Polariton waveguide modes in two-dimensional van der Waals crystals: an analytical model and correlative nano-imaging

Tailoring Phonon Polaritons with a Single-Layer Photonics-Empowered Polaritonic Crystal

Photonic crystals (PhCs) are artificial periodic structures that can compress and control light at the nanoscale. Recently, the emerging van der Waals (vdW) materials with extreme anisotropy exhibit exotic hyperbolic phonon resonances and ray-like propagation. However, localization and manipulation of these hyperbolic phonon polaritons (PhPs) in polaritonic crystals (PoCs) on a scale deeply below the polariton wavelength have remained elusive so far. Here, we experimentally demonstrate tailored PhP localization in a single layer PoC of patterned α-MoO3. The biaxial PoCs have a rotation degree of freedom between the lattice orientation and the optical axis of α-MoO3. By tailoring the rotation angle, the bandgap exhibits a transition from open to closed at certain wavelengths. Two-dimensional localization of PhPs in these rotated PoCs have been directly revealed in real space by infrared nanoimaging. Our work provides a robust platform to construct polaritonic cavities for ultrastrong light-matter interactions and nanoscale polariton manipulation.

Multiple hyperbolic waves

This study presents a conceptual design for a hyperbolic material utilizing transformation optics. This material is designed to produce multiple hyperbolic wave fields or polaritons excited by a point source. The design dictates key parameters including branch number, propagation range, and overall propagation direction of deflection. Through this approach, the hyperbolic material demonstrates new effects compared to traditional hyperbolic materials. These advancements offer possibilities for the design and applications of photonic devices in other degrees of freedom.

Isotopic effects on in-plane hyperbolic phonon polaritons in MoO3

Hyperbolic phonon polaritons (HPhPs), hybrids of light and lattice vibrations in polar dielectric crystals, empower nanophotonic applications by enabling the confinement and manipulation of light at the nanoscale. Molybdenum trioxide (α-MoO3) is a naturally hyperbolic material, meaning that its dielectric function deterministically controls the directional propagation of in-plane HPhPs within its reststrahlen bands. Strategies such as substrate engineering, nano- and heterostructuring, and isotopic enrichment are being developed to alter the intrinsic die ectric functions of natural hyperbolic materials and to control the confinement and propagation of HPhPs. Since isotopic disorder can limit phonon-based processes such as HPhPs, here we synthesize isotopically enriched 92MoO3 (92Mo: 99.93 %) and 100MoO3 (100Mo: 99.01 %) crystals to tune the properties and dispersion of HPhPs with respect to natural α-MoO3, which is composed of seven stable Mo isotopes. Real-space, near-field maps measured with the photothermal induced resonance (PTIR) technique enable comparisons of inplane HPhPs in α-MoO3 and isotopically enriched analogues within a reststrahlen band (≈820 cm-1 to ≈ 972 cm-1). Results show that isotopic enrichment (e.g., 92MoO3 and 100MoO3) alters the dielectric function, shifting the HPhP dispersion (HPhP angular wavenumber × thickness vs IR frequency) by ≈-7% and ≈ +9 %, respectively, and changes the HPhP group velocities by ≈ ±12 %, while the lifetimes (≈ 3 ps) in 92MoO3 were found to be slightly improved (≈ 20 %). The latter improvement is attributed to a decrease in isotopic disorder. Altogether, isotopic enrichment was found to offer fine control over the properties that determine the anisotropic in-plane propagation of HPhPs in α-MoO3, which is essential to its implementation in nanophotonic applications.

Terahertz Twistoptics-Engineering Canalized Phonon Polaritons

The terahertz (THz) frequency range is key to studying 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-molecule 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 (HPhPs) 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 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 α-molybdenum trioxide (α-MoO3), hence extending twistoptics to this intriguing frequency range. Our images, recorded by near-field optical microscopy, show the frequency- and twist-angle-dependent changes 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 α-MoO3 at 8.67 THz for a twist angle of 50°. Our results demonstrate the precise control and manipulation of confined collective excitations at THz frequencies, particularly offering possibilities for nanophotonic applications.

Flatband polaritonic router in twisted bilayer van der Waals materials

In recent years, van der Waals (vdW) polaritons excited by the hybrid of matter and photons have shown great promise for applications in nanoimaging, biosensing, and on-chip light guiding. In particular, polaritons with a flatband dispersion allow for mode canalization and diffractionless propagation, which showcase advantages for on-chip technologies requiring long-range transportation of optical information. Here, we propose a flatband polaritonic router based on twisted α-MoO₃ bilayers, which allows for on-chip routing of highly confined and low-loss phonon polaritons (PhPs) along multichannel propagating paths under different circular polarized dipole excitations. Our work combines flatband physics and optical spin- orbit coupling, with potential applications in nanoscale light propagation, on-chip optical switching, and communication.

Observation of directional leaky polaritons at anisotropic crystal interfaces

Extreme anisotropy in some polaritonic materials enables light propagation with a hyperbolic dispersion, leading to enhanced light-matter interactions and directional transport. However, these features are typically associated with large momenta that make them sensitive to loss and poorly accessible from far-field, being bound to the material interface or volume-confined in thin films. Here, we demonstrate a new form of directional polaritons, leaky in nature and featuring lenticular dispersion contours that are neither elliptical nor hyperbolic. We show that these interface modes are strongly hybridized with propagating bulk states, sustaining directional, long-range, sub-diffractive propagation at the interface. We observe these features using polariton spectroscopy, far-field probing and near-field imaging, revealing their peculiar dispersion, and - despite their leaky nature - long modal lifetime. Our leaky polaritons (LPs) nontrivially merge sub-diffractive polaritonics with diffractive photonics onto a unified platform, unveiling opportunities that stem from the interplay of extreme anisotropic responses and radiation leakage.

In-plane hyperbolic polariton tuners in terahertz and long-wave infrared regimes

One of the main bottlenecks in the development of terahertz (THz) and long-wave infrared (LWIR) technologies is the limited intrinsic response of traditional materials. Hyperbolic phonon polaritons (HPhPs) of van der Waals semiconductors couple strongly with THz and LWIR radiation. However, the mismatch of photon - polariton momentum makes far-field excitation of HPhPs challenging. Here, we propose an In-Plane Hyperbolic Polariton Tuner that is based on patterning van der Waals semiconductors, here α-MoO3, into ribbon arrays. We demonstrate that such tuners respond directly to far-field excitation and give rise to LWIR and THz resonances with high quality factors up to 300, which are strongly dependent on in-plane hyperbolic polariton of the patterned α-MoO3. We further show that with this tuner, intensity regulation of reflected and transmitted electromagnetic waves, as well as their wavelength and polarization selection can be achieved. Our results can help the development of THz and LWIR miniaturized devices.

Twist-tunable polaritonic nanoresonators in a van der Waals crystal

Optical nanoresonators are key building blocks in various nanotechnological applications (e.g., spectroscopy) due to their ability to effectively confine light at the nanoscale. Recently, nanoresonators based on phonon polaritons (PhPs)-light coupled to lattice vibrations-in polar crystals (e.g., SiC, or h-BN) have attracted much attention due to their strong field confinement, high quality factors, and their potential to enhance the photonic density of states at mid-infrared (mid-IR) frequencies, where numerous molecular vibrations reside. Here, we introduce a new class of mid-IR nanoresonators that not only exhibit the extraordinary properties previously reported, but also incorporate a new degree of freedom: twist tuning, i.e., the possibility of controlling their spectral response by simply rotating the constituent material. To achieve this result, we place a pristine slab of the van der Waals (vdW) α-MoO3 crystal, which supports in-plane hyperbolic PhPs, on an array of metallic ribbons. This sample design based on electromagnetic engineering, not only allows the definition of α-MoO3 nanoresonators with low losses (quality factors, Q, up to 200), but also enables a broad spectral tuning of the polaritonic resonances (up to 32 cm-1, i.e., up to ~6 times their full width at half maximum, FWHM ~5 cm-1) by a simple in-plane rotation of the same slab (from 0 to 45°). These results open the door to the development of tunable and low-loss IR nanotechnologies, fundamental requirements for their implementation in molecular sensing, emission or photodetection applications.

Perfectly matched layer for biaxial hyperbolic materials

Hyperbolic materials have attracted considerable interest for their unique open hyperbolic dispersion properties. These materials support high-momentum propagating modes and strong light confinement, leading to a wide range of applications including super-resolution technologies, negative refraction and long-life propagation. Even with these wonderful optical properties, hyperbolic materials, however, cause problems when applying perfectly matched layer (PML) boundary conditions in numerical simulation software such as COMSOL Multiphysics. Due to the unfit embedded attenuation function, the built-in PML of simulation software would result in a mass of reflections in the computational domain when the background medium is hyperbolic materials. Here, we take advantage of an imaginary coordinate mapping and the complex coordinate stretching of transformation optics theory to design a PML for biaxial hyperbolic materials, which avoids any reflections and can be tuned flexibly. The proposed recipe can provide antidote and new insights for hyperbolic material studies.

Germanium Monosulfide as a Natural Platform for Highly Anisotropic THz Polaritons

Terahertz (THz) electromagnetic radiation is key to access collective excitations such as magnons (spins), plasmons (electrons), or phonons (atomic vibrations), thus bridging topics 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 circumventing the large footprint and inherently low spectral power density of far-field THz radiation. For that purpose, phonon polaritons (PhPs) in anisotropic van der Waals (vdW) materials have recently emerged as a promising platform for THz nanooptics. Hence, there is a demand for the exploration of materials that feature not only THz PhPs at different spectral regimes but also host anisotropic (directional) electrical, thermoelectric, and vibronic properties. To that end, we introduce here the semiconducting vdW-material alpha-germanium(II) sulfide (GeS) as an intriguing candidate. By employing THz nanospectroscopy 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 lifetimes (τ > 2 ps) and excellent THz light confinement (λ0/λ > 45) but also an intrinsic, phonon-induced anomalous dispersion as well as signatures of naturally occurring, substrate-mediated PhP canalization within a single GeS slab.

Unidirectionally excited phonon polaritons in high-symmetry orthorhombic crystals

Advanced control over the excitation of ultraconfined polaritons-hybrid light and matter waves-empowers unique opportunities for many nanophotonic functionalities, e.g., on-chip circuits, quantum information processing, and controlling thermal radiation. Recent work has shown that highly asymmetric polaritons are directly governed by asymmetries in crystal structures. Here, we experimentally demonstrate extremely asymmetric and unidirectional phonon polariton (PhP) excitation via directly patterning high-symmetry orthorhombic van der Waals (vdW) crystal α-MoO₃. This phenomenon results from symmetry breaking of momentum matching in polaritonic diffraction in vdW materials. We show that the propagation of PhPs can be versatile and robustly tailored via structural engineering, while PhPs in low-symmetry (e.g., monoclinic and triclinic) crystals are largely restricted by their naturally occurring permittivities. Our work synergizes grating diffraction phenomena with the extreme anisotropy of high-symmetry vdW materials, enabling unexpected control of infrared polaritons along different pathways and opening opportunities for applications ranging from on-chip photonics to directional heat dissipation.

Surface plasmons induce topological transition in graphene/α-MoO3 heterostructures

Polaritons in hyperbolic van der Waals materials-where principal axes have permittivities of opposite signs-are light-matter modes with unique properties and promising applications. Isofrequency contours of hyperbolic polaritons may undergo topological transitions from open hyperbolas to closed ellipse-like curves, prompting an abrupt change in physical properties. Electronically-tunable topological transitions are especially desirable for future integrated technologies but have yet to be demonstrated. In this work, we present a doping-induced topological transition effected by plasmon-phonon hybridization in graphene/α-MoO3 heterostructures. Scanning near-field optical microscopy was used to image hybrid polaritons in graphene/α-MoO3. We demonstrate the topological transition and characterize hybrid modes, which can be tuned from surface waves to bulk waveguide modes, traversing an exceptional point arising from the anisotropic plasmon-phonon coupling. Graphene/α-MoO3 heterostructures offer the possibility to explore dynamical topological transitions and directional coupling that could inspire new nanophotonic and quantum devices.

Lithography-free tunable absorber at visible region via one-dimensional photonic crystals consisting of an α-MoO3 layer

Flexible control of light absorption within the lithography-free nanostructure is crucial for many polarization-dependent optical devices. Herein, we demonstrated that the lithography-free tunable absorber (LTA) can be realized by using two one-dimensional (1D) photonic crystals (PCs) consisting of an α-MoO₃ layer at visible region. The two 1D PCs have different bulk band properties, and the topological interface state-induced light absorption enhancement of α-MoO₃ can be realized as the α-MoO₃ thin film is inserted at the interface between the two 1D PCs. The resonant cavity model is proposed to evaluate the anisotropic absorption performances of the LTA, and the results are in good agreement with those of the transfer matrix method (TMM). The absorption efficiency of the LTA can be tailored by the number of the period of the two PCs, and the larger peak absorption is the direct consequence of the larger field enhancement factor (FEF) within the α-MoO₃ layer. In addition, near-perfect absorption can be achieved as the LTA is operated at the over-coupled resonance. By varying the polarization angle, the absorption channels can be selected and the reflection response can be effectively modulated due to the excellent in-plane anisotropy of α-MoO₃.

Ultrahigh-Resolution, Label-Free Hyperlens Imaging in the Mid-IR

The hyperbolic phonon polaritons supported in hexagonal boron nitride (hBN) with long scattering lifetimes are advantageous for applications such as super-resolution imaging via hyperlensing. Yet, hyperlens imaging is challenging for distinguishing individual and closely spaced objects and for correlating the complicated hyperlens fields with the structure of an unknown object underneath. Here, we make significant strides to overcome each of these challenges. First, we demonstrate that monoisotopic h¹¹BN provides significant improvements in spatial resolution, experimentally resolving structures as small as 44 nm and those with sub 25 nm spacings at 6.76 μm free-space wavelength. We also present an image reconstruction algorithm that provides a structurally accurate, visual representation of the embedded objects from the complex hyperlens field. Further, we offer additional insights into optimizing hyperlens performance on the basis of material properties, with an eye toward realizing far-field imaging modalities. Thus, our results significantly advance label-free, high-resolution, spectrally selective hyperlens imaging and image reconstruction methodologies.

Focusing of in-plane hyperbolic polaritons in van der Waals crystals with tailored infrared nanoantennas

Phonon polaritons (PhPs)—light coupled to lattice vibrations—with in-plane hyperbolic dispersion exhibit ray-like propagation with large wave vectors and enhanced density of optical states along certain directions on a surface. As such, they have raised a surge of interest, promising unprecedented manipulation of infrared light at the nanoscale in a planar circuitry. Here, we demonstrate focusing of in-plane hyperbolic PhPs propagating along thin slabs of α-MoO₃. To that end, we developed metallic nanoantennas of convex geometries for both efficient launching and focusing of the polaritons. The foci obtained exhibit enhanced near-field confinement and absorption compared to foci produced by in-plane isotropic PhPs. Foci sizes as small as λ_p/4.5 = λ₀/50 were achieved (λ_p is the polariton wavelength and λ₀ is the photon wavelength). Focusing of in-plane hyperbolic polaritons introduces a first and most basic building block developing planar polariton optics using in-plane anisotropic van der Waals materials.

Interface nano-optics with van der Waals polaritons

Polaritons are hybrid excitations of matter and photons. In recent years, polaritons in van der Waals nanomaterials-known as van der Waals polaritons-have shown great promise to guide the flow of light at the nanoscale over spectral regions ranging from the visible to the terahertz. A vibrant research field based on manipulating strong light-matter interactions in the form of polaritons, supported by these atomically thin van der Waals nanomaterials, is emerging for advanced nanophotonic and opto-electronic applications. Here we provide an overview of the state of the art of exploiting interface optics-such as refractive optics, meta-optics and moiré engineering-for the control of van der Waals polaritons. This enhanced control over van der Waals polaritons at the nanoscale has not only unveiled many new phenomena, but has also inspired valuable applications-including new avenues for nano-imaging, sensing, on-chip optical circuitry, and potentially many others in the years to come.

Hybridized Hyperbolic Surface Phonon Polaritons at α-MoO3 and Polar Dielectric Interfaces

Surface phonon polaritons (SPhPs) in polar dielectrics offer new opportunities for infrared nanophotonics. However, bulk SPhPs inherently propagate isotropically with limited photon confinement, and how to collectively realize ultralarge confinement, in-plane hyperbolicity, and unidirectional propagation remains elusive. Here, we report an approach to solve the aforementioned issues of bulk SPhPs in one go by constructing a heterostructural interface between biaxial van der Waals material (e.g., α-MoO₃) and bulk polar dielectric (e.g., SiC, AlN, and GaN). Because of anisotropy-oriented mode couplings, the hybridized SPhPs with a large confinement factor (>100) show in-plane hyperbolicity that has been switched to the orthogonal direction as compared to that in natural α-MoO₃. More interestingly, this proof of concept allows steerable and unidirectional polariton excitation by suspending α-MoO₃ on patterned SiC air cavities. Our finding exemplifies a generalizable framework to manipulate the flow of nanolight in many other hybrid systems consisting of anisotropic materials and polar dielectrics.