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![Crystalline structure of α‐MoO3. a. Sketch of the unit cell of α‐MoO3 and correspondence between the crystallographic directions [100], [001], [010], and the spatial coordinates x, y, z; the lattice constants are a = 0.396 nm, b = 1.385 nm, and c = 0.369 nm. The blue/red spheres represent molybdenum/oxygen atoms. b) Optical image of an α‐MoO3 flake on top of AgCl. α‐MoO3 crystals typically appear to be rectangular owing to the anisotropic crystal structure. Labeled arrows indicate crystal directions.](profile/Gonzalo-Alvarez-Perez-2/publication/341905940/figure/fig1/AS:11431281173115487@1688764763255/Crystalline-structure-of-a-MoO3-a-Sketch-of-the-unit-cell-of-a-MoO3-and-correspondence.png)
Crystalline structure of α‐MoO3. a. Sketch of the unit cell of α‐MoO3 and correspondence between the crystallographic directions [100], [001], [010], and the spatial coordinates x, y, z; the lattice constants are a = 0.396 nm, b = 1.385 nm, and c = 0.369 nm. The blue/red spheres represent molybdenum/oxygen atoms. b) Optical image of an α‐MoO3 flake on top of AgCl. α‐MoO3 crystals typically appear to be rectangular owing to the anisotropic crystal structure. Labeled arrows indicate crystal directions.
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![Dispersion of PhPs on a thin α‐MoO3 slab. Transfer‐matrix[³⁵]...](profile/Gonzalo-Alvarez-Perez-2/publication/341905940/figure/fig3/AS:11431281173079216@1688764764028/Dispersion-of-PhPs-on-a-thin-a-MoO3-slab-Transfer-matrix-calculations-false-color_Q320.jpg)
The biaxial van der Waals semiconductor α‐phase molybdenum trioxide (α‐MoO3) has recently received significant attention due to its ability to support highly anisotropic phonon polaritons (PhPs)—infrared (IR) light coupled to lattice vibrations—offering an unprecedented platform for controlling the flow of energy at the nanoscale. However, to fully...
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... Finally, the observation of tunable, low-loss hyperbolic plasmons across a wide IR frequency range benefits from the unique combination of features in Kagome metals, including a high density of itinerant carriers, a quasi-2D structure, and electronic correlations. We demonstrated the feasibility of deriving the out-of-plane dielectric function ϵ c ðωÞ in CsV 3 Sb 5 via employing the evanescent near-field detection, which has also been utilized in biaxial α-MoO 3 to extract its dielectric function 54 . Unlike the extensively studied hyperbolic phonon polaritons, our findings represent the first occurrence of possible hyperbolic plasmons in a natural crystal facilitated by electronic correlations. ...
Plasmon polaritons, or plasmons, are coupled oscillations of electrons and electromagnetic fields that can confine the latter into deeply subwavelength scales, enabling novel polaritonic devices. While plasmons have been extensively studied in normal metals or semimetals, they remain largely unexplored in correlated materials. In this paper, we report infrared (IR) nano-imaging of thin flakes of CsV3Sb5, a prototypical layered Kagome metal. We observe propagating plasmon waves in real-space with wavelengths tunable by the flake thickness. From their frequency-momentum dispersion, we infer the out-of-plane dielectric function ϵc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{\boldsymbol{\epsilon }}}}}}}_{{{{{{\boldsymbol{c}}}}}}}$$\end{document} that is generally difficult to obtain in conventional far-field optics, and elucidate signatures of electronic correlations when compared to density functional theory (DFT). We propose correlation effects might have switched the real part of ϵc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{\boldsymbol{\epsilon }}}}}}}_{{{{{{\boldsymbol{c}}}}}}}$$\end{document} from negative to positive values over a wide range of middle-IR frequencies, transforming the surface plasmons into hyperbolic bulk plasmons, and have dramatically suppressed their dissipation.
... Numerical Simulations: The simulation results were obtained using a well-established full-wave simulation method demonstrated in multiple previous publications. [16,59] In the simulations, the illuminated s-SNOM tip was modeled as a vertically oriented point dipole source located 200 nm above the top surface of the MoO 3 microcrystal. The cross-sectional electric field distributions shown in Figure 1f,g as well as Figures S3 and S4, Supporting Information were obtained from 2D FDTD simulations on a stack of MoO 3 /hBN/gold. ...
Phonon polaritons, the hybrid quasiparticles resulting from the coupling of photons and lattice vibrations, have gained significant attention in the field of layered van der Waals heterostructures. Particular interest has been paid to hetero‐bicrystals composed of molybdenum oxide (MoO3) and hexagonal boron nitride (hBN), which feature polariton dispersion tailorable via avoided polariton mode crossings. In this work, the polariton eigenmodes in MoO3‐hBN hetero‐bicrystals self‐assembled on ultrasmooth gold are systematically studied using synchrotron infrared nanospectroscopy. It is experimentally demonstrated that the spectral gap in bicrystal dispersion and corresponding regimes of negative refraction can be tuned by material layer thickness, and these results are quantitatively matched with a simple analytic model. Polaritonic cavity modes and polariton propagation along “forbidden” directions are also investigated in microscale bicrystals, which arise from the finite in‐plane dimension of the synthesized MoO3 micro‐ribbons. The findings shed light on the unique dispersion properties of polaritons in van der Waals heterostructures and pave the way for applications leveraging deeply sub‐wavelength mid‐infrared light‐matter interactions.
... In the following, we introduce the vdW crystal LiV 2 O 5 (Fig. 2) by describing its crystal structure and extracting its optical permittivity. Resulting from the intercalation of α-V 2 O 5 with the alkaline atom Li 33,34 (see "Methods"), LiV 2 O 5 has an orthorhombic crystal lattice consisting of VO 5 pyramids that are connected along their edges forming zigzag chains along the b direction of the crystal ( Fig. 2b shows an optical image of the LiV 2 O 5 layer used for these measurements and placed on a BaF 2 substrate, which is transparent in the spectral range of our measurements 35 . Previous studies provided the initial dielectric function fit values 34 . ...
... To ensure robust agreement, these values were then tailored to align with our experimental spectra. By fitting the resulting spectra with a Lorentz model of coupled oscillators 35 (black dashed curves in Fig. 2b), we derived the dielectric permittivity tensor along the three crystallographic directions. In particular, we extract the parameters ω TO , ω LO , γ TO , and γ LO (Fig. 2c, d, see Supplementary Table 1 and Supplementary Fig. 3), i.e., the frequencies of the transverse (TO) and longitudinal optical (LO) phonons together with the corresponding damping rate. ...
Polariton canalization is characterized by intrinsic collimation of energy flow along a single crystalline axis. This optical phenomenon has been experimentally demonstrated at the nanoscale by stacking and twisting van der Waals (vdW) layers of α-MoO3, by combining α-MoO3 and graphene, or by fabricating an h-BN metasurface. However, these material platforms have significant drawbacks, such as complex fabrication and high optical losses in the case of metasurfaces. Ideally, it would be possible to canalize polaritons “naturally” in a single pristine layer. Here, we theoretically predict and experimentally demonstrate naturally canalized phonon polaritons (PhPs) in a single thin layer of the vdW crystal LiV2O5. In addition to canalization, PhPs in LiV2O5 exhibit strong field confinement (λp~λ027\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{\boldsymbol{\lambda }}}}}}}_{{{{{{\bf{p}}}}}}} \sim \frac{{{{{{{\boldsymbol{\lambda }}}}}}}_{{{{{{\bf{0}}}}}}}}{{{{{{\bf{27}}}}}}}$$\end{document}), slow group velocity (0.0015c), and ultra-low losses (lifetimes of 2 ps). Our findings are promising for the implementation of low-loss optical nanodevices where strongly directional light propagation is needed, such as waveguides or optical routers.
... [30,31] These materials feature biaxial permittivity tensors due to the low symmetry of their atomic lattices. [32][33][34] This sophisticated anisotropy enables complex optical phenomena, such as hyperbolic dispersion, [35] anomalous refraction, [36] canalization, [37,38] and many others. Despite the diversity of possible anisotropic optical properties, bulk vdW crystals are typically achiral. ...
Chirality is one of the most mysterious symmetry transformations. Very readily broken in biological systems, it is practically absent in naturally occurring inorganic materials and is very challenging to create artificially. Chiral optical wavefronts are often used for the identification, control, and discrimination of left-and right-handed biological and other molecules. Thus, it is crucially important to create materials capable of chiral interaction with light, which would allow one to assign arbitrary chiral properties to a light field. This study utilizes van der Waals technology to assemble helical homostructures with chiral properties (e.g., circular dichroism). Because of the large range of van der Waals materials available, such helical homostructures can be assigned with very flexible optical properties. The approach is demonstrated by creating helical homostructures based on multilayer As 2 S 3 (arsenic trisulfide), which offers the most pronounced chiral properties even in thin structures due to its strong biaxial optically anisotropy. The work showcases that the chirality of an electromagnetic system may emerge at an intermediate level between the molecular and the mesoscopic one due to the tailored arrangement of non-chiral layers of van der Waals crystals and without additional patterning.
... There are two types of Drude-Lorenz model widely used in calculating the dielectric functions of materials containing PhPs. One is called LOTO formalism or four-parameter semi-quantum model 2,[22][23][24] : ...
... experiment. The incident wave vector forms a 25-degree angle with the z-axis22 and then the refraction wave vector direction is determined self-consistently. The refraction angle (the wave vector direction inside h-BN) obtained with calculation method section 2.2 is shown inFigure 4. ...
... Fabrication and characterization of α-MoO 3 flakes We mechanically exfoliate flakes of α-MoO 3 from bulk crystals and transfer them to silicon and gold-coated glass substrates to realize phase retarders that operate in transmission and reflection mode, respectively. Exfoliated flakes of α-MoO 3 typically possess a rectangular shape, due to the crystal's orthorhombic structure 29 (Fig. 2a). We refer to the crystal directions [100], ...
... We measure the dielectric permittivity of α-MoO 3 using Fourier transform infrared (FTIR) spectroscopy, implementing the method described in 46 . The results we obtain, shown in Fig. 2b, c, are in agreement with previous reports [27][28][29] . As shown in panel b, near 12 μm, the dielectric function along the x-axis (ε x ) resonates due to a transverse optical phonon occurring at the corresponding photon energy, while ε y remains very small. ...
Phase retardation is a cornerstone of modern optics, yet, at mid-infrared (mid-IR) frequencies, it remains a major challenge due to the scarcity of simultaneously transparent and birefringent crystals. Most materials resonantly absorb due to lattice vibrations occurring at mid-IR frequencies, and natural birefringence is weak, calling for hundreds of microns to millimeters-thick phase retarders for sufficient polarization rotation. Here, we demonstrate mid-IR phase retardation with flakes of α-MoO3 that are more than ten times thinner than the operational wavelength, achieving 90 degrees polarization rotation within one micrometer of material. We report conversion ratios above 50% in reflection or transmission mode, and wavelength tunability by several micrometers. Our results showcase that exfoliated flakes of low-dimensional crystals can serve as a platform for mid-IR miniaturized integrated low-loss polarization control.
... One particular research focus lies with hyperbolic phonon polaritons (HPPs) originating from the coupling between photons and lattice vibrations. These phenomena occur in vdW materials with permittivities of opposite signs along different directions, e.g., hexagonal boron nitride (hBN) [4], [11]- [13] and alpha-phase molybdenum trioxide (α-MoO 3 ) [1], [14], [15]. HPPs feature ultra-confined and highly directional light beam with hyperbolic dispersion, enabling novel nanophotonic applications such as hyperlensing [16], negative refraction [17], [18], molecular sensing [19]- [22], and nanofocusing [23], [24]. ...
... For spatially decaying modes, we considered real-valued frequencies and complex momenta. The dielectric permittivities of hBN, α-MoO 3 , and IST were modelled after references [15], [20], [32]. ...
Hyperbolic polaritons that originate from the extreme optical anisotropy in van der Waals (vdW) crystals have gained much attention for their potential in controlling nanolight. For practical use, there has been a strong interest to develop various manipulation strategies to customize the propagation of hyperbolic polaritons on a deeply sub-diffractional scale. In this regard, phase-change materials (PCMs) that possess two phases with different refractive indices offer suitably a tunable dielectric environment. Here, we report on the tuning of hyperbolic phonon polaritons in natural vdW crystals, hexagonal boron nitride (hBN), and alpha-phase molybdenum trioxide (α-MoO 3 ), using the plasmonic phase-change material In 3 SbTe 2 (IST). Unlike conventional PCMs whose both phases are dielectric, IST features a metallic crystalline phase that is stable at room temperature. The coupling between polaritons with their mirror charges in the underneath crystalline IST triggers an even stronger field confinement for polaritons. Moreover, benefited from the metallicity of laser-writable crystalline IST, we show an all-optical material platform in which crystalline IST boundaries efficiently excite and focus hyperbolic phonon polaritons in α-MoO 3 . Our experiments highlight the possibility to obtain new degrees of freedom in polariton engineering with plasmonic PCMs, thereby expanding the toolkit of tunable nanophotonics with flexible, on-demand fabrication and reconfiguration capabilities.
... As a biaxial vdW material with a low crystalline structural symmetry, it has multiple RBs ranging from the middle-infrared to far-infrared spectral region 20,34,35 , as shown in Fig. 1a and b. Notable, there are additional spectral regimes where theses RBs overlap, resulting in fascinating polaritonic properties. ...
The canalization effect of phonon polaritons (PhPs) shows highly directional, and diffraction-less propagation characteristics in van der Waals (vdW) materials, offering new opportunities to mold the light flow at nanoscale for near-field energy, information and thermal managements. Previously, canalized PhPs have only been experimentally realized in the hexagonal boron nitride metasurface, heterostructures of twisted α -phase molybdenum trioxide ( α -MoO 3 ) crystal flakes or the hybridized system. However, these systems typically have complex structures, and require strict operational conditions, such as fine structural parameters, a specific photonic magic angle or a doping level of graphene, for realizing polariton canalization with a modest performance. Here, we demonstrate the high-quality PhPs canalization in a single-layer natural α -MoO 3 crystal flake. The canalized PhPs exhibit the highly directional, and diffraction-free propagation features, associated with lateral confinement ratio up to λ 0 /80 (where λ 0 is the free-space wavelength of the incident laser). We believe this work is important to effectively manipulate PhPs in natural vdW materials, with potential applications in nanoimaging, directional energy transfer and enhanced nonlinearity at the deep subwavelength scale.
... The record-holder is BaTiS3, with a birefringence of 0.76 in the midinfrared spectral regions and a degree of linear polarization (DLP) is 0.9 in the visible spectral region 23 . Meanwhile, researchers found that the differences in intra-layer and inter-layer bonding are responsible for the highly anisotropic nature of atomically thin van der Waals layered materials [25][26][27] , such as h-BN 28 , α-MoO3 29,30 , α-V2O5 31 , ReS2 32 , GeSe2 33 , Sb2Se3 34 , and black phosphorus 35,36 . In particular, MoS2 possesses a giant birefringence of 1.5 in the infrared spectral region and 3.0 in the visible light 37 . ...
Optical anisotropy (e.g., birefringence and dichroism), a light-matter interaction phenomenon observed three centuries ago in natural Iceland crystal, is paramount for manipulating light polarization in modern optics. To date, various natural birefringent crystals are widely used, but their birefringence is limited to < 0.3. Here, we demonstrate a solution-processable natural crystal C 3 H 8 N 3 I 6 ·3H 2 O with giant birefringence up to 2.8 from visible to infrared spectral region, which hits a new high among natural crystals. Combining critical point analysis and the first-principles calculations, we reveal that this giant optical anisotropy mainly comes from the linear (I 3 ) ⁻ structural units in a parallel arrangement, which maximizes the difference of polarizability along the different crystallographic axes. This work highlights the potential of natural polyiodide crystals as an outstanding platform to satisfy the increasing demand for next-generation polarized photonic applications in optical communication, 3D imaging, ultra-high-resolution sensing, etc.
... Without loss of generality, we choose the coordinate system in which the dielectric permittivity tensor is diagonal ̂= diag , , , so that the coordinates , and are collinear to the main crystal axes [100], [001], and [010], respectively. Figure 1B represents the real parts of , and as a function of frequency in the long-wave-infrared (LWIR) 7 and upper far-infrared frequency ranges. 37 α-MoO3 has several reststrahlen bands (RBs) characterized by a negative sign of at least one of the diagonal elements of the tensor Re(). ...
