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Van der Waals (vdW) materials supporting phonon polaritons (PhPs) - light coupled to lattice vibrations - have gathered significant interest because of their intrinsic anisotropy and low losses. In particular, $\alpha$-MoO$_3$ supports PhPs with in-plane anisotropic propagation, which has been exploited to tune the optical response of twisted bilayers and trilayers. Additionally, various studies have explored the realization of polaritonic crystals (PCs) - lattices with periods comparable to the polariton wavelength -. PCs consisting of hole arrays etched in $\alpha$-MoO$_3$ slabs exhibit Bragg resonances dependent on the angle between the crystallographic axes and the lattice vectors. However, such PC concept, with a fixed orientation and size of its geometrical parameters, constrains practical applications and introduces additional scattering losses due to invasive fabrication processes. Here we demonstrate a novel PC concept that overcomes these limitations, enabling low-loss optical tuning. It comprises a rotatable pristine $\alpha$-MoO$_3$ layer located on a periodic hole array fabricated in a metallic layer. Our design prevents degradation of the $\alpha$-MoO$_3$ optical properties caused by fabrication, preserving its intrinsic low-loss and in-plane anisotropic propagation of PhPs. The resulting PC exhibits rotation of the Bloch modes, which is experimentally visualized by scanning near-field microscopy. In addition, we experimentally determine the polaritons momentum and reconstruct their band structure. These results pave the way for mechanically tunable nanooptical components based on polaritons for potential lasing, sensing, or energy harvesting applications.

Phonon polaritons (PhPs) (light coupled to lattice vibrations) in the highly anisotropic polar layered material molybdenum trioxide (\alpha-MoO_3) are currently the focus of intense research efforts due to their extreme subwavelength field confinement, directional propagation and unprecedented low losses. Nevertheless, prior research has primarily concentrated on exploiting the squeezing and steering capabilities of \alpha-MoO_3 PhPs, without inquiring much into the dominant microscopic mechanism that determines their long lifetimes, key for their implementation in nanophotonic applications. This study delves into the fundamental processes that govern PhP damping in \alpha-MoO_3 by combining ab initio calculations with scattering-type scanning near-field optical microscopy (s-SNOM) and Fourier-transform infrared (FTIR) spectroscopy measurements across a broad temperature range (from 8 to 300 K). The remarkable agreement between our theoretical predictions and experimental observations allows us to identify third-order anharmonic phonon-phonon scattering as the main damping mechanism of \alpha-MoO_3 PhPs. These findings shed light on the fundamental limits of low-loss PhPs, a crucial factor for assessing their implementation into nanophotonic devices., Comment: 24 pages, 4 figures

Polaritonic crystals - periodic structures where the hybrid light-matter waves called polaritons can form Bloch states - promise a deeply subdiffractional nanolight manipulation and enhanced light-matter interaction. In particular, polaritons in van der Waals materials boast extreme field confinement and long lifetimes allowing for the exploitation of wave phenomena at the nanoscale. However, in conventionally patterned nanostructures, polaritons are prone to severe scattering loss at the sharp material edges, making it challenging to create functional polaritonic crystals. Here, we introduce a new concept of a polaritonic Fourier crystal based on a harmonic modulation of the polariton momentum in a pristine polaritonic waveguide with minimal scattering. We employ hexagonal boron nitride (hBN) and near-field imaging to reveal a neat and well-defined band structure of phonon-polaritons in the Fourier crystal, stemming from the dominant excitation of the first-order Bloch mode. Furthermore, we show that the fundamental Bloch mode possesses a polaritonic bandgap even in the relatively lossy naturally abundant hBN. Thus, our work provides a new paradigm for polaritonic crystals essential for enhanced light-matter interaction, dispersion engineering, and nanolight guiding.

Canalization is an optical phenomenon that enables unidirectional propagation of light in a natural way, i.e., without the need for predefined waveguiding designs. Predicted years ago, it was recently demonstrated using highly confined phonon polaritons (PhPs) in twisted layers of the van der Waals (vdW) crystal alpha-MoO3, offering unprecedented possibilities for controlling light-matter interactions at the nanoscale. However, despite this finding, applications based on polariton canalization have remained elusive so far, which can be explained by the complex sample fabrication of twisted stacks. In this work, we introduce a novel canalization phenomenon, arising in a single vdW thin layer (alpha-MoO3) when it is interfaced with a substrate exhibiting a given negative permittivity, that allows us to demonstrate a proof-of-concept application based on polariton canalization: super-resolution (up to ~{\lambda}0/220) nanoimaging. Importantly, we find that canalization-based imaging transcends conventional projection constraints, allowing the super-resolution images to be obtained at any desired location in the image plane. This versatility stems from the synergetic manipulation of three distinct parameters: incident frequency, rotation angle of the thin vdW layer, and thickness. These results provide valuable insights into the fundamental properties of canalization and constitute a seminal step towards multifaceted photonic applications, encompassing imaging, data transmission, and ultra-compact photonic integration., Comment: 11 pages, 3 figures

Polaritons in strongly anisotropic thin layers have recently captured the attention in nanophotonics because of their directional propagation at the nanoscale, which offers unique possibilities for nanooptical applications. However, exploiting the full potential of anisotropic polaritons requires a thorough understanding of their properties, including field confinement, energy and phase propagation direction and losses. Here we fill this critical gap by providing fundamental insights into the propagation of anisotropic polaritons in thin biaxial layers. In particular, we introduce a novel methodology that allows us to represent isofrequency curves of polaritons in strongly anisotropic materials considering that the real and imaginary parts of the wavevector are not parallel. In fact, we analytically show that the direction of the imaginary part of the wavevector is parallel to the group velocity, which can have different, even perpendicular or opposite, directions with respect to the phase velocity. This finding is crucial for understanding polaritonic phenomena in anisotropic media, yet it has so far been widely overlooked in the literature. Additionally, we introduce a criterion for classifying the polaritonic modes in biaxial layers into volume and surface categories, and analyze their dispersion, field structure, and losses. Finally, we discover the existence of anisotropic transverse electric modes, which can exhibit natural canalization. Taken together, our results shed light on hitherto unexplored areas of the theory of electromagnetic modes in thin biaxial layers. Although exemplified for van der Waals MoO3 layers, our findings are general for polaritons in other strongly anisotropic biaxial hyperbolic crystals., Comment: 25 pages, 5 figures, including supplementary information

The terahertz (THz) frequency range is key to study collective excitations in many crystals and organic molecules. However, due to the large wavelength of THz radiation, the local probing of these excitations in smaller crystalline structures or few-molecular arrangements, requires sophisticated methods to confine THz light down to the nanometer length scale, as well as to manipulate such a confined radiation. For this purpose, in recent years, taking advantage of hyperbolic phonon polaritons (HPhP) in highly anisotropic van der Waals (vdW) materials has emerged as a promising approach, offering a multitude of manipulation options such as control over the wavefront shape and propagation direction. Here, we demonstrate the first THz application of twist-angle-induced HPhP manipulation, designing the propagation of confined THz radiation between 8.39 and 8.98 THz in the vdW material alpha-molybdenum trioxide ($\alpha-MoO_{3}$), hence extending twistoptics to this intriguing frequency range. Our images, recorded by near-field optical microscopy, show the frequency- and twist-angle-dependent change between hyperbolic and elliptic polariton propagation, revealing a polaritonic transition at THz frequencies. As a result, we are able to allocate canalization (highly collimated propagation) of confined THz radiation by carefully adjusting these two parameters, i.e. frequency and twist angle. Specifically, we report polariton canalization in $\alpha-MoO_{3}$ at 8.67 THz for a twist angle of 50{\deg}. Our results demonstrate an unprecedented control and the manipulation of highly-confined collective excitations at THz frequencies, offering novel possibilities for nanophotonic applications., Comment: 25 pages, 4 figures, article, submitted

Polaritons - hybrid light-mater excitations - are very appealing for the confinement of light at the nanoscale. Recently, different kinds of polaritons have been observed in thin slabs of van der Waals (vdW) materials, with particular interest focused on phonon polaritons (PhPs) - lattice vibrations coupled to electromagnetic fields in the mid-infrared spectral range with - in biaxial crystals, such as e.g. MoO3. In particular, hyperbolic PhPs - having hyperbola-like shape of their isofrequency curves - in MoO3 can exhibit ultra-high momenta and strongly directional in-plane propagation, promising novel applications in imaging, sensing or thermal management at the nanoscale and in a planar geometry. However, the excitation and manipulation of in-plane hyperbolic PhPs have not yet been well studied and understood. Here we propose a technological platform for the effective excitation and control of in-plane hyperbolic PhPs based on polaritonic crystals (PCs) - lattices formed by elements separated by distances comparable to the PhPs wavelength -, twisted with respect to the natural vdW crystal axes. In particular, we develop a general analytical theory valid for an arbitrary PC made in a thin biaxial slab. As a practical example, we consider a twisted PC formed by rectangular hole arrays made in MoO3 slab and demonstrate the excitation of Bragg resonances tunable by the twisting angle. Our findings open novel avenues for both fundamental studies of PCs in vdW crystals and the development of mid-infrared sensing and photodetection applications

Negative reflection occurs when light is reflected towards the same side of the normal to the boundary from which it is incident. This exotic optical phenomenon, which provides a new avenue towards light manipulation, is not only yet to be visualized in real space but remains largely unexplored both at the nanoscale and in natural media. Here, we directly visualize nanoscale-confined polaritons negatively reflecting on subwavelength mirrors fabricated in a low-loss van der Waals crystal. Our near-field nanoimaging results unveil an unconventional and broad tunability of both the polaritonic wavelength and direction of propagation upon negative reflection. Based on these findings, we introduce a novel device in nano-optics: a hyperbolic nanoresonator, in which hyperbolic polaritons with different momenta reflect back to a common point source, enhancing its intensity. These results pave the way to realize nanophotonics in low-loss natural media, providing a novel and efficient route to confine and control the flow of light at the nanoscale, key for future optical on-chip nanotechnologies.

Terahertz (THz) electromagnetic radiation is key to optically access collective excitations such as magnons (spins), plasmons (electrons), or phonons (atomic vibrations), thus bridging between optics and solid-state physics. Confinement of THz light to the nanometer length scale is desirable for local probing of such excitations in low dimensional systems, thereby inherently circumventing the large footprint and low spectral density of far-field THz optics. For that purpose, phonon polaritons (PhPs, i.e., light coupled to lattice vibrations in polar crystals) in anisotropic van der Waals (vdW) materials have recently emerged as a promising platform for THz nanooptics; yet the amount of explored, viable materials is still exiguous. Hence, there is a demand for the exploration of novel materials that feature not only THz PhPs at different spectral regimes, but also exhibit unique anisotropic (directional) electrical, thermoelectric, and vibronic properties. To that end, we introduce here the semiconducting alpha-germanium(II) sulfide (GeS) as an intriguing candidate. By employing THz nano-spectroscopy supported by theoretical analysis, we provide a thorough characterization of the different in-plane hyperbolic and elliptical PhP modes in GeS. We find not only PhPs with long life times ($\tau$ > 2 ps) and excellent THz light confinement ($\lambda_0/\lambda$ > 45), but also an intrinsic, phonon-induced anomalous dispersion as well as signatures of naturally occurring PhP canalization within one single GeS slab.

Phonon polaritons (PhPs) -- lattice vibrations coupled to electromagnetic fields -- in highly anisotropic media display a plethora of intriguing optical phenomena (including ray-like propagation, anomalous refraction, and topological transitions, among others), which have potential for unprecedented manipulation of the flow of light at the nanoscale. However, the propagation properties of these PhPs are intrinsically linked to the anisotropic crystal structure of the host material. Although in-plane anisotropic PhPs can be steered (and even canalized) by twisting individual crystal slabs in a van der Waals (vdW) stack, active control of their propagation via external stimuli presents a significant challenge. Here, we report on a technology in which anisotropic PhPs supported by biaxial vdW slabs are actively tunable by simply gating an integrated graphene layer. Excitingly, we predict active tuning of optical topological transitions, which enable controlling the canalization of PhPs along different in-plane directions in twisted heterostructures. Apart from their fundamental interest, our findings hold promises for the development of optoelectronic devices (sensors, photodetectors, etc.) based on PhPs with dynamically controllable properties.

Plasmon polaritons in topological insulators attract attention from a fundamental perspective and for potential THz photonic applications. Although polaritons have been observed by THz far-field spectroscopy on topological insulator microstructures, real-space imaging of propagating THz polaritons has been elusive so far. Here, we show spectroscopic THz near-field images of thin Bi2Se3 layers (prototypical topological insulators) revealing polaritons with up to 12 times increased momenta as compared to photons of the same energy and decay times of about 0.48 ps, yet short propagation lengths. From the images we determine and analyze the polariton dispersion, showing that the polaritons can be explained by the coupling of THz radiation to various combinations of Dirac and massive carriers at the Bi2Se3 surfaces, massive bulk carriers and optical phonons. Our work provides critical insights into the nature of THz polaritons in topological insulators and establishes instrumentation and methodology for imaging of THz polaritons.

Phonon polaritons (PhPs),light coupled to lattice vibrations,with in-plane hyperbolic dispersion exhibit ray-like propagation with large wavevectors and enhanced density of optical states along certain directions on a surface. As such, they have raised a surge of interest as they promise unprecedented possibilities for the manipulation of infrared light with planar circuitry and at the nanoscale. Here, we demonstrate, for the first time, the focusing of in-plane hyperbolic PhPs propagating along thin slabs of MoO3. To that end, we developed metallic nanoantennas of convex geometries for both the efficient launching and focusing of the polaritons. Remarkably, the foci obtained exhibit enhanced near-field confinement and absorption compared to foci produced by in-plane isotropic PhPs. More intriguingly, foci sizes as small as lamdap/5 =lamda0/50 were achieved (lamdap is the polariton wavelength and lamda0 the photon wavelength). Focusing of in-plane hyperbolic polaritons introduces a first and most basic building block developing planar polariton optics utilizing in-plane anisotropic van der Waals materials and metasurfaces.

Recent discoveries of polaritons in van der Waals (vdW) crystals with directional in-plane propagation, ultra-low losses, and broad spectral tunability have opened the door for unprecedented manipulation of the flow of light at the nanoscale. However, despite their extraordinary potential for nano-optics, these unique polaritons also present an important limitation: their directional propagation is intrinsically determined by the crystal structure of the host material, which imposes forbidden directions of propagation and hinders its control. Here, we theoretically predict and experimentally demonstrate that directional polaritons (in-plane hyperbolic phonon polaritons) in a vdW biaxial slab (alpha-phase molybdenum trioxide) can be steered along previously forbidden directions by inducing an optical topological transition, which naturally emerges when placing the slab on a substrate with a given negative permittivity (4H-SiC). Importantly, due to the low-loss nature of this topological transition, we are able to visualize in real space exotic intermediate polaritonic states between mutually orthogonal hyperbolic regimes, which permit to unveil the unique topological origin of the transition. This work provides new insights into the emergence of low-loss optical topological transitions in vdW crystals, offering a novel route to efficiently steer the flow of energy at the nanoscale.

Phonon polaritons (PPs) in van der Waals (vdW) materials can strongly enhance light-matter interactions at mid-infrared frequencies, owing to their extreme infrared field confinement and long lifetimes. PPs thus bear potential for achieving vibrational strong coupling (VSC) with molecules. Although the onset of VSC has recently been observed spectroscopically with PP nanoresonators, no experiments so far have resolved VSC in real space and with propagating modes in unstructured layers. Here, we demonstrate by real-space nanoimaging that VSC can be achieved between propagating PPs in thin vdW crystals (specifically h-BN) and molecular vibrations in adjacent thin molecular layers. To that end, we performed near-field polariton interferometry, showing that VSC leads to the formation of a propagating hybrid mode with a pronounced anti-crossing region in its dispersion, in which propagation with negative group velocity is found. Numerical calculations predict VSC for nanometer-thin molecular layers and PPs in few-layer vdW materials, which could make propagating PPs a promising platform for ultra-sensitive on-chip spectroscopy and strong coupling experiments.

As we read this text, our eyes dynamically adjust the focal length to keep the line image in focus on the retina. Similarly, in many optics applications the focal length must be dynamically tunable. In the quest for compactness and tunability, flat lenses based on metasurfaces were introduced. However, their dynamic tunability is still limited because their functionality mostly relies upon fixed geometry. In contrast, we put forward an original concept of a tunable Optical Magnetic Lens (OML) that focuses photon beams using a subwavelength-thin layer of a magneto-optical material in a non-uniform magnetic field. We applied the OML concept to a wide range of materials and found out that the effect of OML is present in a broad frequency range from microwaves to visible light. For terahertz light, OML can allow 50% relative tunability of the focal length on the picosecond time scale, which is of practical interest for ultrafast shaping of electron beams in microscopy. The OML based on magneto-optical natural bulk and 2D materials may find broad use in technologies such as 3D optical microscopy and acceleration of charged particle beams by THz beams.

Electromagnetic field confinement is crucial for nanophotonic technologies, since it allows for enhancing light-matter interactions, thus enabling light manipulation in deep sub-wavelength scales. In the terahertz (THz) spectral range, radiation confinement is conventionally achieved with specially designed metallic structures - such as antennas or nanoslits - with large footprints due to the rather long wavelengths of THz radiation. In this context, phonon polaritons - light coupled to lattice vibrations - in van der Waals (vdW) crystals have emerged as a promising solution for controlling light beyond the diffraction limit, as they feature extreme field confinements and low optical losses. However, experimental demonstration of nanoscale-confined phonon polaritons at THz frequencies has so far remained elusive. Here, we provide it by employing scattering-type scanning near-field optical microscopy (s-SNOM) combined with a free-electron laser (FEL) to reveal a range of low-loss polaritonic excitations at frequencies from 8 to 12 THz in the vdW semiconductor ${\alpha}-MoO_3$. We visualize THz polaritons with i) in-plane hyperbolic dispersion, ii) extreme nanoscale field confinement (below ${\lambda}_o/75$) and iii) long polariton lifetimes, with a lower limit of > 2 ps.

Recent discoveries have shown that when two layers of van der Waals (vdW) materials are superimposed with a relative twist angle between their respective in-plane principal axes, the electronic properties of the coupled system can be dramatically altered. Here, we demonstrate that a similar concept can be extended to the optics realm, particularly to propagating polaritons, hybrid light-matter interactions. To do this, we fabricate stacks composed of two twisted slabs of a polar vdW crystal (MoO3) supporting low-loss anisotropic phonon polaritons (PhPs), and image the propagation of the latter when launched by localized sources (metal antennas). Our images reveal that under a critical angle the PhPs isofrequency curve (determining the PhPs momentum at a fixed frequency) undergoes a topological transition. Remarkably, at this angle, the propagation of PhPs is strongly guided along predetermined directions (canalization regime) with no geometrical spreading (diffraction-less). These results demonstrate a new degree of freedom (twist angle) for controlling the propagation of polaritons at the nanoscale with potential for nano-imaging, (bio)-sensing, quantum applications and heat management.

Resonant optical antennas supporting plasmon polaritons (SPPs) - collective excitations of electrons coupled to electromagnetic fields in a medium - are relevant to sensing, photovoltaics, and light-emitting devices, among others. Due to the SPP dispersion, a conventional antenna of fixed geometry, exhibiting a narrow SPP resonance, cannot simultaneously operate in two different spectral bands. In contrast, here it is demonstrated that in metallic disks, separated by a nanometric spacer, the hybridized antibonding SPP mode stays in the visible range, while the bonding one can be pushed down to the mid-infrared range. Such an SPP dimer can sense two materials of nanoscale volumes, whose fingerprint central frequencies differ by a factor of 5. Additionally, the mid-infrared SPP resonance can be tuned by employing a phase-change material (VO2) as a spacer. The dielectric constant of the phase-change material is controlled by heating the material at the frequency of the antibonding optical mode. These findings open the door to a new class of optoelectronic devices able to operate in significantly different frequency ranges in the linear regime, and with the same polarization of the illuminating wave.

The biaxial van der Waals semiconductor $\alpha$-phase molybdenum trioxide ($\alpha$-MoO$_3$) has recently received significant attention due to its ability to support highly anisotropic phonon polaritons (PhPs) -infrared (IR) light coupled to lattice vibrations in polar materials-, offering an unprecedented platform for controlling the flow of energy at the nanoscale. However, to fully exploit the extraordinary IR response of this material, an accurate dielectric function is required. Here, we report the accurate IR dielectric function of $\alpha$-MoO$_3$ by modelling far-field, polarized IR reflectance spectra acquired on a single thick flake of this material. Unique to our work, the far-field model is refined by contrasting the experimental dispersion and damping of PhPs, revealed by polariton interferometry using scattering-type scanning near-field optical microscopy (s-SNOM) on thin flakes of $\alpha$-MoO$_3$, with analytical and transfer-matrix calculations, as well as full-wave simulations. Through these correlative efforts, exceptional quantitative agreement is attained to both far- and near-field properties for multiple flakes, thus providing strong verification of the accuracy of our model, while offering a novel approach to extracting dielectric functions of nanomaterials, usually too small or inhomogeneous for establishing accurate models only from standard far-field methods. In addition, by employing density functional theory (DFT), we provide insights into the various vibrational states dictating our dielectric function model and the intriguing optical properties of $\alpha$-MoO$_3$.

Anisotropic crystals have recently attracted considerable attention because of their ability to support polaritons with a variety of unique properties, such as hyperbolic dispersion, negative phase velocity, or extreme confinement. Particularly, the biaxial crystal $\alpha$-MoO$_3$ has been demonstrated to support phonon polaritons, light coupled to lattice vibrations, with in-plane anisotropic propagation and unusually long lifetime. However, the lack of theoretical studies on electromagnetic modes in biaxial crystal slabs impedes a complete interpretation of the experimental data, as well as an efficient design of nanostructures supporting such highly anisotropic polaritons. Here, we derive the dispersion relation of electromagnetic modes in biaxial slabs surrounded by semi-infinite isotropic dielectric half-spaces with arbitrary dielectric permittivities. Apart from a general dispersion relation, we provide very simple analytical expressions in typical experiments in nano-optics: the limits of short polaritonic wavelength and/or very thin slabs. The results of our study will allow for an in-depth analysis of anisotropic polaritons in novel biaxial van der Waals materials., Comment: 16 pages, 4 figures

Although the detection of light at terahertz (THz) frequencies is important for a large range of applications, current detectors typically have several disadvantages in terms of sensitivity, speed, operating temperature, and spectral range. Here, we use graphene as a photoactive material to overcome all of these limitations in one device. We introduce a novel detector for terahertz radiation that exploits the photothermoelectric (PTE) effect, based on a design that employs a dual-gated, dipolar antenna with a gap of 100 nm. This narrow-gap antenna simultaneously creates a pn junction in a graphene channel located above the antenna and strongly concentrates the incoming radiation at this pn junction, where the photoresponse is created. We demonstrate that this novel detector has an excellent sensitivity, with a noise-equivalent power of 80 pW-per-square-root-Hz at room temperature, a response time below 30 ns (setup-limited), a high dynamic range (linear power dependence over more than 3 orders of magnitude) and broadband operation (measured range 1.8-4.2 THz, antenna-limited), which fulfills a combination that is currently missing in the state-of-the-art detectors. Importantly, on the basis of the agreement we obtained between experiment, analytical model, and numerical simulations, we have reached a solid understanding of how the PTE effect gives rise to a THz-induced photoresponse, which is very valuable for further detector optimization., Comment: 26 pages, 3 main figures and 10 supplementary figures

Metasurfaces with strongly anisotropic optical properties can support deep subwavelength-scale confined electromagnetic waves (polaritons) that promise opportunities for controlling light in photonic and optoelectronic applications. We develop a mid-infrared hyperbolic metasurface by nanostructuring a thin layer of hexagonal boron nitride supporting deep subwavelength-scale phonon polaritons that propagate with in-plane hyperbolic dispersion. By applying an infrared nanoimaging technique, we visualize the concave (anomalous) wavefronts of a diverging polariton beam, which represent a landmark feature of hyperbolic polaritons. The results illustrate how near-field microscopy can be applied to reveal the exotic wavefronts of polaritons in anisotropic materials, and demonstrate that nanostructured van der Waals materials can form a highly variable and compact platform for hyperbolic infrared metasurface devices and circuits.

Enhanced light-matter interactions are the basis of surface enhanced infrared absorption (SEIRA) spectroscopy, and conventionally rely on plasmonic materials and their capability to focus light to nanoscale spot sizes. Phonon polariton nanoresonators made of polar crystals could represent an interesting alternative, since they exhibit large quality factors, which go far beyond those of their plasmonic counterparts. The recent emergence of van der Waals crystals enables the fabrication of high-quality nanophotonic resonators based on phonon polaritons, as reported for the prototypical infrared-phononic material hexagonal boron nitride (h-BN). In this work we use, for the first time, phonon-polariton-resonant h-BN ribbons for SEIRA spectroscopy of small amounts of organic molecules in Fourier transform infrared spectroscopy. Strikingly, the interaction between phonon polaritons and molecular vibrations reaches experimentally the onset of the strong coupling regime, while numerical simulations predict that vibrational strong coupling can be fully achieved. Phonon polariton nanoresonators thus could become a viable platform for sensing, local control of chemical reactivity and infrared quantum cavity optics experiments.

The magnetic circular dichroism and the Faraday rotation are the fundamental phenomena of great practical importance arising from the breaking of the time reversal symmetry by a magnetic field. In most materials the strength and the sign of these effects can be only controlled by the field value and its orientation. Furthermore, the terahertz range is lacking materials having the ability to affect the polarisation state of the light in a non-reciprocal manner. Here we demonstrate, using broadband terahertz magneto-electro-optical spectroscopy, that in graphene both the magnetic circular dichroism and the Faraday rotation can be modulated in intensity, tuned in frequency and, importantly, inverted using only electrostatic doping at a fixed magnetic field. In addition, we observe strong magneto-plasmonic resonances in a patterned array of graphene antidots, which potentially allows exploiting these magneto-optical phenomena in a broad THz range., Comment: 7 pages, 3 figures, supplementary information included

Van der Waals (vdW) materials exhibit intriguing structural, electronic and photonic properties. Electron Energy Loss Spectroscopy (EELS) within Scanning Transmission Electron Microscope (STEM) allows for nanoscale mapping of such properties. However, typical STEM-EELS detection is limited to energy losses in the eV range, which are too large for probing important low-energy excitation such as phonons or mid-IR plasmons. Here we adapt a conventional STEM-EELS system to probe energy loss down to 100 meV, and apply it to map phononic states in h-BN, a representative van der Waals (vdW) material. The h-BN EELS spectra, surprisingly, depend on the h-BN thickness and the distance of the electron beam to h-BN flake edges. To explain this observation, we developed a classical response theory describing the interaction of fast electrons with (anisotropic) slabs of vdW materials. Theoretical and numerical calculations perfectly match the experimental h-BN spectra, and reveal that the electron loss is dominated by the excitation of hyperbolic phonon polaritons, and not of bulk phonons as often reported. Thus, STEM-EELS offers the possibility to probe low-energy polaritons in vdW materials, with our theory being of fundamental importance for interpreting future experiments.

Terahertz (THz) fields are widely applied for sensing, communication and quality control. In future applications, they could be efficiently confined, enhanced and manipulated - well below the classical diffraction limit - through the excitation of graphene plasmons (GPs). These possibilities emerge from the strongly reduced GP wavelength, lp, compared to the photon wavelength, l0, which can be controlled by modulating the carrier density of graphene via electrical gating. Recently, GPs in a graphene-insulator-metal configuration have been predicted to exhibit a linear dispersion (thus called acoustic plasmons) and a further reduced wavelength, implying an improved field confinement, analogous to plasmons in two-dimensional electron gases (2DEGs) near conductive substrates. While infrared GPs have been visualised by scattering-type scanning near-field optical microscopy (s-SNOM), the real-space imaging of strongly confined THz plasmons in graphene and 2DEGs has been elusive so far - only GPs with nearly free-space wavelength have been observed. Here we demonstrate real-space imaging of acoustic THz plasmons in a graphene photodetector with split-gate architecture. To that end, we introduce nanoscale-resolved THz photocurrent near-field microscopy, where near-field excited GPs are detected thermoelectrically rather than optically. The on-chip GP detection simplifies GP imaging, as sophisticated s-SNOM detection schemes can be avoided. The photocurrent images reveal strongly reduced GP wavelengths (lp = l0/66), a linear dispersion resulting from the coupling of GPs with the metal gate below the graphene, and that plasmon damping at positive carrier densities is dominated by Coulomb impurity scattering. Acoustic GPs could thus strongly benefit the development of deep subwavelength-scale THz devices.

We demonstrate that the interaction between two emitters can be controlled by means of the efficient excitation of surface plasmon modes in graphene. We consider graphene surface plasmons supported by either two-dimensional graphene sheets or one-dimensional graphene ribbons, showing in both cases that the coupling between the emitters can be strongly enhanced or suppressed. The super- and subradiant regimes are investigated in the reflection and transmission configurations. Importantly, the length scale of the coupling between emitters, which in vacuum is fixed by the free space wavelength, is now determined by the wavelength of the graphene surface plasmons that can be extremely short and be tuned at will via a gate voltage.