Introduction

Phonon polaritons (PhPs) are quasiparticles arising from the interaction of light with polar dielectric materials, which can confine free-space light to the subwavelength scale with significantly reduced optical loss and much higher quality factors1,2,3,4,5,6,7,8,9,10. This feature is advantages in the mid-infrared and terahertz spectral ranges, unmatched by other polaritons currently under investigation, leading to potential applications, such as sensing11,12,13,14,15, focusing16,17,18, and thermal management19,20,21,22,23. In recent years, hyperbolic phonon polaritons (HPhPs) with tunable characteristics have garnered tremendous attention24,25. If the permittivity tensors in the two orthogonal directions of the material have opposite signs, phonon polaritons with hyperbolic dispersions can be realized, such as in vdW crystals h-BN7,26,27, α-MoO38,28,29,30,31, α-V2O532, and ε-GaSe33. More importantly, the propagation of HPhPs can be manipulated by material34,35,36,37, physical stimulus38,39,40, dielectric environment41,42,43,44,45,46,47,48,49 and interaction50,51,52,53,54,55. This characteristic provides a new avenue for manipulating optical fields at the nanoscale4. Therefore, many applications would greatly benefit from the in-plane HPhPs that possess highly tunable directional propagation in the plane, which can support the manipulation within ultra-thin layers. The resulting search for novel in-plane HPhPs leads to the discovery and development of a new class of anisotropic 2D vdW natural materials, such as natural vdW material α-MoO3. To fully unlock the potential of in-plane HPhPs, it is important to summarize and understand the exotic properties of in-plane HPhPs from the perspectives of materials, optical properties, and nanophotonic devices.

Here, we review recently emerged natural materials supporting in-plane HPhPs based on crystal structure and Reststrahlen band. We also discuss the fundamental and exotic characteristics of in-plane HPhPs in anisotropic 2D vdW and bulk crystals, and explore recent discoveries related to directional, unidirectional, canalization, negative reflection, and negative refraction phenomena. Finally, we engage in a thorough examination of the properties and mechanisms of nanophotonic devices that utilize in-plane HPhPs in vdW materials, aiming to catalyze advancements in integrated nanophotonics.

In-plane HPhP materials

The intrinsically in-plane HPhPs exist in materials with two dielectric constants of opposite signs within the plane. Currently, natural materials exhibiting this characteristics mainly include α-MoO38,28, α-V2O532, calcite(CaCO3)9, β-Ga2O310, and CdWO456. Their crystal structures are shown in Fig. 1a. Their frequency distributions of HPhP responses are plotted according to the negative signs of the dielectric constants in the x, y, and z directions (Fig. 1b). For instance, the strong phonon resonances in α-MoO3 generate two Reststrahlen bands in the frequency range of 818–1010 cm−1, allowing for low-loss PhPs with strong electromagnetic confinement8,57.

Fig. 1: In-plane HPhP materials.
figure 1

a Crystal structure of α-MoO3, α-V2O5, β-Ga2O3, CdWO4 and CaCO3, respectively. b Negative permittivity tensors at different frequencies of α-MoO3, α-V2O5, β-Ga2O3, CdWO4 and CaCO3, respectively.

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Optical properties of in-plane HPhPs

To understand the mechanism driving the present and potential nanophotonic devices, we summarize the distinctive optical properties of in-plane HPhPs (Fig. 2), delineated according to their unique propagation characteristics in the plane.

Fig. 2: Propagation principle of in-plane HPhPs.
figure 2

a Directional propagation. The PhP fringes appear only when θ < σ, where the angle θ is the edge orientation, σ is open-angle range57. b Rotated direction. The propagation direction of hyperbolic PhPs can be orthogonally rotated via heterointerface mode hybridization. The red and blue arrows are the wavevectors of PhPs and dielectric-tailored surface PhPs (d-SPhPs), respectively. Meanwhile, the dashed arrow signifies that no polariton mode is permitted in this direction. c Unidirection. The propagation of HPhPs is only along one direction by breaking diffraction symmetry, in which the wave vector k (energy flow S) can only occur in the one side due to the selective first (+1st) order diffraction62. d Canalization. The polariton group velocities are fixed to the same direction, leading to diffractionless propagation of PhPs. Red dashed lines are the polariton wavevectors and green solid lines are the group velocity directions. e Negative reflection. Incident light is reflected to the same side of the incident boundary normal, where the ki is equal to minus kr and Si is equal to minus Sr. Here, ki,r and Si,r are the incident/reflected wavefronts and incident/reflected Poynting vectors, respectively69. f Negative refraction. Incident light is refracted to the same side of the incident boundary normal, where kin/out is the incident/refracted wavevector, and Sin/out is incident/refracted Poynting vector71.

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The slice in the momentum-frequency space (kx, ky; ω) with a plane of constant frequency ω0 is called isofrequency curve (IFC), that is, the polariton dispersion, which can be used to exactly elucidate the propagation of in-plane HPhPs. In general, the IFCs are open hyperbolas, as shown in Fig. 2a. Therefore, not all wavevectors k are allowed in the media, implying that the only directional propagation in the section of Eq. (1) can work. According to Eq. (2)57, the in-plane HPhPs can only be observed when θ < σ, where the angle θ is the edge orientation, σ is open-angle. It means the directional propagation of PhPs can be achieved by manipulating the edge orientations58,59.

$$|\tan ({k}_{x}/{k}_{y})| < \sqrt{-{\varepsilon }_{{\rm{y}}}/{\varepsilon }_{{\rm{x}}}}$$
(1)
$${{\rm{k}}}_{\theta }=\frac{\varPsi }{d}\left[a\,\tan \left(\frac{{\varepsilon }_{1}}{{\varepsilon }_{z}}\varPsi \right)+a\,\tan \left(\frac{{\varepsilon }_{3}}{{\varepsilon }_{z}}\varPsi \right)+l\pi \right]$$
(2)

Furthermore, the dielectric environment is also an important factor in controlling the propagation. For instance, PhPs with 100 nm thick α-MoO3 suspended on air have a different direction of IFC contours to the dielectric-tailored surface PhPs (d-SPhPs) with 100 nm thick α-MoO3 suspended on SiC substrate (Fig. 2b)60,61. The red arrows denote the wavevector of PhPs at different orientation angle θ with respect to the [100] direction, and the blue arrows denote the wavevector of d-SPhPs. From the Fig. 2b, it can be concluded that d-SPhPs can be observed in the region of θopen < θ < 90°, but PhPs can only be excited when θ < θopen. Surprisingly, unidirectional excitation and diffraction of in-plane HPhPs can be realized by controlling symmetry breaking of momentum matching between hyperbolic dispersion and grating orientation, which thus leads to directional, bidirectional and unidirectional propagation of HPhPs (Fig. 2c)62.

The development of twistronics and topological photonics has inspired highly collimated, diffraction-free canalization of in-plane HPhPs. Canalization is characterized by almost-fixed group velocity directions \({\overrightarrow{v}}_{g}={\nabla }_{\mathop{k}\limits^{\rightharpoonup }}\omega\), which means an almost constant group velocity direction independent of the phase velocity (Fig. 2d). This has been demonstrated in twisted bilayers63,64,65,66 and trilayers67,68 of in-plane hyperbolic crystals. Such canalization can be actively tunable in graphene and α-MoO3 heterostructures52,53,54,55.

Negative reflection is an unusual phenomenon when incident light is reflected to the same side of the incident boundary normal, which has recently been visualized in real space at in-plane hyperbolic material surfaces (Fig. 2e)69,70. Such negative reflection effect has been proposed to construct perfect hyperbolic cavity with an unclosed cavity boundary.

Negative refraction is another peculiar phenomenon that occurs for hyperbolic media. Firstly, planar refraction between two hyperbolic media is different from conventional refraction between two isotropic media. Poynting vector S (energy flux), which determines the propagation direction of the polariton and is normal to the IFC, is not in general collinear with wavevector k (Fig. 2f)71, in which they are collinear only along the x-axis. As such, the properties of propagating polaritons in hyperbolic media are different to those in isotropic media; the isotropic IFCs are circular and polaritons have the same k value, which is always collinear to S. As for negative refraction, the refracted polariton beam emerges on the same side of the interface normal as the incident polariton ray. This has been visualized when a polariton beam passes through a planar interface between the two hyperbolic vdW materials, α-MoO3/hBN72 and α-MoO3/graphene73.

High field confinement

Extremely high electromagnetic field confinement of in-plane HPhPs is able to compress the incident long-wave infrared light into nano-thickness by dozens or even hundreds of factors. The confinement factors, β = λ0/λPhPs, of HPhPs are summarized and listed in Table 1.

Table 1 Summary of confinement factors of in-plane HPhPs in vdW materials
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The confinement factor of HPhPs is strongly dependent on the thicknesses because of the volume nature of HPhPs in vdW materials. For instance, the confinement factor of PhPs in α-MoO3 can reach a value as high as 87 at 953 cm–1, which increases to 120 when the thickness is reduced to 10 nm28. In addition, the confinement factor can be tuned from 12.5 to 25.5 when changing edge orientations of α-MoO3 with 5°, 30°, 45°, and 60°58.

Stacking individual flakes into bilayers or heterostructures can modulate the confinement factor. The electromagnetic confinement factor for the canalized PhPs can reach 40 at 903.8 cm–1 in a twisted α-MoO3 bilayer63 and 5 at 8.67 THz74. In addition, vdW heterostructures can significantly affect the confinement factor mainly due to the change of dielectric environment or interface hybridization. For example, a theoretically predicted confinement factor exceeding 100 can be obtained by placing thick α-MoO3 on bulk polar dielectrics (e.g., SiC, AlN, and GaN)60.

Directional propagation

Hyperbolic direction

The hyperbolic material intrinsically determines the propagation direction of in-plane HPhPs within the open angle of the hyperbolic dispersion curve, which also imposes the forbidden directions. The in-plane HPhPs in α-MoO3 were reported to realize both elliptic and hyperbolic in-plane dispersions by infrared nano-imaging and nano-spectroscopy (Fig. 3a)8. Specifically, the interference pattern of in-plane HPhPs at a frequency of 983 cm–1 in upper reststrahlen band, (represented U-RB) shows an elliptical shape. By contrast, the pattern at a frequency of 893 cm–1 in lower reststrahlen band (represented L-RB) manifests as a hyperbolic shape, in which the PhPs show low-loss propagation along the [100] direction. This implies the directional propagation is restricted to the [100] direction, more strictly, within a fixed range of angles according to hyperbolic dispersion.

Fig. 3: Directional propagation along the hyperbolic direction.
figure 3

a In-plane elliptical and hyperbolic PhPs in an α-MoO3 disk8. Subpanels a, b depict near-field amplitude images of an α-MoO3 disk with a diameter of 144 nm, captured at imaging frequencies of 983 cm−1 (labeled as U-RB for the upper reststrahlen band) and 893 cm−1 (also L-RB, indicating the lower reststrahlen band). White dashed lines mark the [100] and [001] surface directions. Subpanels c, d present the absolute values of the Fourier transforms |S4(kx, ky)| corresponding to the near-field images in subpanels a, b, respectively. The contours of the IFCs of the PhPs are outlined by solid lines. Reproduced with permission8. Copyright 2018, Springer Nature Limit. b Edge-tailored PhPs at angle-dependent α-MoO3 edges58. As θ increases from 0° to 45° across Ed1 to Ed4, interference fringes align with the edge line. The angle between the Poynting vector’s propagation direction (Se, black arrow) and the wavevector (ke, colored arrows) grows, with the wavevector remaining perpendicular to the groove. Notably, when θ exceeds 60°, no PhPs fringes align with Ed5 to Ed7, despite hyperbolic wavefronts maintaining shape at endpoints. Reproduced with permission58. Copyright 2020, Springer Nature Limit.

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Furthermore, by shaping α-MoO3 nanocavities with different geometries, edge-oriented and steerable in-plane HPhPs as well as polariton meandering exclusion zones can be achieved. The angle between the edge orientation (θ) and the crystallographic direction (σ) is the key tuning parameter to tailor the pattern of in-plane HPhPs58,59. For instance, as θ increases from 0° to 45° (Ed1–Ed4 of Fig. 3b), the fringes of interference persist in parallelism with the edge line, despite the growing angle formed between the direction of propagation (denoted by the black solid arrow, Se) and the wavevector (illustrated by solid arrows of various colors, ke), which maintains perpendicularity to the groove. It is noteworthy that, despite the preservation of hyperbolic wavefronts at the two end points, no PhPs fringes aligned with the edges (Ed5–Ed7 of Fig. 3b) are observed when θ reaches or exceeds 60°. Thus, the propagation of in-plane HPhPs in a specific direction is forbidden if there is no intersection between the wavevector and the hyperbolic dispersion for θ > σ. It’s worth noting that when the shape of the hyperbolic isofrequency surface evolves, PhPs have a different range of allowed propagation directions.

Forbidden direction

In-plane HPhPs propagating along the [100] direction can be switched to forbidden directions by introducing an optical topological transition. For example, the in-plane HPhPs in α-MoO3 can be supported in the forbidden [001] direction when the slab is placed on a substrate with a specified negative permittivity (e.g., 4H-SiC), as shown in Fig. 4a. In the α-MoO3/4H-SiC heterostructure, the propagation direction of in-plane HPhPs undergoes a 90° rotation, leading to their occurrence along intrinsically forbidden directions within the spectral range of 948–937 cm–1. The observed polaritonic states transition between mutually orthogonal hyperbolic regimes originate from an opening gap in dispersion61.

Fig. 4: Orthogonally rotated propagation of in-plane HPhPs along originally forbidden directions.
figure 4

a Illustration of dipole-launched HPhPs in an α-MoO3/4H-SiC heterostructure61. Reproduced with permission61. Copyright 2021, American Association for the Advancement of Science. b Schematic of 90 degree-rotated in-plane HPhPs in an α-MoO3/6H-SiC heterointerface60. Reproduced with permission. Copyright 2018, The Royal Society of Chemistry. c Topological transition of the polaritonic dispersions between orthogonal hyperbolic regimes in α-MoO3/4H-SiC61. Reproduced with permission61. Copyright 2021, American Association for the Advancement of Science. d, e Propagation direction switching induced by geometrical confinement75. Reproduced with permission75. Copyright 2023, American Chemical Society.

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Such concept is universal, not limited to α-MoO3 or 4H-SiC. By constructing hetero-structural interfaces between biaxial vdW materials (e.g. α-MoO3, α-V2O5) and bulk polar dielectric (e.g. 6H-SiC, AlN, and GaN), the hybridized surface PhPs (SPhPs) with a large confinement factor (>100) can be switched to the orthogonal direction compared to those in natural α-MoO3 (Fig. 4b)60. The hyperbolic open angle transits from the [100] direction to the [001] direction after replacing the SiO2 substrate with 6H-SiC. It is found that the dielectric-tailored SPhP mode of α-MoO3 inherits from the SPhPs in 6H-SiC but manifests directional propagation with in-plane hyperbolic dispersion (Fig. 4c)61.

In addition, the transition of propagation direction can also be induced by geometric confinement within an in-plane hyperbolic medium. It was reported that the HPhPs can propagate along the forbidden [001] direction in α-MoO3 by regulating geometrical confinement in the [100] axis (Fig. 4d)75. The transition happens with tailored nanobelt widths at varying frequencies due to the frequency-dependent dispersions. Importantly, the transition is tunable within the frequency domain. Rotated HPhPs propagate in plane at lower frequencies as the polaritonic wavelength is comparable to the width, while normal HPhPs propagate at higher frequencies with shrinking wavelength (Fig. 4e).

Unidirectional excitation

The excitation and propagation of HPhPs only along a specific direction is an intriguing feature, which could enable unexpected control of infrared polaritons along different pathways and open opportunities for applications ranging from on-chip nanophotonics to directional heat dissipation.

Unidirectional propagation of in-plane HPhPs has been achieved in anisotropic 2D vdW materials. When rotating the α-MoO3 flake located above the in-plane air-SiC heterointerface, tunable and directional polariton excitation only at one side of the edge between air and SiC. As shown in Fig. 5a, when the rotation angle θ = 20° < θopen = 45°, it means that the normal of the edge (excited polariton wavevector) deviates 20° from the [100] direction. The unidirectional excitation of original HPhPs occurs only at the left side of the edge between air and SiC. In contrast, when the rotation angle changes to θ = 70° > θopen = 45°, the wavevector aligns within the hyperbolic dispersion of dielectric-tailored PhPs and thus the propagation of fringes flips to the right side (Fig. 5a).

Fig. 5: Unidirectional excitation and propagation of in-plane HPhPs.
figure 5

a Rotation control at α-MoO3/SiC heterointerface. The schematic shows directional excitation of PhPs or d-SPhPs via α-MoO3 stacking on an air-SiC interface. θ is the angle between the edge normal at the interface and α-MoO3’s [100] crystal direction. θ < θopen = 45° permits PhP excitation on the left. As θ nears θopen, both modes are forbidden. θ > θopen excites only d-SPhP on the right. Reproduced with permission60. Copyright 2021, American Chemical Society. b Selective and unidirectional diffraction of in-plane HPhPs in α-MoO3 by orientated blazed gratings. Left: Momentum matching for a circular-hole grating at φ = 25°; k-D/k+U are wave vectors, S-D/S+U are energy flows, indicating bidirectional diffraction. Top-right: near-field images of first-order diffraction of grating-excited PhPs, showing bidirectional wavefronts flanking the circular-hole and unidirectional wavefronts on either side of the blazed grating. Bottom-right: FT images of the PhPs from top-right. Reproduced with permission62. Copyright 2022, American Association for the Advancement of Science.

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Unidirectional excitation of in-plane HPhPs can also be realized by designer grating diffraction. The diffraction principle of hyperbolic polaritons is distinct from free-space optics and isotropic polaritons. This originates from symmetry breaking of momentum matching in hyperbolic polaritonic diffraction62. As depicted in Fig. 5b, the grating pattern applied to the α-MoO3 flake enables the in-plane propagation of PhPs to be highly adjustable and resilient through modifications in the size and orientation of the grating. Specifically, the circular hole grating, with a periodicity of Λ of 600 nm and an orientation angle of φ = 25° relative to the [100] direction of α-MoO3, can support two distinct diffraction states, labeled as |±, U or D > . Here, the ± symbol represents the k-vector direction in the first diffraction order, while U or D indicates the PhPs positioned above or below the physical edge of the grating, respectively. In contrast, the triangular hole grating (with Λ= 600 nm and φ = 25°) solely facilitates the propagation of unidirectional PhPs along the upper or lower edges of the blazed grating62.

Canalization

Canalization is an important property of HPhPs, implying highly concentrated directional propagation properties, which can be achieved by nanostructured metasurfaces or natural 2D vdW materials. Due to non-diffractive wave propagation, exciting opportunities are opened up for nanoimaging, radiative energy transfer, and enhanced local density of states.

Polariton canalization in metasurfaces has been observed on a metasurface of hexagonal boron nitride (h-BN) nanoribbons and a deeply subwavelength canalization mode near transition frequency can be visualized (Fig. 6a)76. In addition to metasurface, canalization of in-plane HPhPs in natural vdW materials is also achievable, particularly in twisted bilayers of α-MoO3. The tunable topological transitions from hyperbolic to elliptic dispersion contours are induced by polariton hybridization, which are robustly controlled by a topological quantity. The twisted bilayer system exhibits low-loss tunable canalization of in-plane HPhPs and diffractionless propagation with a high resolution below λ0/40 (Fig. 6b)63. By further twisting trilayer α-MoO3, the canalization direction of polaritons can be arbitrarily programmed along any desired in-plane direction (0-180°) with a wide spectral range (Fig. 6c)68. Active control over polariton canalization can be achieved via a graphene/α-MoO3 heterostructure52,53,54,73, in which the hybridized plasmon-phonon polariton dispersion is controlled by electric-field-tunable graphene Fermi level.

Fig. 6: Topological transition and canalization.
figure 6

a Canalized phonon polaritons in a h-BN metasurface. The schematic shows a 20-nm-thick h-BN metasurface with a grating of nanoribbons. The nanoribbons have a width of 70 nm, gap size of 30 nm, and thickness of 20 nm. Analysis of dipole-launched polaritons at 1479 cm–1 frequency shows a unique phenomenon. The Fourier transform of the near-field distribution Ez reveals highly collimated elliptical PhP modes. Reproduced with permission76. Copyright 2020, Springer Nature Limit. b Photonic magic angles and rotation-induced topological transition of HPhPs in α-MoO3. Schematic of twisted bilayer (tBL) α-MoO3 with twisted angle (Δθ) between layers. Topological PhP dispersion map shows transition from hyperbolic (Δθ < θTP, NACP = 2) to elliptic (Δθ > θTP, NACP = 4) regimes at θTP. Near-field image captures tBL α-MoO3 behavior at various topological transition angles: -44°, -50°, -63°, -79°. Reproduced with permission63. Copyright 2020, Springer Nature Limit. c Spectrally robust polariton canalization in reconfigurable trilayer α-MoO3. Schematic of twisted α-MoO3 trilayers using s-SNOM. θ1–2 and θ1–3 are twists between crystal directions of layers. Near-field amplitude images captured at φc = 140°, 80°, 50° for trilayer. Reproduced with permission68. Copyright 2023, Springer Nature Limit.

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Additionally, canalization at THz band was also obtained in semiconducting alpha-germanium (II) sulfide (GeS). Long lifetime (>2 ps) and high THz light confinement (λ0/λP > 45) were demonstrated77. The canalization propagation of confined THz radiation can be manipulated by two parameters of frequency and twist-angle74. Specifically, the polariton canalization in α-MoO3 is at 8.67 THz for a twist angle of 50°.

Negative reflection and negative refraction

Negative reflection and negative refraction are exotic optical phenomena that have long been pursued by utilizing double-negative metamaterial, hyperbolic metamaterial, etc. Recently, biaxial vdW materials, supporting in-plane HPhPs, emerge as promising platforms for planar reflective and refractive optics. Negative reflection occurs if light is reflected toward the same side of the boundary normal as the incident one, and negative refraction occurs when the refracted beam emerges on the same side of the interface normal. Both exotic phenomena have already been investigated by using vdW materials69,70,72,73,78,79. This has demonstrated the significant potential of using natural 2D vdW materials for peculiar nanophotonic elements and devices.

Direct visualization of negatively reflected HPhPs on subwavelength mirrors has been achieved in α-MoO3, unveiling broad tunability of both the polaritonic wavelength and direction of propagation upon negative reflection (Fig. 7a)69. An unconventional hyperbolic nanoresonator has been proposed, in which HPhPs with different momenta totally reflect to a common point source. Negative refraction at the interface between two strongly anisotropic media shows an exotic bending-free refraction effect. In the interface of hyperbolic α-MoO3 and isotopically pure h-BN, the rays passing through the interface can circulate along closed diamond-shaped trajectories at a special frequency72. The collimated rays formed by polaritons show an electrically tunable negative refraction when transmitting through a planar interface between two natural vdW materials, α-MoO3 and graphene (Fig. 7b)73.

Fig. 7: Negative reflection and negative refraction.
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a Negative reflection at tilted interfaces of α-MoO3. Left: Real-space image of negative HPhPs reflection, deflecting from normal with negative θr. Si and Sr on same side. Right: Experimental near-field images of HPhPs back-reflecting on mirrors at φ = 38° and 60° in α-MoO3 at incident frequency of 889 cm−1. Reproduced with permission72. Copyright 2022, American Association for the Advancement of Science. b Gate-tunable negative refraction at planar graphene/α-MoO3 interface At the top is a device schematic, while below are IFCs of polaritons in hyperbolic (α-MoO3) and elliptic (graphene/α-MoO3) media. Negative refraction occurs at their interface due to tangential wave vector conservation. θ1/θ2 are incidence/refraction angles of polaritons with k1/k2, while φ1/φ2 are those of Poynting vectors S1/S2. Angles are positive/negative on the upside/downside of the interface normal. Reproduced with permission73. Copyright 2023, American Association for the Advancement of Science.

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Nanophotonic devices

The exotic optical properties of in-plane HPhPs in Fig. 2 endow the possibilities to fabricate new and efficient nanophotonic devices. The properties of directional propagation, rotated direction, unidirection, canalization, negative reflection, and negative refraction can bring subdiffractional focusing lenses, waveguides, ultra-thin sensors, infrared tuners and resonators. More impressively, these devices can be planarized, which has a great effort on the development of infrared integration.

In-plane focusing lenses

The hyper-focusing lenses have previously been demonstrated by hyperbolic h-BN crystals16,17,18. Launched by metallic disks, the subdiffractional focal spot of 200 nm at frequency \(\omega\) = 1515 cm–1 (λ = 6.6 µm) was observed17, which corresponded to a resolution of λ/33. Besides, the focal size in the system is limited by the finite thickness of Au disks, and the focal spot as small as ~λ/100 can be achieved using thinner disks. The nano-focusing of HPhPs was also achieved by tapered h-BN slab80, predicting that the field enhancement factor was up to 90. By integrating h-BN with phase-change materials of Ge3Sb2Te6 (GST), controllable HPhP propagation could be realized by writing, erasing, and re-writing arbitrary patterns in the h-BN-GST heterostructure. The reconfigurable polariton metalenses have been obtained with 1.6 µm focal spot (23% of the free space wavelength), smaller than the diffraction-limited 2 µm (Fig. 8a)81.

Fig. 8: In-plane hyperbolic focusing lenses.
figure 8

a Planar PhP metalens based on phase-change material coated h-BN, which is s-SNOM image of a metalens showing focusing of polaritons at 1452 cm−1. Reproduced with permission81. Copyright 2019, Springer Nature Limit. b Frequency-dependent focusing of in-plane HPhPs at the α-MoO3 surface. Experimental near-field images of PhPs, excited by an Au nanoantenna on a 165-nm α-MoO3 crystal, are shown at λ0 = 10.70 μm (left) and λ0 = 10.85 μm (right). PhP interference creates a focal spot, with varying size and focal length f based on λ0. The dashed arrows show the angle θ. Reproduced with permission82. Copyright 2021, American Association for the Advancement of Science. c Antenna size-tunable focusing for in-plane hyperbolic α-MoO3. Reproduced with permission83. Copyright 2021, American Chemical Society. d Negative-refraction-induced planar focusing. Experimental (top) and simulated (bottom) near-field images show negative refraction from a hyperbolic wave in α-MoO3 to an elliptic wave in a graphene/α-MoO3 heterostructure. Reproduced with permission73. Copyright 2023, American Association for the Advancement of Science.

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To focus in-plane HPhPs, three different strategies need to be considered54,73,82,83,84, that is, the dimension of the antenna, light frequency, and phonon-plasmon hybridization. Focusing in-plane HPhPs in α-MoO3 with metal nanoantennas of customized convex geometries enables focal spots with dimensions as small as 225 nm (1/5 of PhP wavelength, 1/50 of light wavelength) (Fig. 8b)82. It was found that the curvature of the Au antenna extremity strongly affects the subwavelength focusing behaviors, e.g., focal length and spot size (Fig. 8c)84. Another tunable planar focusing device based on α-MoO3 was fabricated with an effective focal length of polariton waves from 0.7 to 7.4 µm83. The high confinement characteristics of PhPs in α-MoO3 permit the focal length and focal spot size to reduce to 1/15 and 1/33 of the incident wavelength, respectively. In particular, the combination of anisotropic PhPs in α-MoO3 with tunable surface plasmon polaritons in graphene enables in situ dynamic control of the focusing performance. Experimentally, it has been demonstrated that an in-plane refractive lens with a focal spot as small as 240 nm (1/6 of PhP wavelength) can be realized by using the negative refraction at the interface of two strongly anisotropic media (Fig. 8d)73.

In summary, in-plane focusing lenses based on polaritons can break through the diffraction limit, obtain focal points of several hundred nanometers, and their focal lengths and focal points can be structurally designed and regulated. However, lenses of different or broad wavelengths are required. In addition, the current in-plane focusing lenses still have relatively simple functions, and in-plane focusing lenses with multiple functions such as focusing and collimation still need to be explored.

Planar waveguides

The in-plane HPhP waveguides exhibit strong wavelength compression at nanoscale. Currently, multiple approaches are developed to manipulate the hyperbolic waveguide modes. Particularly, fundamental and higher-order in-plane HPhP modes can be tailored by waveguide width, frequency, and rotation angle. Therefore, in-plane HPhP waveguides provide a platform to configure electromagnetic waves at the deep-subwavelength scales for a range of IR applications.

For h-BN waveguides, the fundamental volume mode propagating in linear ribbons exhibits a cutoff width, which can be lowered by reducing the waveguide thickness (Fig. 9a)85. Hybridization of surface modes was observed, which evolved with frequency and waveguide width, showing that the cutoff width did not occur for symmetrically hybridized surface modes. Similarly, HPhP Fabry-Perot resonances in α-MoO3 nanobelts exhibited significant anisotropic propagation and strong frequency dependence86. It was estimated that a confinement factor of about 80 for the fundamental mode was achieved. In addition, in-plane HPhPs in α-MoO3 can propagate along the forbidden direction by geometrical confinement in the [100] direction (Fig. 9b)75. It was observed that a heterostructure consisting of one-dimensional 3C-SiC nanowires and α-MoO3 can launch the mode of higher-order HPhPs87. The manipulation of higher-order HPhPs was also demonstrated by altering the geometric orientation between 3C-SiC nanowire and α-MoO3 crystal from 0° to 45° (Fig. 9c). In addition, the integration of in-plane hyperbolic α-MoO3 with phase-change materials are expected to enable reconfigurable and rewritable waveguides42,45,46,81,88. Apart from rectangular waveguide, Y-shaped polariton splitter has also been reported. It can manipulate polaritons rooted in the dielectric environment engineering of polaritons89.

Fig. 9: Planar waveguides.
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a–c Tailored HPhP waveguide modes with varied (a) width of h-BN ribbon. Reproduced with permission85. Copyright 2020, John Wiley & Sons. b Tailored HPhP waveguide modes with variedfrequency and width of α-MoO3. In the top row, s-SNOM images are shown at frequencies 900 cm−1, 881 cm−1, and 875 cm−1, with varying m and width. Below, wavevectors of a nanobelt sample at different frequencies are plotted, including analytically calculated (dashed curves), experimental (solid spheres), and FDTD (empty spheres) results. A gray dashed curve represents the calculated positive dispersion of HPhP in unconfined α-MoO3. Reproduced with permission75. Copyright 2023, American Chemical Society. c Tailored HPhP waveguide modes with varied angle between SiC nanowire and α-MoO387, the calculated direction-dependent phonon polariton dispersions are shown with experimental data extracted from nanowire launched modes for θ = 0°, θ = 15°, θ = 30° and θ = 45°. Reproduced with permission87. Copyright 2023, John Wiley & Sons.

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In addition to modulating modes, in-plane HPhPs waveguides have significant application prospects in thermal management. Through the coupling of optical phonons and photons, they can provide a new heat dissipation channel for integrated systems in fields such as microelectronics and silicon-based optoelectronics. The waveguides like SiO2 nanoribbon waveguides (20–50 nm thick, 1–10 μm wide) show a 34% boost in thermal conductivity beyond the phonon limit. This was achieved by designing the waveguide to control PhPs mode size and coupling with thermal reservoirs22. Besides, coupling of surface plasmon polaritons supported by graphene and HPhPs supported by hyperbolic materials (such as α-MoO3) could effectively promote photon tunneling, and hence the radiative heat transfer90.

In summary, planar waveguides based on polaritons can transmit modes through geometric structures and angular tailoring, and achieve single-mode transmission without cut-off. They also have great potential in heat management in integrated systems. However, the theory of in-plane anisotropic single-mode waveguides still needs to be explored, and their preparation is still relatively difficult. In addition, multifunctional waveguides still need to be developed, including wavelength tunable waveguides, wavelength division multiplexing waveguides, etc.

Molecular sensors

Strong coupling between the infrared field and molecular vibrations can be achieved through HPhPs. Notably, the recent advent of hyperbolic vdW materials introduces possibilities for ultra-sensitive polariton sensors, ranging from organic, gas, and biomolecules12,13,14,91,92,93,94,95.

PhP resonances of h-BN have been used for surface-enhanced infrared absorption (SEIRA) spectroscopy of small amounts of organic molecules in Fourier transform infrared (FTIR) spectroscopy (Fig. 10a)12. Strikingly, the interaction between PhPs and molecular vibrations reaches the onset of the strong coupling regime. PhP nanoresonators thus can bring new light to applications in sensing, local control of chemical reactions and infrared quantum cavity optics experiments. Functionalized h-BN nanoresonators can also be used to assemble mid-infrared CO2 sensors (Fig. 10b). It is found that the PhP resonances shift, weaken, and broaden to lower frequencies as the CO2 concentration increases15. This is because CO2 adsorption changes the dielectric constant of the polymer PEI. Moreover, the PhP resonance exhibits a high signal-to-noise ratio even for small ribbon arrays of 30 × 30 μm2.

Fig. 10: Molecular sensors.
figure 10

a Infrared transmission spectra of h-BN ribbon arrays with differently thick CBP molecule coating12. Illustrations of sensor devices are on the left. In the middle, experimental transmission spectra of a 20 × 20 µm2 h-BN ribbon array (D = 400 nm, w = 158 nm) are shown. The black curve represents bare h-BN, while red to blue curves show spectra for increasing CBP thickness. Brown curves at the top show spectra for bare CBP layers. On the right, simulated spectra for bare and CBP-covered h-BN arrays, as well as bare CBP layers, are displayed. Gray shaded areas highlight differences between spectra. Reproduced with permission12. Copyright 2017, Springer Nature Limit. b Gas sensor consisting of h-BN nanoribbons on CaF2 substrate with a 75 nm PEI layer coating. Top row shows a schematic of the IR gas sensing setup with a sensor chip on a heating stage in a gas cell with IR windows. Bottom row displays a cross-section of reversible CO2 chemisorption and thermal desorption in the amine-rich PEI layer. Reproduced with permission15. Copyright 2022, American Chemical Society. c Real-space observation of vibrational strong coupling between HPhPs and organic molecules11. The nanoimaging experiment illustrates a metallic s-SNOM tip exciting PP modes in a thin h-BN layer on a CBP layer. The tip-launched PPs propagate, reflect at the h-BN edge, and return to the tip. Reproduced with permission11. Copyright 2021, Springer Nature Limit. d Schematic of in-plane HPhP biosensor based on α-MoO3. As a general rule, the intensity of polaritonic field confinement directly correlates with the sensitivity of the sensor to subtle variations in the adjacent dielectric environment. Reproduced with permission6. Copyright 2024, Springer Nature Limit.

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Vibrational strong coupling has been visualized in real space between propagating PhPs in h-BN and molecular vibrations of CBP (Fig. 10c)11. Near-field polariton interferometry shows that vibrational strong coupling leads to the formation of a propagating hybrid mode; the dispersion has a pronounced anti-crossing region in which it propagates with negative group velocity. However, current research on PhP sensors focuses on h-BN, and there is a lack of research on other natural materials such as in-plane hyperbolic α-MoO36. It is important for the diversification and practicability of both natural hyperbolic materials and sensors. Particularly, in-plane HPhPs are expected to have sensitivity to molecule orientations because of in-plane polarized resonances (Fig. 10d).

In summary, sensors based on polaritons can achieve sensing in the mid-infrared or terahertz bands. The structured sensors further increase diversity. However, sensors based on natural vdW materials for thinner sensors still need to be studied.

Infrared tuners and resonators

An in-plane hyperbolic polariton tuner is proposed based on patterning vdW material α-MoO3 into micro or nano ribbon arrays (Fig. 11a)96. It has been demonstrated that this tuner responds directly to far-field excitations and produces low-temperature infrared and terahertz resonances with quality factors up to 300, which are determined by the in-plane HPhPs of patterned α-MoO3. With this tuner, it is possible to realize the intensity adjustment of reflected and transmitted electromagnetic waves, as well as the selection of wavelengths and polarizations.

Fig. 11: Infrared tuner and resonator based on in-plane HPhPs.
figure 11

a In-plane hyperbolic polariton tuners with rotated 1D ribbon arrays of α-MoO3. The left side depicts tuners with vdW α-MoO3 patterns and FTIR measurement. The right compares theoretical (false color) and experimental (color spheres) HPhP dispersions. Spheres are extracted from reflectance spectra, while the plot normalizes the polariton wavevector by α-MoO3 thickness and displays Imrp for the air/α-MoO3/SiO2/Si structure. Theory and experiments align in HPhP resonance frequencies. Reproduced with permission96. Copyright 2023, Springer Nature Limit. b Hyperbolic polaritonic crystals constructed on 2D holey α-MoO3 with tunable low-symmetry resonating modes. The left shows a 235 nm-thick square-lattice photonic crystal (PoC) schematic with a SEM image displaying 2.3 µm periodicity, 0.6 µm diameter, and a unit cell marked by a red dashed square. The right presents resonant interference patterns and FFT maps of PoCs with 1.3 μm periodicity at 15°, 30°, and 45° rotation angles. Reproduced with permission97. Copyright 2023, Springer Nature Limit.

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Patterning an in-plane hyperbolic material can also lead to a type of hyperbolic polaritonic crystal (PoC). Hyperbolic PoCs based on periodically perforated α-MoO3 exhibit configurable and low-symmetry deep-subwavelength Bloch modes97. While the PoC resonances can be tuned by lattice scale and orientation as usual, they display peculiar robust properties that are insensitive to lattice rearrangements in the hyperbolic forbidden directions (Fig. 11b). This robustness is not observed in isotropic PoCs made of graphene98,99 and h-BN100,101. Due to the in-plane anisotropy of α-MoO3, twist-angle-tunable Bragg resonances102 and anisotropic resonant strengths103 are expected in twisted PoCs made of α-MoO3.

In summary, polariton-based tuners and resonators can be achieved through structural design, with high quality factors and stability. They are representatives of functional polariton devices. However, their working frequency range is currently limited to a narrow band. In addition, composite tuners and resonators combined with other media need to be developed.

Conclusion and outlook

We systematically summarize and discuss in-plane HPhPs from the perspectives of materials, optical properties, and nanophotonic devices. Natural vdW materials supporting in-plane HPhPs offer diverse pathways for achieving exotic optical properties. In-plane HPhPs exhibit unique propagation phenomena, including directional propagation, unidirectional diffraction, canalization, negative reflection, and negative refraction. Recent applications of in-plane HPhPs have been demonstrated in the development of in-plane focusing lenses, waveguides, sensors, tuners and resonators.

Previous groundbreaking initiatives in in-plane HPhPs showcase exciting optical features and characteristics. Nevertheless, it is noteworthy that the exploration of in-plane HPhPs remains in its early stages, and further compelling investigations into device applications are highly anticipated. Some perspectives for future research directions are presented below.

Non-reciprocal characteristics and isolators

The dynamic and static modulation of in-plane HPhPs have been realized through various approaches. However, the non-reciprocal property of in-plane HPhPs crucial for optical integration and communication systems, has been overlooked. Non-reciprocal optical devices have the function of one-way transmission, which are very promising in integrated photonic systems104. Hereby, in-plane HPhPs not only can provide strong optical field compression down to nanoscale, but also can address the challenge to make non-reciprocal optical devices in the infrared band. The previous grating-based unidirectional PhPs and polariton microfluidics may provide some new ways to regulate light transmission direction and construct planar non-reciprocal devices. Therefore, efforts are required to explore new materials and structures capable of achieving non-reciprocal in-plane HPhPs. Additionally, optical isolator devices based on this property could be developed to practically apply the non-reciprocal characteristics of in-plane HPhPs.

Amplification and laser applications

While the propagation and resonances of in-plane HPhPs in nanocavities and whispering gallery cavity structures have been reported, their amplification and lasing characteristics are still under investigation. Currently, only plasmon and exciton polaritons have exhibited amplification and lasing. The mechanisms underlying the amplification and lasing of in-plane HPhPs remain unexplored. Such exploration is meaningful to accelerate the swift development of on-chip communications.

Ultra-thin flexible sensors

HPhPs can strongly interact with vibrational resonances of organic or gas molecules at the nanoscale. However, materials capable of coupling with in-plane HPhPs are still in the developmental stage. One specific focus is addressing oriented coupling between in-plane hyperbolic dispersion and molecular resonances, with the goal of enhancing bio-sensing and monitoring across the infrared wavelength range. Although the sensing signal intensity of ultra-thin polaritonic materials may decrease, it is expected to achieve ultra-thin sensing by designing the device structure and selecting the appropriate measurement approaches105.

Logic gates and quantum communication

The waveguide properties of in-plane HPhPs have garnered substantial interest, including their propagation modes and wavelength selectivity. However, their switch characteristics and logic gate properties have not been explored at present. The investigation of these features is expected to advance the development of in-plane HPhPs in future integrated nanophotonic chips and circuits. Although traditional photonic logic gates have achieved some results, especially in the visible-near infrared band, the complexity of their preparation and construction system remains a challenge. Therefore, the use of PhPs with the characteristics of low loss and subdiffractional confinement is expected to realize the application of infrared logic gates.