limited. All rights reserved.http://www.nature.com/naturecommunicationsInfrared s-SNOM measurements. An s-SNOM (commercially available, NeaspecGmbH) system was used to simultaneously measure the optical near fields andtopography. The laser system used in Type I hyperbolic band was developed by theFraunhofer ILT32,33. It consists of a commercially available picosecond-laser as thepump source and two subsequent nonlinear converter steps to cover the mid-infrared range. The peak wavelength is continuously tunable from o¼ 625 cm� 1(B16 mm) to o¼ 1,100 cm� 1 (B9 mm) with bandwidths of some tens to morethan hundred wavenumbers. At a repetition rate of 20 MHz and pulse duration of10 ps, the system provides an average power of up to 10 mW. To address the lowerType-I hyperbolic region of the hBN, the peak position of the laser spectrum in ourmeasurements was set to be at around o¼ 790 cm� 1 (12.7 mm) with a FWHM ofabout 90 cm� 1. To suppress the far-field background contribution and solelymeasure the near-field contribution, the optical signal was demodulated at higherharmonics (nO) of the oscillation frequency (OB270 kHz) of the cantilever (in ourcases, n¼ 2 for the broadband s-SNOM). Nano-FTIR spectra were obtained byconstantly moving the mirror in the reference arm of the Michelson interferometer,recording the resulting interferograms and their corresponding complex Fouriertransformation11,33. In contrast to conventional far-field FTIR, this setup allows torecord 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 positionabout l/8 away from the maximum of the interference signals. This allows for avisualization of even small spectral changes31. The extracted line profiles shown inFig. 3g were numerically smoothed by using a fast Fourier transform smoothingwith three adjacent pixels. This smoothing does not improve the resolution, butrather leads to a conservative estimation of resolution (details in SupplementaryFigs 2 and 3). The monochromatic quantum cascade laser used in the Type IIband (Figs 4 and 5) is commercially available from Daylight Solutions. Thedemodulation order n ¼ 3 is chosen for the monochromatic s-SNOM imaging.Near-field optical amplitude (sn) and phase (jn) are separated with aninterferometric setup11,19.Numerical simulations. 2D simulations (Fig. 1) were carried out by the finite-element software COMSOL Multiphysics. A plane-wave illumination was set byusing scattering boundary condition. The surrounding boundaries used perfectlymatched layer absorbing boundary conditions. 3D simulations (Fig. 2) were doneby using CST Microwave Studio. Open boundary conditions were used. We alsochecked different mesh sizes to make sure that all the simulations reach properconvergence. The dielectric data of hBN used in all the simulations are extractedfrom far-field FTIR measurements10.References1. Poddubny, A., Iorsh, I., Belov, P. & Kivshar, Y. Hyperbolic metamaterials.Nat. Photon. 7, 948–957 (2013).2. Jacob, Z., Alekseyev, L. V. & Narimanov, E. Optical hyperlens: far-field imagingbeyond the diffraction limit. Opt. Express 14, 8247–8256 (2006).3. Salandrino, A. & Engheta, N. Far-field subdiffraction optical microscopyusing metamaterial crystals: theory and simulations. Phys. Rev. B 74, 075103(2006).4. Liu, Z., Lee, H., Xiong, Y., Sun, C. & Zhang, X. Far-field optical hyperlensmagnifying sub-diffraction-limited objects. Science 315, 1686 (2007).5. Hoffman, A. J. et al. Negative refraction in semiconductor metamaterials. Nat.Mater. 6, 946–950 (2007).6. Yao, J. et al. Optical negative refraction in bulk metamaterials of nanowires.Science 321, 930 (2008).7. Krishnamoorthy, H. N. S., Jacob, Z., Narimanov, E., Kretzschmar, I. &Menon, V. M. Topological transitions in metamaterials. Science 336, 205–209(2012).8. Ishii, S., Kildishev, A. V., Narimanov, E., Shalaev, V. M. & Drachev, V. P.Sub-wavelength interference pattern from volume plasmon polaritons in ahyperbolic medium. Las. Photon. Rev. 7, 265–271 (2013).9. Yang, X., Yao, J., Rho, J., Yin, X. & Zhang, X. Experimental realization ofthree-dimensional indefinite cavities at the nanoscale with anomalous scalinglaws. Nat. Photon. 6, 450–454 (2012).10. Caldwell, J. D. et al. Sub-diffraction, volume-confined polaritons in the naturalhyperbolic material: hexagonal boron nitride. Nat. Commun. 5, 5221 (2014).11. Dai, S. et al. Tunable phonon polaritons in atomically thin van der Waalscrystals of boron nitride. Science 343, 1125–1129 (2014).12. Prokes, S.M. et al. Hyperbolic and plasmonic properties of silicon/Ag alignednanowire arrays. Opt. Express 21, 14962–14974 (2013).13. Khurgin, J. B & Boltasseva, A. Reflecting upon the losses in plasmonics andmetamaterials. MRS Bull 37, 768–779 (2012).14. West, P. R. et al. Searching for better plasmonic materials. Las. Photon. Rev 4,795–808 (2010).15. Tassin, P., Koschny, T., Kafesaki, M. & Soukoulis, C. M. A comparison ofgraphene, superconductors and metals as conductors for metamaterials andplasmonics. Nat. Photon. 6, 259–264 (2012).16. Hillenbrand, R., Taubner, T. & Keilmann, F. Phonon-enhanced light–matterinteraction at the nanometre scale. Nature 418, 159–162 (2002).17. Caldwell, J. D. et al. Low-loss, infrared and terahertz nanophotonics usingsurface phonon polaritons. Nanophotonics 4, 44–68 (2015).18. Caldwell, J. D. et al. Low-loss, extreme sub-diffraction photon confinement viasilicon carbide surface phonon polariton nanopillar resonators. Nano Lett. 13,3690–3697 (2013).19. Wang, T., Li, P., Hauer, B., Chigrin, D. N. & Taubner, T. Optical properties ofsingle infrared resonant circular microcavities for surface phonon polaritons.Nano Lett. 13, 5051–5055 (2013).20. Chen, Y. et al. Spectral tuning of localized surface phonon polariton resonatorsfor low-loss mid-ir applications. ACS Photon. 1, 718–724 (2014).21. Xu, X. G. et al. One-dimensional surface phonon polaritons in boron nitridenanotubes. Nat. Commun. 5, 4782 (2014).22. Da Silva, R. E. et al. Far-infrared slab lensing and subwavelength imaging incrystal quartz. Phy. Rev. B 86, 155152 (2012).23. Fonoberov, V. A. & Balandin, A. A. Polar optical phonons in wurtzitespheroidal quantum dots: theory and application to ZnO and ZnO/MgZnOnanostructures. J. Phys. Condens. Matter 17, 1085–1097 (2005).24. Thompson, D. W., De Vries, M. J., Tiwald, T. E. & Woollam, J. A.Determination of optical anisotropy in calcite from ultraviolet to mid-infraredby generalized ellipsometry. Thin Solid Films 313, 341–346 (1998).25. Sun, J., Litchinitser, N. M. & Zhou, J. Indefinite by nature: from ultraviolet toterahertz. ACS Photon. 1, 293–303 (2014).26. Zhang, Y., Fluegel, B. & Mascarenhas, A. Total negative refraction inreal crystals for ballistic electrons and light. Phys. Rev. Lett. 91, 157404 (2003).27. Chen, X. L., He, M., Du, Y. X., Wang, W. Y. & Zhang, D. F. Negativerefraction: an intrinsic property of uniaxial crystals. Phys. Rev. B 72, 113111(2005).28. Geick, R., Perry, C. H. & Rupprecht, G. Normal modes in hexagonal boronnitride. Phy. Rev. B 146, 543–547 (1966).29. Pendry, J. B. Negative refraction makes a perfect lens. Phys. Rev. Lett. 85,3966–3969 (2000).30. Fang, N. et al. Sub-diffraction-limited optical imaging with a silver superlens.Science 308, 534–537 (2005).31. Taubner, T., Korobkin, D., Urzhumov, Y., Shvets, G. & Hillenbrand, R.Near-field microscopy through a SiC superlens. Science 313, 1595 (2006).32. Wueppen, J., Jungbluth, B., Taubner, T. & Loosen, P. Ultrafast tunable mid IRsource. in Infrared, Millimeter and Terahertz Waves (IRMMW-THz), 36th-International Conference, IEEE, 1–2 (2011).33. Bensmann, S. et al. Near-field imaging and spectroscopy of locallystrained GaN using an IR broadband laser. Opt. Express 22, 22369–22381(2014).34. Dai, S. et al. Subdiffractional focusing and guiding of polaritonic rays in anatural hyperbolic material. Nat. Commun. 6, 6963 (2015).35. Taubner, T., Keilmann, F. & Hillenbrand, R. Nanoscale-resolved subsurfaceimaging by scattering-type near-field optical microscopy. Opt. Express 13,8893–8899 (2005).36. Li, P., Wang, T., Bockmann, H. & Taubner, T. Graphene-enhanced infrarednear-field microscopy. Nano Lett 14, 4400–4405 (2014).37. Geim, A. K. & Grigorieva, I. V. Van der Waals heterostructures. Nature 499,419–425 (2013).38. Taniguchi, T. & Watanabe, K. Synthesis of high-purity boron nitride singlecrystals under high pressure by using Ba-BN solvent. J. Cryst. Growth 303,525–529 (2007).39. Watanabe, K., Taniguchi, T. & Kanda, H. Direct-bandgap properties andevidence for ultraviolet lasing of hexagonal boron nitride single crystal. Nat.Mater. 3, 404–409 (2004).40. Kretinin, A. V. et al. Electronic Properties of graphene encapsulated withdifferent two-dimensional atomic crystals. Nano Lett. 14, 3270–3276 (2014).AcknowledgementsThis work was supported by the Excellence Initiative of the German federal and stategovernments, the Ministry of Innovation of North Rhine-Westphalia, the DFG underSFB 917 and the Korean Defense Acquisition Program Administration and the Agencyfor Defense Development as a part of a basic research program under the contractUD110099GD. Funding for J.D.C. was provided by the Office of Naval Research andadministered by the NRL Nanoscience Institute and was carried out at the University ofManchester through the NRL Long-Term Training (Sabbatical) Program. A.K. andK.S.N. acknowledge support from the Engineering and Physical Sciences ResearchCouncil (UK), The Royal Society (UK), European Research Council and EC-FET Eur-opean Graphene Flagship. P.L. and Th.T. thank G. von Plessen and D. Chigrin forvaluable comments and the proofreading.Author contributionsP.L., J.D.C., Th.T. and K.S.N. conceived the original ideas. P.L. performed the s-SNOMmeasurements and numerical simulations. M.L and F.G. performed the broadbands-SNOM measurements. A.V.K. and J.D.C. fabricated the samples with hBN-covered AuARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms85078 NATURE COMMUNICATIONS | 6:7507 | DOI: 10.1038/ncomms8507 | www.nature.com/naturecommunications& 2015 Macmillan Publishers Limited. All rights reserved.http://www.nature.com/naturecommunicationsstructures. K.W. and T.T. grew the hBN crystals used in the experiment. P.L, J.D.C. andTh.T. wrote the manuscript. The project was supervised by J.D.C, Th.T. and K.S.N.Additional informationSupplementary Information accompanies this paper at http://www.nature.com/naturecommunicationsCompeting financial interests: The authors declare no competing financial interests.Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/How to cite this article: Li, P. et al. Hyperbolic phonon-polaritons in boron nitride fornear-field optical imaging and focusing. Nat. Commun. 6:7507 doi: 10.1038/ncomms8507(2015).This work is licensed under a Creative Commons Attribution 4.0International License. The images or other third party material in thisarticle are included in the article’s Creative Commons license, unless indicated otherwisein the credit line; if the material is not included under the Creative Commons license,users will need to obtain permission from the license holder to reproduce the material.To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/NATURE COMMUNICATIONS | DOI: 10.1038/ncomms8507 ARTICLENATURE COMMUNICATIONS | 6:7507 | DOI: 10.1038/ncomms8507 | www.nature.com/naturecommunications 9& 2015 Macmillan Publishers Limited. All rights reserved.http://www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationshttp://npg.nature.com/reprintsandpermissions/http://npg.nature.com/reprintsandpermissions/http://creativecommons.org/licenses/by/4.0/http://www.nature.com/naturecommunications title_link Results Theory and simulations Experimental results in Type I hyperbolic band Figure™1Frequency-dependent directional angles of the hyperbolic polaritons propagating inside the hBN.Solid lines in (a,b) the critical angle theta of the HPs as a function of the frequency ohgr in the Type-I (760ltohgrlt825thinspcm-1, epsivtgt0 and epsi Figure™2Three dimensional simulations of imaging different structures through the hBN layer.(a,b) 3D simulations of imaging a gold disc (0.6-mgrm diameter) below the 1-mgrm-thick hBN layer (scale bars, 0.6thinspmgrm). Simulated electric-field distribution Experimental results in Type II hyperbolic band Figure™3Experimental demonstration of super-resolution imaging with tunable hyperbolic polaritons in the Type I band.(a) Sketch of the experimental setup. The right inset is the normalized laser spectrum of the used mid-infrared broadband laser. The gold  HPs for sub-diffractional focusing and selective waveguiding Discussion Figure™4Experimental demonstration of enlarged imaging of a Au stripe with tunable HPs in the Type II band.(a) Sketch of the imaged object--a Au stripe (not to scale), located below the 0.15thinspmgrm thick hBN flake. The length l of the stripe is about 1 Methods Sample preparation Figure™5Experiments of imaging the arrays of Au nanodiscs with hyperbolic polaritons in the Type II band.(a) Sketch of the arrays of the Au nanodiscs, located below the 0.15thinspmgrm thick hBN flake. The diameter of the discs is fixed to be 300thinspnm.  Infrared s-—SNOM measurements Numerical simulations PoddubnyA.IorshI.BelovP.KivsharY.Hyperbolic metamaterialsNat. Photon.79489572013JacobZ.AlekseyevL. V.NarimanovE.Optical hyperlens: far-field imaging beyond the diffraction limitOpt. Express14824782562006SalandrinoA.EnghetaN.Far-field subdiffraction optica This work was supported by the Excellence Initiative of the German federal and state governments, the Ministry of Innovation of North Rhine-Westphalia, the DFG under SFB 917 and the Korean Defense Acquisition Program Administration and the Agency for Defe ACKNOWLEDGEMENTS Author contributions Additional information