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Non-diffractive propagation of infrared nanofields in Science Advances

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Introduction

Photons, like electrons, can be used as information carriers to generate, process, and transmit information. Compared with electrons, photons offer advantages such as faster speed, higher bandwidth, and larger capacity. Photonic chips are expected to solve problems such as power consumption, memory access capabilities, and overall computer performance that electronic chips cannot, and are considered the infrastructure for next-generation communication technologies (optical communication). Although significant progress has been made in photonic chip research, the development, integration, and application of next-generation nano-photonic chips have two key challenges:

1. Light field diffraction limits the miniaturization and integration of optoelectronic devices (light field localization problem);

2. The bosonic nature of photons leads to weak light-matter interaction, making photons harder to manipulate than electrons (light field manipulation problem).

In nanophotonics, utilizing polaritons (special electromagnetic modes generated by the coupling of photons with Others particles) to achieve optical pathways and on-chip integration is a cutting-edge direction in photonic chip research. The high light field localization characteristics of polaritons are expected to solve the light field localization problem, and their semi-light-semi-matter properties also provide powerful means for solving the light field manipulation problem. It is particularly noteworthy that the recent development of twisted photonics has brought new hope for the nano-localization and low-loss propagation control of infrared light fields. Studies have found that when the twist angle between two or three layers of anisotropic two-dimensional materials is a fixed value (optical magic angle), the Poynting vectors corresponding to all wave vector components of the polariton point in the same direction, i.e., the light field energy propagates with low loss and non-diffraction in a specific direction, which is a natural nano-waveguide for infrared light. However, the fabrication process of multilayer two-dimensional material twisted structures is relatively complex, and precise control of the twist angle and two-dimensional material thickness requires multiple material preparation and sample alignment processes, which is not conducive to the practical application of non-diffractive polaritons.

To address this issue, recently, researchers from Beijing Institute of TechnologyProfessor Jiahua Duanand the University of Oviedo, Spain,Professor Pablo Alonso Gonzalezcollaborated to achieve non-diffractive propagation of polaritons in a single molybdenum oxide thin layer by controlling the dielectric environment of the polariton material, avoiding the complex sample preparation process of twisted structures. Based on this, they proposed a super-resolution optical imaging scheme based on the non-diffractive propagation of polaritons, with an imaging resolution of 1/220 of the incident light wavelength.

The findings were published inScience Advances，titled “Super-resolution imaging based on waveguiding using a single van der Waals monolayer”. Beijing Institute of TechnologyJiahua Duanand the University of OviedoAitana Tarazaga Luengo, Christian Lanzaare the co-first authors of the paper, Beijing Institute of TechnologyJiahua Duanand the University of OviedoPablo Alonso Gonzalezare the co-corresponding authors.

Mini Encyclopedia: “Optical Magic Angle” in Twisted Photonics

Previous studies have shown that when two layers of molybdenum oxide crystals are superimposed and rotated, due to the electromagnetic field coupling between the layers, the equifrequency contours of the polaritons will change significantly, thus affecting their propagation (related report《Optical topological transformation: Nanollight source regulation technology》). When the twist angle is zero, the bilayer molybdenum oxide and the monolayer molybdenum oxide exhibit similar properties: the polaritons exhibit an inward-recessed wavefront, i.e., the equifrequency contours are hyperbolas with symmetry axes along the [100] crystal direction; when the twist angle increases to 90°, the polaritons in the bilayer molybdenum oxide become propagating along all in-plane directions, i.e., closed equifrequency contours. Interestingly, when the twist angle is at a fixed angle between 0-90°, the equifrequency contours of the polaritons in the bilayer twisted molybdenum oxide become two parallel straight lines (optical flat bands), i.e., the Poynting vectors corresponding to all wave vectors point in the same direction, and correspondingly, the polaritons propagate highly directionally along a certain direction (i.e., non-diffractive propagation). Analogous to magic-angle graphene (whose energy band is a flat band), this special twist angle between bilayer molybdenum oxide is called the “optical magic angle”, and the related research direction is called “twisted photonics” [Nano Letters 20, 6935 (2020)]. Compared to a single optical magic angle in bilayer twisted molybdenum oxide, there are multiple optical magic angles in trilayer twisted molybdenum oxide [related report《Nat. Mater. | Multiple optical magic angles: Nanometer light field control》]，in-plane full-angle control of the non-diffractive propagation direction of polaritons can be achieved through twist angle reconstruction, and a very wide spectral frequency range is covered, which provides an important idea for the precise control of nanometer light fields.

Design Ideas and Working Principles

Due to its evanescent field properties, the optical properties of polaritons are very sensitive to the surrounding dielectric environment. When the molybdenum oxide material is transferred from a low refractive index (e.g., air) to a high refractive index (e.g., silicon dioxide) substrate, the polaritons exhibit stronger light field localization, and their wavelength becomes shorter. However, previous studies on the regulation of polariton properties by the dielectric environment have mostly focused on the case where the substrate dielectric constant is greater than zero, and the case where the substrate dielectric constant is less than zero has not been studied in depth. In view of this phenomenon, the researchers calculated the optical dispersion of polaritons in molybdenum oxide materials with different substrates. The calculation results show (Figure 1) that when the substrate changes from silicon dioxide to silicon carbide (dielectric constant is approximately -10), the polaritons change from a typical inward-recessed wavefront (hyperbolic propagation) to highly directional propagation (non-diffractive propagation) along a certain direction.

Figure 1: Hyperbolic propagation (silicon dioxide substrate) and non-diffractive propagation (silicon carbide substrate) of molybdenum oxide polaritons on different substrates

Based on the above calculation results, the researchers believe that it is possible to achieve non-diffractive propagation of polaritons in a single molybdenum oxide thin layer by changing the dielectric environment, thus avoiding the complex sample preparation process of multi-layer twisted structures. To find a suitable substrate, the researchers first determined a quantitative standard for measuring whether the polariton equifrequency lines are parallel straight lines (i.e., whether it is non-diffractive propagation). Based on this, the ideal substrate dielectric constant for achieving non-diffractive propagation was calculated (red solid line in Figure 2). By comparison, it can be found that the dielectric constants of traditional silicon dioxide in the mid-infrared band (black solid line) and gold (orange solid line) substrates differ greatly from the ideal dielectric constant, which is also the reason why they cannot achieve non-diffractive propagation of polaritons. Interestingly, the dielectric constant of silicon carbide (green solid line) is very close to the ideal dielectric constant, providing an effective means to achieve non-diffractive propagation of polaritons in a single molybdenum oxide thin layer.

Figure 2: Comparison of the dielectric constants of different substrates with the ideal dielectric constant for non-diffractive propagation. It can be seen that the dielectric constant of the silicon carbide substrate is very close to the ideal dielectric constant.

Non-diffractive Propagation Nano-optical Imaging of Polaritons

To verify the above theory, the researchers used scanning near-field optical microscopy (s-SNOM) to measure the propagation behavior of polaritons in molybdenum oxide materials on a silicon carbide substrate (Figure 3). The gold nano-antenna on molybdenum oxide can generate a strong localized electromagnetic field, effectively exciting polaritons. Point-by-point scanning with the tip can obtain the real-space imaging of molybdenum oxide polaritons.

Figure 3: Real-space imaging of molybdenum oxide polaritons.

Experimental results show (Figure 4), that in molybdenum oxide materials on a silicon carbide substrate, polaritons propagate highly directionally along the [100] crystal direction, verifying the non-diffractive propagation of polaritons in a single molybdenum oxide thin layer. In addition, unlike the optical magic angle in bilayer twisted molybdenum oxide that only appears at a certain fixed frequency (i.e., non-diffractive propagation only exists at a single frequency), the non-diffractive propagation phenomenon of polaritons in the molybdenum oxide-silicon carbide system can exist in a certain wide band frequency range. This characteristic not only helps to control the low-loss propagation of mid-infrared broadband nano-optical fields, but also provides a platform for measuring key physical parameters of polaritons. For example, to obtain the key physical quantity of polariton propagation lifetime, we need to measure its propagation length and propagation speed, the latter of which needs to be measured at different incident light frequencies. The wide spectral range of polariton non-diffractive propagation in the molybdenum oxide-silicon carbide system provides a good platform for measuring its propagation speed. Based on near-field optical imaging technology, the researchers finally measured the non-diffractive propagation lifetime of polaritons to be about 2 ps.

Figure 4: Near-field optical image of polariton propagation in the molybdenum oxide-silicon carbide system. The yellow rectangular box is the gold nano-antenna, and the excited polaritons propagate highly directionally in the horizontal direction.

Application (Super-resolution Imaging)

Traditional optical lens imaging is affected by the diffraction effect of light, and there is a resolution limit, which is approximately half of the incident light wavelength. The image information beyond the diffraction limit that is lost is carried by evanescent waves. Previous studies have shown that hyperbolic metamaterials, due to their unique dispersion characteristics, can transmit the evanescent waves of the imaging object. The lens designed based on this principle is called a hyperbolic metalens (Hyperlens). The working process of a hyperbolic metalens is divided into two parts: (1) imaging magnification of the imaging object in the near field; (2) converting evanescent waves into propagating fields and scattering them to far-field detectors. The non-diffractive propagation of polaritons in the molybdenum oxide-silicon carbide system has natural advantages for optical imaging applications. AsFigure 5shows, the non-diffractive propagation of polaritons completely reconstructs the surface electromagnetic field distribution of the gold nano-antenna buried below on the molybdenum oxide surface. When the incident light is 11 μm, two metal antennas with a spacing of only 50 nm can be resolved, which is the first demonstration of optical imaging application based on the channeled propagation of polaritons. It is worth pointing out that the super-resolution imaging scheme here consists of two parts: the molybdenum oxide-silicon carbide polariton system and the s-SNOM technology, which respectively transmit the gold nano-antenna information to the upper surface of molybdenum oxide (near-field reconstruction) and transmit the near-field signal to the far-field detector (far-field detection). In the future, researchers will try to use methods other than s-SNOM to scatter the near-field optical signal to the far-field detector to further achieve far-field super-resolution imaging.

Figure 5: Super-resolution optical imaging scheme based on the molybdenum oxide-silicon carbide polariton system. Based on the non-diffractive propagation of polaritons, two gold nano-disks with a spacing of 50 nm can be resolved when the incident light is 11 μm, and the imaging resolution is about 1/220 of the incident light wavelength.

Paper Information

Jiahua Duan et al., Super-resolution imaging based on channeled propagation using a single van der Waals layer. Science Adv. 11, eads0569 (2025).

https://doi.org/10.1126/sciadv.ads0569