资讯｜Negative refraction realization by interfacing 𝛼-MoO3 crysta

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Figure 1: Interfacing three α-MoO₃ slabs with crystal orientations θ₁, θ₂, and θ₃, isofrequency contours, and the Re(E_z) field distribution.

1. Pre-reading

Negative refraction (NR) has a wide range of applications in diverse fields such as imaging, sensing, and waveguides and typically entails the fabrication of intricate metamaterials endowed with hyperbolic features. In contrast to artificially engineered hyperbolic materials, natural van der Waals (vdW) materials are more accessible owing to their inherent strong in-plane covalent bonding and weak interlayer interactions. However, most vdW materials manifest uniaxial crystal properties, which restrict their behavior solely to out-of-plane hyperbolicity. This characteristic poses a considerable challenge to their seamless integration via planar fabrication techniques, unless a suitable pattern is employed. Recent advances have identified natural biaxial α-phase molybdenum trioxide (α-MoO₃) as a promising vdW material capable of exhibiting in-plane hyperbolicity.

In this study, the research team led by Prof. Chia-Chien Huang suggested a unique technique in this study for integrating differentially oriented 𝛼-MoO₃ slabs covered with a tunable graphene layer on an Au substrate. By tailoring the orientations of the 𝛼-MoO₃ slabs and modulating the Fermi energy of the graphene layer, three remarkable outcomes were achieved: broadband and all-angle NR, simultaneous positive refraction and NR, and diffractionless propagation for flexible manipulation of mid-infrared polaritons. The significance of these findings extends beyond the materials and structures considered in this study, as they are potentially applicable to other types of vdW materials.

The proposed mechanism presents an innovative platform for effectively manipulating mid-IR polaritons for further advances in the development of polaritonic devices.

2. Background

NR is a counterintuitive physical phenomenon where the refracted ray of light is deflected to the same side of the interface normal as the incident ray. Subwavelength dielectrics and metallic elements are used to artificially construct hyperbolic media, which are characterized by permittivity tensors with one component along a principal axis having an opposite sign compared to the other two components. However, fabricating hyperbolic media using bulk materials is a major challenge. Therefore, researchers have turned to natural 2D vdW materials, which offer numerous advantages including low-loss characteristics, giant optical anisotropy, and ultrahigh mode confinement for enhanced light–matter interactions. These vdW heterostructures exhibit hybrid properties derived from the unique advantages of their constituent elements, which provide an additional degree of freedom for manipulating optical properties and designing novel photonic devices.

However, uniaxial hexagonal boron nitride (hBN) and certain transition metal dichalcogenides (TMDs) exhibit out-of-plane hyperbolic and in-plane isotropic dispersions. This behavior arises from the permittivity tensors, which possess two negative components in the in-plane direction and a positive component in the out-of-plane direction. The out-of-plane hyperbolicity poses a major challenge for the design of planar photonic circuits. hBN and TMDs require nanostructured patterning to achieve in-plane hyperbolicity, but this introduces surface roughness and defects that increase optical losses. Recently, a natural biaxial vdW semiconductor, α-MoO₃, has been discovered that exhibits in-plane hyperbolic dispersion. A twisted bilayer and interface engineering of the structure have been proposed to further manipulate the properties of α-MoO₃ and realize exotic phenomena such as topological transitions, wavefront control, directional canalization, and diffractionless propagation. By covering the α-MoO₃ slabs with monolayer graphene, their optical properties can be tuned by varying the charge carrier density of the graphene.

3. Innovative research

We investigated NR when two α-MoO₃ slabs, both covered by monolayer graphene, were interfaced with different orientations. Figure 2A depicts the left and right slabs in light green and light red, respectively. Under the conditions of ω = 910 cm⁻¹, t= 150 nm, E_f = 0.15 eV, and θ₁ = 20°, we investigated the Re(E_z) field distributions and corresponding IFCs for θ₂ of −10° to −90°. Figures 3B, 3C, 3F, 3G, and 3H depict the field distributions of Re(E_z) with P_i and P_nt. The black dashed line indicates the interface between the two slabs. Figures 3D, 3E, and 3I–3K depict the corresponding IFCs where they overlapped. Here, we have superimposed the analytically calculated IFCs onto the numerical results, as illustrated in Figures 3D, 3E, and 3I–3K. In the case of the left α-MoO₃ slab with a fixed orientation angle of θ₁= 20°, we have indicated the inner elliptical and outer hyperbolic IFCs using green dashed lines. For the right α-MoO₃ slab, we have indicated the elliptical IFCs with different angles of θ₂ using cyan dashed lines. The trajectories of the incident (k_i) and refracted (k_nt) wavevectors are depicted with dashed green and red lines, respectively, while the incident (P_i) and refracted (P_nt) Poynting vectors are represented by solid green and red lines, respectively. The dashed white line represents the fixed y-component (k_y) of the incident wavevector, which was preserved as light passed through the interface. Notably, P_nt was refracted toward the opposite side of the interface normal to P_i. Consequently, NR was achieved by manipulating the crystal orientations of the α-MoO₃ slab, and the NR angle can be arbitrarily determined by θ₂. These results demonstrate the ability of the proposed structure to achieve all-angle NR in the mid-IR regime.

Figure 2: (A) Graphene-covered α-MoO₃ slabs with different crystal orientations on an Au substrate, where θ₁ and θ₂ are the angles between the x-axis and directions of the individual slabs. The left and right α-MoO₃ slabs are indicated by light green and light red colors, respectively. Re(E_z) field distributions under the conditions of ω = 910 cm⁻¹, t= 150 nm, E_f = 0.15 eV, and θ₁ = 20° at θ₂of (B) −10°, (C) −30°, (F) −50°, (G) −70°, and (H) −90° and (D), (E), (I)–(k) the corresponding IFCs, where the green and cyan dashed lines indicate the analytical calculated IFCs of the left and right α-MoO₃ slabs, respectively.

Figure 1A shows the extension of the proposed structure to multiple interfaces comprising three α-MoO₃ slabs. This configuration allowed the crystal orientations of each α-MoO₃ slab to be manipulated and introduced additional degrees of freedom for controlling the optical properties of the system. Figure 1B shows a three-dimensional view of the Re(E_z) field distribution under the conditions ω = 910 cm⁻¹, t = 150 nm, E_f = 0.15 eV, θ₁ = 0°, θ₂ = −30°, and θ₃= 30°. The polariton was split and refracted into two preset transmission directions corresponding to θ₂= −30° and θ₃ = 30°. Figure 1C visualizes k_i and the two transmitted wavevectors k_pt and k_nt, where k_pt is the positive refraction in the IFCs derived from the three differently oriented α-MoO₃ slabs. The corresponding P_i, P_pt, and P_nt are also indicated, where P_pt is the positive refractive Poynting vector. Figure 1D shows a top view of the Re(E_z) field distribution and highlights the power flows represented by the Poynting vectors P_i, P_pt, and P_nt.

To further control the polaritons, we interfaced two α-MoO₃ slabs partially covered with graphene, as shown in Figure 3A. The left α-MoO₃ slab had a crystal orientation of θ₁ = 0°, as shown in Figure 3B, and was completely covered with monolayer graphene, which was electrically gated with E_f1. The right slab had the crystal orientation θ₂, and it was partially covered with graphene, which was electrically gated with E_f2. The separation between the graphene layers was denoted as S. A z-polarized electric dipole was positioned at a distance of d= 1 µm from the left interface on the x-y plane. The other conditions were set to ω = 910 cm⁻¹, t = 150 nm, S = 1 µm, E_f1= 0.3 eV, θ₁ = 0°, and E_f2 = 0.25 eV. Figure 3C to 3E display the Re(E_z) field distributions for θ₂= 0°, 20°, and −20°, respectively. The partially covering graphene on the right α-MoO₃ slab with a suitable E_f2 = 0.25 eV overcame the diffraction of the light beam, and diffractionless propagation was achieved.

Figure 3: (A) Interfacing two α-MoO₃ slabs, in which the left slab is entirely covered with graphene (E_f1) but the right slab is partially covered with graphene (E_f2). (B) The same as (A), except peeling off the graphene layer to clearly show the orientations of α-MoO₃ slabs. The two graphene layers have a separation distance of S = 1 µm, where θ₁ = 0° (left slab) and θ₂ = 0° or −20° (right slab). Re(E_z) field distributions for various cases: (C) θ₁ = 0° and θ₂= 0°, (D) θ₁ = 0° and θ₂ = 20°, and (E) θ₁= 0° and θ₂ = −20°. (F)–(H) Corresponding |E| fields.

4. Applications and perspectives

We demonstrated the feasibility of interfacing differently oriented α-MoO₃ slabs covered with tunable graphene on an Au substrate to realize NR. Three remarkable outcomes were achieved: broadband and all-angle NR, simultaneous positive refraction and NR, and diffractionless propagation for flexible manipulation of mid-infrared polaritons. The integration of multiple α-MoO₃ slabs opens up exciting approaches for designing and implementing photonic devices such as beam splitters and Mach–Zehnder modulators. Therefore, the proposed approach also opens up the possibility for diffractionless propagation in imaging systems and steering the diffractionless beam in wide angles to any desired direction by presetting the crystal orientation by controlling the geometry and material parameters. Our proposed mechanism presents an innovative platform for effectively manipulating mid-IR polaritons for further advances in the development of polaritonic devices. 

These research results are published online with the title "Interfacing differently oriented biaxial van der Waals crystals for negative refraction" on Nanophotonics. 

The authors of this article are Ruey-Tarng Liu and Chia-Chien Huang. Chia-Chien Huang is the corresponding authors of this work. Prof. Chia-Chien Huang's research group is affiliated to the Department of Physics and Graduate Institute of Nanoscience, National Chung Hsing University, Taiwan.