Broadband mid-infrared plasmon-polaritons in metallic-dielectric interfaces

We report real-space near-field images of mid-infrared (IR) surface plasmon-polariton (SPP) waves in the insulating/metal/insulating (IMI) heterostructure: hexagonal boron nitride/gold/silicon dioxide (hBN/Au/SiO 2 ). The SPPs are observed in the 750 – 1500 cm -1 (~13.3 – ~6.7  m) range, feature micrometer-sized wavelengths and propagation lengths ( 𝐿 𝑆𝑃𝑃 ) exceeding 20  m at room temperature. Comparatively, real-space mapping of SPP waves in the mid-IR has been shown only in graphene, but with nanometer sized-wavelength and 𝐿 𝑆𝑃𝑃 ~ 10  m at cryogenic temperatures. Interestingly, we show interference between different polariton types in the IMI since the lower momenta SPPs in the metal surface interfere with higher momenta hyperbolic phonon polaritons (HPhP) in the hBN top layer creating SPP-HPhP overlapped waves. In agreement with theory, we quantify momentum and damping governing the SPP waves. Tunability is discussed upon changing the IMI heterostructure. Our theory predicts SPP group velocities reaching 20 % of the light velocity in vacuum and 0.2 – 0.4 ps lifetimes. We further demonstrate that the SPP waves interact with SiO 2 and hBN phonons in the strong coupling regime. As a general effect of the metal/dielectric interface, the mid-IR SPP waves can be compelling for fast metal-based plasmonics, whilst their ability to strongly couple to phonons can be further explored for enhanced sensing in the mid-IR.

Surface plasmon-polaritons (SPP) 1-3 , quasi-particles originated from the coupling of photons to collective oscillations of free charge carries, are intrinsically two-dimensional (2D) modes of the interface between a material with metallic character and a dielectric insulator. Such ultimate 2D confinement originates from the fact that SPPs are nonevanescent in the interface plane, but evanescent along the normal direction. Being photon-charge coupled modes, they feature a wave-particle behavior endowing them optical properties from the photon part, permitting guiding and focusing for instance, whilst the charge-inherited character can provide for desirable electronical control. In the ultraviolet-visible to near-infrared (IR) range, such compelling virtues of SPPs have been exploited in waveguiding 3 , plasmonic circuits 4,5 , sensing 2 , lasing [6][7][8] , light harvesting 2 and for quantum information processing 9 . In the technologically attractive midinfrared (IR) range, SPPs can access and retrieve information from interface states associated to molecular vibrations, electronic transitions of energy around 50 -300 meV and room temperature thermodynamical reactions 10 . But, in analogy to free space waves or propagating optical modes in fibers, the use of SPPs as information carriers is critically dependent on their propagative properties in media supporting mid-IR plasmonic waves.
Despite semiconducting 11 and metallic 12 micro-and nanostructures can bear stationary and localized SPPs enabling functionalities as antennas [13][14][15][16][17][18] and resonators 10,14,[19][20][21] in the mid-IR, these media are reported to have high ohmic losses 11,12,22,23 that hamper the efficiency of propagative modes. Only graphene [24][25][26][27] , to date, was shown to support tunable and high momenta (10 5 −1 ) mid-IR SPP waves of propagation length reaching 10 μm at cryogenic temperatures 28 . As a promising alternative, we present here the first real-space, nanoscale resolved imaging/spectroscopy of micrometer-sized wavelength SPP waves in insulator/metal/insulator (IMI) heterostructures with propagation lengths exceeding 20 at room temperature in the 750 − 1450 −1 mid-IR range. By scatteringtype scanning near-field optical microscopy (s-SNOM) and synchrotron infrared nanospectroscopy (SINS), which are optical nanoscopies 29 able to fully characterize polariton waves 30,31 , we measure the plasmonic waves in two IMIs: air/Au/SiO2 and hexagonal boron nitride (hBN)/Au/SiO2. An antenna-like structure and a groove in the metal layer 32 are the main couplers of free space light into the observed plasmon waves. The s-SNOM images and SINS spectral linescan provide for a complete data set permitting us to quantify the complex momentum ( = q SPP + γ SPP , q SPP is phonon-polaritons (HPhP), we observe SPP-HPhP overlapped waves consisting in high momenta HPhPs (q HPhP ~ 10 5 −1 ) 33-35 modulating lower momenta SPPs. In general, type II hyperbolic materials 36  To explain the mid-IR SPP modes, we model the IMIs as a multilayer system to calculate the theorical − .
The theoretical dispersion is given by the solution of the Maxwell's equation, applying the boundary conditions in which are obtained by the continuity of the fields at the interfaces (see suppl. mat.). These calculations intrinsically account the coupling of the plasmonic modes at each I/M interface yielding a resultant parameter-free − in excellent quantitative agreement with the experimental observations. Moreover, the theoretical and the experimental − s reveal spectral gaps, near the SiO2 and in-plane hBN phonon absorption peaks, where the amplitudes of the SPP waves are considerably attenuated. We attribute such gaps to anti-crossing (AC) regions owing to the interaction of SPPs and phonons of the surrounding media in a strong coupling regime as evaluated from the couple-oscillator modelling 37 .
Additionally, the theoretical − enables us to predict that the SPP waves travel with an average group velocity of 0.2 ( is the light velocity in vacuum) and lifetimes between 0.2 to 0.4 ps.  The sketch in Fig. 1a illustrates a HPhP-SPP wave in a cross-section of an hBN/Au/SiO2 heterostructure, with an Au disk-like antenna atop, probed by s-SNOM. The s-SNOM microscope is an atomic force microscope (AFM) equipped with a suitable optical apparatus for the measurement of optical near-field. Basically, this nanoscopy uses a metalized AFM tip as a high-spatial resolution and high-momenta optical probe to detect optical phenomena belonging to the near-field regime, including SPP and HPhP waves (see methods for details). The model-fit to the profile P1' (Fig. 1e), considering the sum of a HPhP wave and a SPP wave in eq. 1, yields q SPP = 1.12 × 10 4 −1 and q HPhP = 18.8 × 10 4 −1 . As the wavelength = 2 q ⁄ , we verify that > ℎ in P1' as stated above. The model-fit to the profile P2', extracted from the hBN onto the groove (Fig. 1d Moreover, using the model described in ref. 34  In comparison with the just discussed HPhP resonant case ( Fig. 1c-e), we present in Fig. 1h-j the S 3 image of the same antenna-hBN/Au/SiO2 heterostructure illuminated at = 1200 −1 , which is off-resonant with HP 2 s. As highlighted in Fig. 1i,j, solely SP 3 waves are unveiled at = 1200 −1 , requiring the use of one propagative term as confirmed by Fourier Transform analysis (sup. mat.), to fit the profiles P1 to P3 (Fig. 1j) with eq.1. As discussed above, the fits P2 and P3, which have more oscillations, yield more accurate values of q SPP . In Fig. 1l, we observe edge-launched SP 3 waves in the Au/SiO2, for = 1200 −1 , with q SPP = 1.14 × 10 4 −1 determined from the model-fit to P4 ( Fig. 1m). IMI 1.2 | 0.12 1.14 | 0.16 In Table 1 we compare the model-determined values of q SPP and SPP for hBN/Au/SiO2 and Au/SiO2 at the two excitation frequencies, for the two frequencies q SPP is larger on hBN than on air whilst SPP presents small variations upon changing the material. To further confirm these analyses, we inspect the SPP waves in a broader range by a spectral linescan from SINS nanoscopy (Fig. 2). Concisely, SINS employs the highly brilliant and broadband synchrotron IR radiation as the excitation source for a s-SNOM microscope. Thereby, SINS produces the broadband near-field spectrum with the high spatial resolution of s-SNOM via interferometry with an asymmetric Michelson interferometer. The spectral linescan measurement consists of a × map built by plotting SINS spectra acquired along a defined direction 30 . In Fig. 2b, we present the SINS spectral linescan of the hBN/Au/SiO2 heterostructure illustrated in Fig. 2a. The linescan direction is normal to the groove, the same direction as P1' in Figure 1d. The linescan data in the hBN upper RS band (1365 -1610 cm -1 ) clearly show SPP-HPhP waves, thus, experimentally corroborating our observations from the s-SNOM on-resonant image (Figure 1c-e). Such overlapped waves are model-fitted using eq. 1 with two propagating components similarly to the one employed for the correlate waves in Fig. 1d,e. As an example, we exhibit in Fig. 2c the profile data of the SPP-HPhP wave at = 1415 cm -1 and its corresponding model-fit. In the remaining spectral range from 750 to ~ 1365 cm -1 , however, the waves are model-fitted with a single component in eq. 1 due to having only the SPP component. It is worth commenting that in the hBN lower RS band (749 -816 cm -1 ), out-of-plane HPhPs emerge but with much shorter amplitude than the SPP waves. Thus, the contribution from HPhPs in the fits of the corresponding spectral interval is neglected. Hence, the full data analysis yields the − throughout the whole 750 -1450 cm -1 probed range. Such experimental dispersion is shown in Fig. 2d  Moreover, experiment and theory also consistently reveal gaps in the dispersion relation, i.e., regions without SPP modes, near the hBN in-plane and SiO2 phonons. These lattice vibrations correspond to peaks in the imaginary part of the electrical permittivities of these materials (Fig. 2e inset) centered at the ω TO s of each material. In Fig. 2c, we remark that inside such gaps the SPP modes present more attenuated amplitudes (1365 cm -1 profile) and even uncharacterized wave shapes ( = 1077 and 818 cm -1 profiles) resulting in overdamped model-fits. We assign these spectral gaps to anti-crossing regions (AC) that rise owing to the coupling of pure SPPs to lattice phonons of the dielectric layers. To evaluate these effect, we use a classical model of two coupled classic harmonic oscillators 37,43 described by a pair of coupled equations of motion: where ( > 1 is fulfilled 37 , the system is classified in the strong coupling regime. Following the method adopted in ref. 37 , we determine those coupling parameters by fitting the extinction coefficient ( SPP , ) in eq. 5 to the experimental iso-momentum spectra extracted from vertical profiles near the AC regions as shown in Fig.   3d-f. By applying this analysis to different iso-momentum spectra in the AC regions, we compute the corresponding + and − dispersion branches, which are displayed as red circles in Fig. 3a-c, overlapping the experimental − s.
As expected, ω and branches, which would take place in absence of coupling, show less agreement with the data. From our calculations, we find that the interaction between SPP waves to both SiO2 and in-plane hBN phonons happens in the strong coupling regime.  In the mid-IR, SPP-phonon coupling has already been discussed 44,45 but from the spectroscopic point of view by the use of far-field techniques lacking spatial resolution for imaging the plasmonic waves. In this context, it was recently reported the ultra-strong coupling between epsilon-near-zero (ENZ) SPP modes of coaxial Au nanocativities and SiO2 phonons 46 . It was also recently observed the strong coupling 37 between propagating HPhP waves and molecular resonances for a hBN crystals lying onto a thin organic film. In the latter case, the strong coupling was characterized by ACs in the HPhP dispersion relation in the upper RS band wherein the HPhP waves presented increased damping for the frequencies coincident with the molecular phonons of the film. Such effects are precisely analogous to those we have describe for the SPP-phonon strong couplings. The notable difference is that the presented plasmon waves can couple to phonons in a broader range spanning over considerable portion of the molecular fingerprint. Furthermore, in Fig. 4 we also examine the photonic properties of the SPP wave found in the group velocity, v g,SPP (v g = ), and lifetime , from the theoretical − (Fig. 2d). Apart from the AC spectral regions, where v g,SPP tends to zero, one can see that the SPP waves reach up to 0.2c (c is the light velocity in vacuum) which is one order of magnitude higher than that of graphene plasmons 47 , and have spanning from 0.02 to 0.1 ps in the most part of the spectral range. The v g,SSP in the upper RS band of hBN assumes values about three orders of magnitude greater than that of HPhPs (v g,HPhP ) 35 . Thus, as v g,SPP ≫ v g,HPhP , the SPP waves can also be used to further explore exotic phenomena as Cherenkov HPhP wakes reported from plasmon modes confined in silver nanowires residing on hBN 15 and the v g,HPhP variation as a function of the distance between hBN and Au in hBN/SiO2(wedge)/Au heterostructures 35 .
Moreover, a broader perspective on the mid-IR SPP waves' photonics is given from their quality factor = q SPP γ SPP ⁄ spanning in the 4-13 interval in the 750-1450 cm -1 range. These values of are comparable to those reported for different plasmonic media studied at room temperature: = 40 for SPPs in graphene monolayers 24,25,47 , = 10 for SPPs in graphene edges 48,49 , = 26 for one-dimensional SPP in carbon nanotubes 50 , and = 3 for Dirac plasmons in topological insulators 51,52 .
In summary, we here report mid-IR SPP waves in IMI heterostructures with reaching 20 m at room temperature. Using s-SNOM and SINS nanoscopies, we show that these plasmon waves exist throughout the broad mid-

Scattering-type Scanning Near-field Optical Microscopy /(s-SNOM)
The s-SNOM (neaSNOM from neaspec, attocube systems AG) uses a metallic tip of an atomic force microscope (AFM) as an optical nanoprobe to measure the optical near-field. Hence, the s-SNOM nanoscope consists in an AFM embodied with a suitable optical arrangement. The AFM operates in semi-contact to the sample mode wherein the metallic tip is electronically-driven to vibrate in its natural mechanical frequency (Ω). By illuminating the tip-sample region with far-field light, it is induced the antenna effect to the tip as the incident electromagnetic field causes charge separation in its metallic coating. Thus, an optical near field rises at the tip surface with higher density at its apex. The optically polarized tip polarizes the surrounding material creating an effective tip-sample polarization. The tip antenna functioning reconverts, by scattering, such tip-sample optical near-field interaction into propagating far-field light that reaches the detector. This scattered light ( ) is composed by the mentioned optical near field component and a higher intensity far field one. To separate such contributions, it is used the fact that the near-field light presents a non-linear temporal dependence on the frequency Ω, due to the strong light-matter interaction at short distances, the far field one has a linear dependence on Ω. Such dependences can be mathematically expressed as S = ∑ S n cos (nΩt) ∞ n=o where is the harmonic order. By lock-in electronics and pseudo-heterodyne (PS) interferometric amplification, the high harmonics, ≥ 2, that correspond to pure optical near-field are detected. In this work, such scheme was used to the acquisition of the polaritonic images in Figure 1. Quantum cascade lasers (QCL) were employed as the illumination sources. The detection of was achieved by a mercury-cadmium-telluride (MCT) detector.

Synchrotron Infrared Nanospectroscopy (SINS)
SINS underlies on the s-SNOM principles concerning the optical near-field excitation and the use of analogous detection scheme. Thereby, SINS comprises of using a s-SNOM microscope with the highly brilliant broadband IR radiation emitted by a synchrotron as the illumination source. Concisely, the IR beam induces the optical polarization to the tip-sample region and the antenna effect. The resulting scattered light (S), then, enters an asymmetric Michelson interferometer (Figure 2a). It is realized interferometry between S and the beam in the reference arm. In analogy to the described for s-SNOM, a locking-based electronics provides for the detection of optical near-field interferograms given from the high harmonics of S (n ≥ 2). By Fourier Transform (FT), it is obtained the optical near field spectrum. The SINS experiments of this work were performed in the Infrared Nanospectroscopy Beamline of the Brazilian Synchrotron Light Laboratory (LNLS). It was used a MCT detector enabling measuring the optical near-field in the 650 to 3000 cm -1 range.

Sample construction
The groove was created by standard photolithography onto SiO2 (2 µm thick)/Si substrates followed by deposition of a 90 nm thick Au film by electron beam. The hBN flakes were then transferred onto the Au groove using PDMS assisted technique 60 . Previously to the hBN transfer, the flakes were exfoliated by standard scotch tape method on the PDMS stamp and were selected based on optical contrast 61 . After the hBN transfer, the Au disk-like antenna, with an average height of 150 nm and an elliptical basis measuring ~ 2.4 and ~ 3.9 μm for short and long axes respectively, was designed atop of the transferred hBN and at the edge of the groove by a new photolithography step, followed deposition of 90nm thick Au film by electron beam and lift-off.