Ultralow loss topological metamaterial in the visible spectrum

Optical metamaterials give birth to the control and regulation of light. However, because of strong energy dissipation and fabrication difficulty in metals, low-loss isotropic three dimentional negative index metamaterials (NIMs) in the visible spectrum has long been regarded as an extremely challenging. Here we report an ultralow loss isotropic topological metamaterials for visible light. The ball-thorn-shaped meta-clusters with symmetrical structure consisting of dielectric and topological silver layer was proposed, the surface plasma resonance is formed inside a cluster unit with a height of two atomic layers, resulting in an optimized silver coating thickness about 1 nm. We invented a unique technique for preparing ultralow loss isotropic clusters and three-dimensional large area samples. The negative refractive index and the inverse Doppler effect of green and red light is measured by the prism method for the first time. This molecular crystals NIMs break through noble metal important energy losses and manufacturing difficulties.

practically difficult route to engineer isotropic infrared and visible light metamaterials.
Metasurfaces that control light waves by introducing an abrupt phase shift at sub-wavelength scale have been proposed as an alternative approach 26,27 . Nevertheless, limited successes in the visible spectrum have been achieved to date 28,29 . Although plasmonic materials with a lower loss than noble metals have long been sought, the stable sodium-based plasmonic devices with state-of-theart performance at near-infrared wavelengths was not available until quite recently 15 .
The resonance is one of the intrinsic properties of metamaterials. Loss at the resonance frequency sometimes severely impairs metamaterial's extraordinary performance 9,10 . This problem becomes more prominent for the visible light because its skin depth is comparable to the thickness of metallic traces that are commonly found in a metamaterial unit cell 11,15 . Noble metals such as silver and gold are primary candidates for engineering frequency selective materials at optical frequencies. Published designs including the metal-dielectric-metal fishnet structures consist of a single functional layer along the direction of propagation 14,16 , the 3D optical NIMs made of cascaded fishnet metamaterial 12,13,17 are all based on the meta-atoms which results in an optimal metal thickness of cell unit being about 20 to 50 nm. As a result, considerable loss is induced by volumetric currents and plasma resonances, making metamaterial properties much less attractive for meaningful applications. Up to this day, a significant scientific breakthrough in the visible zero-loss negative-index 3D isotropic metamaterials remain to be seen 9,15,25,28 .
Here we theoretically and experimentally demonstrate the first ultralow loss isotropic topological metamaterials in the visible spectrum. The molecular crystals metamaterial of ballthorn-shaped meta-clusters with symmetrical structure consisting of dielectric and topological silver layer have replaced the lithographically defined meta-atoms in existing NIMs, the surface plasma resonance can be formed inside a cluster unit with a height of two atomic layers, resulting 4 in an optimized silver coating thickness being about 1 nm. The unique technique for preparing ultralow loss isotropic clusters and three-dimensional large area samples by a bottom-up approach was invented. Using the prism method, we report the negative refractive index and the inverse Doppler effect of green and red light in experiment for the very first time. The proposed molecular crystal structure break through noble metal important energy losses and manufacturing difficulties, opening a door for assembling next-generation 3D molecular crystals NIMs devices of arbitrary shape despite their large physical size.

Design and behavior of the meta-clusters structure
Cells are the basic building blocks of all organisms (see Fig. 1a). Cilia, consisting of internal cytoplasm and surface plasmalemma, can be found on the surface of a cell. Cilia are known for their importance as the 'antennas' of a cell and their functions in terms of stimulating responses to surrounding environment, which include chemical sensation, signal transduction, and control of cell growth. Inspired by the ciliated cell structure, we created a ball-thorn-shaped metamaterial cluster (meta-cluster) model consists of a spherical kernel and many protruding rods (Fig. 1b) as analogous to the cilium-cell structure found in nature. Each ball-thorn-shaped unit is made of titanium dioxide (TiO2) dielectric except for a thin layer of metal (topological silver) coating on the outer surface. Both the kernel and rods are made of TiO2 coated by Ag of 1 nm in thickness. 600 identical rods with cross-sectional diameter of 15 nm are uniformly distributed around the surface of a kernel. l represents the diameter of the meta-cluster, r is the radius of the spherical kernel, and P refers to the lattice constant of the meta-cluster, the meta-cluster is fully immersed in polymethyl methacrylate (PMMA). The relative permittivity of Ag is set to be consistent with the actual Drude model value 30 , of TiO2 is 5.2 with a dissipation factor of 0.003, of PMMA is 2.5.
This meta-cluster model is solved in Computer Simulation Technology (CST) Microwave Studio (Supplementary Information S1). A peak in transmission coefficient indicates the meta-cluster resonates within the wavelength range of the red-light (Extended Data Fig. 1), a Mie resonance 22,31 .
The effective parameters are numerically retrieved based on the Mie scattering theory 22, 31 , which proves that the material composed of this structure is a metamaterial. At λ = 645 nm, the value of Re(n) reaches a minimum of −0.45 (Fig. 1c). The figure of merit (FOM) curve (in red) of the metacluster in the red-light band is shown in Fig.1d, where FOMsim = −Re(n)/Im(n) for Re(n) < 0, and Re(n) and Im(n) are the real and imaginary parts of the refractive index, respectively. FOMsim arrives at a maximum of 10.3 at λ = 623 nm and is about 3.2 at λ = 645 nm where the value of Re(n) is the most negative. To achieve a similar effect in the green-light band, we reduced l = 530 nm, r = 165 nm, P = 560 nm. As expected, the transmission and reflection curves indeed reveals a Mie resonance at the green-light wavelengths (Extended Data Fig. 1). Similarly, the permeability, permittivity and refractive index of the meta-cluster are simultaneously negative at near 530 nm.
At λ = 538 nm, the value of Re(n) reaches a minimum of −0.47 (Fig. 1c). The FOM curve (in green) of the green-light meta-cluster is shown in Fig. 1d. FOMsim arrives at a maximum of 15.9 at λ = 514.5 nm and is about 2.2 at λ=538 nm where the value of Re(n) is the most negative. Based on effect of Ag layer thickness tAg on the response behavior of the red-light meta-cluster in PMMA medium (Extended Data Fig. 2), Fig. 1e shows the relationship between metal film thickness and FOM variation. It can be seen that with silver as resonant material, the plasma resonance can be formed with a height of only two atomic layers, resulting in an optimized silver coating thickness being about 1 nm. However, in the models of meta-atom cell unit, such as double fishing nets 16,17 or nanowires 21 , the optimal metal film thickness of the unit is 20-50 nm (Fig. 1f).
Our cluster design is independent of the previously widely used meta-atom cell design philosophy.
This model greatly reduces the silver coating thickness required for achieving high FOM, the resulting FOM is nearly an order of magnitude greater than the state-of-arts. It is indeed this molecular crystals NIMs significant reduction in silver coating thickness that provides the physical basis for the decreased joule heating and thus the realization of ultra-low losses. It breaks through the dilemma of whether to use noble metals in engineering visible light meta-atom NIMs. In addition, spherically symmetric cluster units directly solve the anisotropy problem of cell structure.

Preparation and characterization of meta-cluster particles
The Ag/AgCl/TiO2@PMMA meta-cluster particles corresponding to red-light and green-light are prepared using the solvothermal synthesis method (see Methods). In order to solve the problem of the coating of nano-silver layer of ball-thorn-shaped clusters, AgCl is firstly formed by mixing a certain amount of AgNO3 into TiCl4 during the process of preparing the TiO2 rods. After a photoreduction method, AgCl further disintegrates into elemental chlorine and metallic silver. The latter precipitates on the outer surface of the ball-thorn-shaped structure to form the topological silver distribution about 1 nm coating. The ball-thorn-shaped particle is shown in the scanning electron microscope (SEM) image (Fig. 2a). Next, these agglomerated particles are immersed in PMMA and illuminated to form the Ag/AgCl/TiO2@PMMA particles (Fig. 2b). Figure 2c shows the TEM images of the particles that resonate in the green (left) and red (right) light spectrum, revealing a classic kernel (AgCl/TiO2)shell (PMMA) structure. A high-magnification view in However, after illumination, noticeable difference in absorption is found in the visible light range for the AgCl/TiO2@PMMA particles. These illuminated AgCl/TiO2@PMMA particles not only exhibit intrinsic absorption behavior of AgCl/TiO2 at ultraviolet light wavelengths, but also achieve a wideband absorption in the visible spectrum. Recall the evidence from previous XRD analysis, the increased absorption appeared in the visible light band is likely due to the local plasmon resonance (LPR) of the precipitated Ag nanoparticles. It is concluded that the composition of the post-illumination particles is Ag/AgCl/TiO2@PMMA, electron microscope analysis shows that topological silver distribution with a thickness of about 1nm can be formed (Extended Data   Fig. 3). Note that conventional cell units, such as fish nets and nanowires, are spatially asymmetric, greatly limiting the possibility for self-assembly. On contrary our meta-clusters are spherically symmetric, making them perfect candidates for self-assembly.  Table S1). The ~1° wedge-shaped sample is 5 mm in width, 1 mm in length, and 20 μm in thickness-which is about the height of 30 vertically stacked layers of Ag/AgCl/TiO2@PMMA particles (Fig. 3a).
Using the method proposed in ref. 11, we designed our own experiment (see Supplementary  nm where the value of Re(n) is the most negative (Fig. 1e). This is because we assumed a uniformly distributed Ag layer of 1 nm in thickness when constructing the meta-cluster model in simulation.
However, as proven by the TEM images ( Fig. 2e and Extended Data Fig. 3b), coverage of the Ag layer on the outer surface of the particles is topological distribution. Less metal presence in the resonance structure likely leads to a reduction in transmission loss caused by volumetric current and plasma resonance. There are direct and indirect methods to test negative refraction in experiments (Extended Data Table 1).The direct prism test method requires large 3D wedge samples, because of the inevitable cost of high resistive loss, the best result in literature to date is obtained in the infrared band λ = 1.76 μm 13 . For the first time, we measured the refractive index of a metamaterial sample at red and green light frequencies using a direct method. Our ultra-low loss, isotropic and three-dimensional large-surface-area samples essentially enabled a successful prism measurement.

Inverse Doppler Effect of metamaterials in visible spectrum
Doppler effect refers to the change of frequency of a wave received by an observer with respect to the wave source when there is a relative movement between each other. It has been widely used in celestial mechanics, medical diagnosis, weather and aviation radar system and many other scientific and engineering fields.    where L is the displacement of the refracted spot, f2 is the distance from lens 2 to the sample, that is, the focal length of lens 2, and θ is the wedge angle of sample.

Data availability
The data that support the findings of this study are available from the corresponding author on reasonable request.