Optical metamaterials as types of emerging materials can alter the temporal and spatial propagation of electromagnetic fields at the nanoscale, resulting in negative refraction [1–5], negative Goos–Hänchen (GH) shift [6,7], anomalous spin Hall effect of light (SHEL) [8,9], super-resolution imaging [10–12], invisibility cloak [13], photoluminescence [14], and other magical functions. The anomalous manipulation of light in metamaterials may bring more attractive and potential applications; the negative GH shift has been proven to achieve slowing down of light [7,15]. However, experimental observation of anomalous SHEL is a real challenge because the spin–orbit interaction is generally weak [16], and its magnitude is exceedingly small. What is more, the development of optical negative index metamaterials has encountered a bottleneck, suffering from extreme propagation losses [17].

In 2015, High et al. [8] proposed a hyperbolic metasurface composed of single-crystal silver nanostructures that can generate anomalous SHEL in the hyperbolic regime ($\lambda <580\mathrm{nm}$). Recently, Chen et al. [9] observed anomalous SHEL at 632.8 nm using metasurfaces assembled by quasiperiodic dendritic cluster sets. Other than these, metamaterials that can generate anomalous SHEL are rarely reported. Many current methods to fabricate optical metamaterials are still lithographic-based approaches. Very few large-scale optical metamaterials can be applied; although metasurfaces [18] overcome the shortcomings of 3D metamaterials to some extent, metamaterials with an optical response at visible and near-infrared frequencies are still particularly challenging to fabricate due to the expensive, time-consuming, and complex preparation process. This problem restricts the application of optical metamaterials and makes the study of anomalous SHEL still a tricky problem.

At present, the bottom-up method can realize the preparation of metamaterials without lithography [19]; it has achieved certain results, but the difficulty lies in accurate control of the size and position of the material structure. Superlattices consisting of noble-metal nanoparticles have emerged as a new platform for bottom-up designed metamaterials [20,21] and are expected to generate new negative index materials at visible frequencies. Noble metals are known to interact very efficiently with visible light due to so-called localized surface plasmon resonance (LSPR) excitation; they are highly sensitive to the size, shape, and environment of nanostructures [22]. On this basis, many effective dielectrics have emerged in visible and infrared wave bands using nanoscale metallic particle arrays, but the highly dispersive and lossy metallic response is also troubling [23]. Assembling metallic nanoparticles into macroscopic structures with well-defined order and symmetry is key to achieving material properties [24]. Recently, we found that the unique 3D symmetrical spherical structure of high-generation dendritic macromolecules [25,26] is a powerful tool to assist in the manufacture of metamaterials with uniform size and orderly distribution of metal nanoparticles. Dendritic macromolecules have excellent fractal characteristics. These unique molecular structures and chemical properties are studied in depth and applied in the fields of catalytic reactions [27], biomedicine [28], molecular functionalization [29], preparation of nanomaterials [30], and material modification [31]. Although dendrimers offer remarkable convenience in the field of material preparation, they have never been mentioned for the preparation of metamaterials. Coincidentally, the metal dendritic model [7,9,32,33] has been proven to be a type of metamaterial with multilevel split-ring and equivalent wires. Nanocomposite metamaterials can be obtained using dendrimers to control the particle size and distribution of metal nanoparticles because dendrimers have multilevel-ordered structures similar to the metal dendritic model. This condition is different from highly lossy metallic metamaterials with tightly packed plasma at visible light frequencies [34]; it is highly transparent due to its small particle size and fractal arrangement.

Here, we experimentally demonstrate poly(amidoamine) (PAMAM) dendrimer-based silver nanocomposite metamaterials with abnormal optical response. Using PAMAM as a template and stabilizers, the photochemically reduced Ag can attach to the molecular cavity and grow. Metamaterials PAMAM-Ag prepared by high-generation PAMAM obtain controllable and well-stabilized Ag nanoparticles that are distributed in a multilevel netlike sphere, thereby resulting in anomalous optical manipulation. Experiments show that fifth-generation (5G) PAMAM-Ag can generate a negative GH shift and an anomalous SHEL in visible light broadband (covering the main bands from green light to red light) over a wide range of incident angles; the 5G PAMAM-Ag flat lens [35] shows efficient focusing effect at 750–1050 nm. Finally, a 2D visible light valley–Hall photonic topological insulator (PTI) is simulated based on the dendritic structure of PAMAM-Ag, which may bring more potential applications in topology transmission. The PAMAM-assisted bottom-up preparation method of metamaterials is simple and convenient and provides a new means for developing optical metamaterials.

The preparation methods of PAMAM [25,26] have been complete. PAMAM is synthesized through repeated iterative growth; each of its repeated branched layers is called a “generation,” and the synthesis methods include divergent synthesis, convergent synthesis, and the combination of these methods. Dendritic macromolecules have a large number of cavities that can wrap nanoparticles inside, preventing their aggregation and better controlling size, shape, and dispersion. More importantly, dendrimers do not passivate nanoparticles, preserving their optical properties. As shown in Fig. 1(a), ${\mathrm{AgNO}}_3$ was weighed according to the molar ratio $n_{\text{PAMAM}}:n_{\mathrm{AgNO}3}=1:2$, and then mixed with PAMAM [Fig. 1(a) left panel shows the schematic diagram of molecular structure] aqueous solution for the reaction in dark conditions (stirring at room temperature for 24 h) to obtain the ${\mathrm{Ag}}^{+}$ full coordinate with “N” atoms of dendritic macromolecules. After sufficient coordination, they were transferred to a UV cold light lamp for photochemical reduction [36,37] of Ag [solid blue dots in Fig. 1(a), right panel]. In this work, 1G–5G PAMAM macromolecules were made by a divergent synthesis method for subsequent studies (Appendix A). As shown in Fig. 1(b), 1G–5G PAMAM samples were characterized by ${}^1\mathrm{H}$ nuclear magnetic resonance (NMR) analysis (using ${\mathrm{D}}_2\mathrm{O}$ as solvent). The high-generation PAMAM molecule has repetitive chain segments on branches, and has the same type of hydrogen atoms in a chemical environment as 1G PAMAM molecules [Fig. 1(b), upper panel]. Hydrogen atoms marked as f and g in the unit structure are active hydrogen and will not appear in ${}^1\mathrm{H}$ NMR spectra when ${\mathrm{D}}_2\mathrm{O}$ is used as an exchange agent, and the remaining five hydrogen atoms are labeled with a, b, c, d, and e. Five major peaks were found in the ${}^1\mathrm{H}$ NMR spectra, and the chemical shifts ($\delta$) of hydrogen atoms at a, b, c, d, and e in 5G PAMAM were 2.66, 2.36, 2.54, 3.17, and 2.75, respectively [Fig. 1(b), lower panel]. The chemical shifts of hydrogen atoms of 1G–5G PAMAM corresponding to the main peaks are almost the same, which is consistent with theory. The prepared composite metamaterial is referred to as PAMAM-Ag, where Ag grew by attaching to the dendrimer molecular cavity. Photochemical reduction of Ag does not introduce new ions in the reaction process and can control the concentration of synthesized particles; this approach exhibits advantages over other reduction processes. During the reaction, dendrimers act as a “network vessel” for capturing ${\mathrm{Ag}}^{+}$ and a reagent for electron transfer. Prior to photochemical reduction, ${\mathrm{Ag}}^{+}$ was fixed by “N” atoms of PAMAM. The reduced Ag spherical nanoparticles of 5G PAMAM had a particle size of $\sim 9\mathrm{nm}$ and were distributed in a multilevel netlike sphere due to the limitation of the PAMAM template [Fig. 1(c)]. The high-resolution transmission electron microscopy (HRTEM) image and selected area electron diffraction (SAED) spectra were analyzed to demonstrate the existence state of Ag. The inset in Fig. 1(d) shows that the lattice spacing is 1.56 Å (1 Å $=$ 0.1 nm), representing the (1 0 5) plane of the Ag hexagonal crystal corresponding to the determination of Ag (PDF#41-1402 standard card). Moreover, the calibrated diffraction ring in the SAED spectra [Fig. 1(e)] corresponds to the diffraction pattern on planes (1 –1 2), (0 0 6), (1 0 5), (1 1 2), and (2 0 3) of the Ag hexagonal crystal.

The film sample is prepared by a spin coating method (1600 r/min for 30 s). The 5G PAMAM-Ag film sample, as an example, has a size of $1.2\mathrm{cm}\times 4\mathrm{cm}$ [Fig. 1(f), left panel], and the scanning electron microscopy (SEM) image shows that the thickness of the film is $\sim 4\mathrm{\mu m}$ [Fig. 1(f), right panel]. We can coat it as a film of almost any shape and size when required. Evidently, the transmission spectra in the visible–near infrared wave band show that PAMAM-Ag is highly transparent, and the transmittance reaches 80%; thus, it is very suitable for optical frequency studies [Fig. 1(g)]. The transmission curve of the pure PAMAM has a transmission peak at 430 nm (which is the inherent transmission peak of PAMAM); the transmission peak of the PAMAM-Ag disappears at 430 nm, and a new transmission peak appears near the wavelength of 400 nm. Generally, the new transmission peak is caused by the resonance of Ag nanoparticles, according to the theory of metal plasma resonance [38]. This finding indirectly proves that ${\mathrm{Ag}}^{+}$ coordinates with dendritic macromolecules and successfully reduces Ag nanoparticles. In addition to the appearance of the silver intrinsic peak, another resonant peak appeared after the wavelength of 500 nm; it is speculated to be the characteristic resonant wave band of the metamaterial. Generally, the third generation of dendritic macromolecules is the boundary between 3D spherical structure and planar linear structure. A 1G–2G PAMAM molecule presents a linear structure with fewer internal cavities and the weak ability to wrap Ag nanoparticles. Therefore, it cannot serve as an ideal template. The low content and poorly ordered distribution of Ag nanoparticles in 1G–2G PAMAM-Ag result in a low intrinsic transmission peak and characteristic resonant wave band. 3G PAMAM-Ag has a higher intrinsic transmission peak, but its characteristic resonant wave band is still not broad enough. When the “generation” is greater than or equal to four, the chemical structure of PAMAM presents a 3D symmetrical sphere, with more abundant internal cavities. It becomes a template and nano reaction container that is more conducive to the preparation of well-dispersed and stable Ag nanoparticles due to these properties. The size and arrangement of Ag nanoparticles in 4G–5G PAMAM-Ag approach the proposed model, and they can generate characteristic resonance in a wider wave band. In addition, the results show that the resonant wave band of PAMAM-Ag moves to the short wavelength with the increase in “generation.” Thus, we can obtain appropriate operating frequencies. Therefore, the experiments mainly discuss the results of 4G–5G PAMAM-Ag.

When a bounded beam is reflected from the interface between two media, it produces small shifts relative to geometric optic prediction. The shift along the interface and in the direction of beam propagation is referred to as GH shift [39], which is described in terms of evanescent wave penetration. Different from GH shift, the SHEL [40] is a result of effective spin–orbit interaction and refers to the transverse splitting in polarizations after reflection or refraction to conserve total angular momentum. These shifts have been used in the field of sensing [41,42]. Furthermore, SHEL can be used to develop spin-dependent devices for precision measurement [43], circular dichroism spectrometric detection [44], and optoelectronic information fields [45]. Some reports focus on enhancing the shift by up to an order of amplification and have made some progress, but they are almost numerical results [46,47]. Current studies have shown that the boundary between the negative index medium and the conventional medium will lead to the reverse anomaly of these shifts, namely, negative GH shift [6,7] and anomalous SHEL [8,9]. Using PAMAM dendrimer-based metamaterials, we experimentally observed clearly identifiable negative GH shift and anomalous SHEL at visible frequencies, covering from the green light wave band to the red light wave band.

5G PAMAM-Ag film samples are measured using the methods proposed by Prajapati et al. [48,49]. Both measurement methods obtain a tiny shift value by analyzing the movement of the interference fringe. GH shift measurement is achieved by the interference of s-polarized and p-polarized beams, and SHEL measurement is achieved by the interference of right-circularly polarized (RCP) and left-circularly polarized (LCP) beams. Figure 2(a) shows a schematic of the experimental setup for GH shift. S-polarized and p-polarized beams from a Wollaston prism are incident on the sample at an angle of $\theta$ and partially reflected from the sample where they experience GH shift. As shown in Figs. 2(c)–2(e), the interference fringes from 45° and 135° ${\mathrm{P}}_2$ are recorded, and then horizontally spliced into an image to calculate the phase difference $\mathrm{\Delta }{\phi }_1$ (an additional phase $\pi$ generated by ${\mathrm{P}}_2$ should be subtracted); thus, we can calculate $D_{\mathrm{GH}}$. Figure 2(b) shows a schematic of the experimental setup for SHEL, and its principle is similar to that of Fig. 2(a). The difference is that a quarter-wave plate at an angle of 45° with respect to the incident light beam converts the s- and p-polarized light into RCP and LCP beams, respectively. The roles of RCP and LCP beams correspond to the upper and lower components of electron spin. These circularly polarized beams are reflected from the sample and experience SHEL. $D_{\mathrm{GH}}$ and $D_{\mathrm{SHEL}}$ are given by Eqs. (1) and (2), respectively: $$D_{\mathrm{GH}}=\frac{\lambda }{2\pi }\frac{\mathrm{\Delta }{\phi }_1}{\sin \theta },$$(1)$$D_{\mathrm{SHEL}}=\frac{\lambda }{2\pi }\frac{\mathrm{\Delta }{\phi }_2}{\cos \theta },$$(2)where $\theta$ is the incident angle, $\lambda$ is the wavelength of incident light, and $\mathrm{\Delta }{\phi }_1$ and $\mathrm{\Delta }{\phi }_2$ are phase changes of the interference fringe produced by the GH effect and SHEL, respectively. Figure 2(f) shows the GH shift of the 5G PAMAM-Ag film sample measured at four typical wavelengths, and $D_{\mathrm{GH}}$ as a function of wavelength and incident angle. K9 glass is measured to verify the accuracy of the experimental method and compare with the PAMAM-Ag film sample. The positive or negative properties of GH shift can be determined from the results of the K9 glass, and the qualitative phenomenon is the movement direction of interference fringes. The interference fringes (left is higher than right) in Fig. 2(e) show the normal GH shift, and the interference fringes caused by a negative GH shift are opposite. Negative GH shifts are observed at 532, 589, and 671 nm, and the normal GH shift at 473 nm (beyond the resonant wave band). In the measured range, the absolute value of $D_{\mathrm{GH}}$ is negatively correlated with the incident angle. The results of these GH shifts are consistent with the position of the resonant wave band in Fig. 1(g), that is, negative GH shifts occur when the wavelength of incident light is in the resonant wave band of the sample. The curves of shift value $D_{\mathrm{SHEL}}$ are measured as shown in Fig. 2(g). The results of K9 glass measured at 532 nm are normal, and the measured values are consistent with the reported results [49]. When the incident wavelengths are 532, 589, and 632.8 nm (within the resonant wave band), the direction of $D_{\mathrm{SHEL}}$ generated by the 5G PAMAM-Ag is opposite to that of K9 glass, indicating anomalous SHEL. The absolute value of $D_{\mathrm{SHEL}}$ increases with the increase in incident wavelength and is positively correlated with the incident angle.

In a previous study, the resonant wave band of the silver dendritic cluster set metasurfaces [7,9] was in the red light band, and the negative GH shift and anomalous SHEL generated by the samples were experimentally observed at 632.8 nm; the hyperbolic metasurface [8] can produce anomalous SHEL at 480–580 nm. Compared with that, PAMAM dendrimer-based silver metamaterials have a wider resonant wave band, which covers at least 532–671 nm in accordance with the experimental results of the negative GH shift and anomalous SHEL. Metamaterial with broadband resonance is conducive to realize the continuous regulation of light, and it contributes to the manufacture of compact and highly integrated devices instead of large volume composite devices.

A slab focusing experiment [35] is performed to further prove the optical properties of PAMAM-Ag [Fig. 3(a)]. The light beam from the focus of the convex lens reaches the sample after 3–5 mm propagation. The inset shows possible situations (focused or divergent) of transmitted light. The intensity distribution of the transmission light is recorded by a fiber optical spectrometer along the $x$ direction. The image of measured field amplitude of a focused beam generated by a 5G PAMAM-Ag film sample at 1050 nm wavelength is shown in Fig. 3(b). A clear point image is focused near the PAMAM-Ag film sample [Fig. 3(b), lower panel], and the distance between the sample and focusing point with maximum light intensity is about 3.75 mm [Fig. 3(b), upper panel]. The results show that the 5G PAMAM-Ag flat lens has a different degree of focusing effect at 450–1500 nm [Fig. 3(c)], and the focusing distance varies from 0.35 to 4.7 mm with wavelength [Fig. 3(d), left axis]. In addition, Fig. 3(d) (right axis) shows the increment of light intensity after focusing relative to that prior to focusing. According to the curves, the 5G sample has the strongest focusing effect at 750–1050 nm, with the maximum focusing light intensity increment of 128% (at 1050 nm). Furthermore, the same measurement was conducted with the 4G PAMAM-Ag flat lens, and the results showed that the 4G sample was effective. However, the focusing wave band was redshifted slightly compared with the 5G sample, and the maximum focusing intensity increment decreased [Figs. 3(e) and 3(f)]. We also measured the pure PAMAM film sample [Fig. 3(g)]; as expected, it did not show any sign of focusing. The slab focusing effect is essentially derived from the negative refraction effect generated by the characteristic resonance of metamaterials [32,33]. According to a previous analysis, the higher generation dendritic macromolecules are more differentiated and have more abundant internal structures. Thus, the higher generation PAMAM-Ag shows superior ability of anomalous manipulation of light.

Furthermore, we proposed a 2D visible light valley–Hall PTI [50] inspired by the multilevel nested dendritic structure of the metamaterial PAMAM-Ag to explore potential applications. As we know, various topological photonic structures with nontrivial bands have been proposed, including coupled ring resonator arrays [51,52], meta-crystals [53], and dielectric photonic crystals [54]. However, existing proposals are mostly limited to macroscale dielectric waveguide structures and complex metamaterials with operation frequency limited to the microwave or infrared bands. The multilevel nested dendritic structure may bring a new design in the field of topological photonics. Especially, it is easy to be directly extended to visible bands with micro-nano scale. The structure of PAMAM-Ag [Fig. 1(a)] was transformed into a hexagonal lattice structure with $C_{3v}$ symmetry as shown in Fig. 4(a). A 3D schematic structure of the designed PTI is displayed in the left panel of Fig. 4(a), and details of 2D structure are shown in the right panel. The lattice constant of the 2D hexagonal lattice is $a=350\mathrm{nm}$. The substrate material is PAMAM (gray part), whose permittivity is 1.812. Ag nanoparticles (blue solid dots) are distributed in the PAMAM, and permittivity of Ag is set to the realistic Drude model value. The unit cell has a four-level branching structure of Ag nanoparticles. The rotation angle $\phi$ is used to change the orientation of dendritic silver nanoparticles as a degree of freedom.

According to the 2D irreducible representation of the $C_{3v}$ wave vector symmetry group of the hexagonal lattice [55], the double degenerate Dirac points appear at the highly symmetric point K in the first Brillouin zone (BZ) if the mirror symmetry of the unit cell is not broken. As shown in Fig. 4(b), the degenerate Dirac point appears at 550 THz at point K, and the inset shows the first BZ and high symmetry points of the hexagonal lattice. The specular symmetry can be broken by rotating the 2D dendritic structures at an angle $\phi$ (the counterclockwise direction is positive). This disturbance increases the energy extremal degeneracy of the Dirac point (at K) and thus breaks the Dirac point to form a complete bandgap. Unit cells with $\phi =-30°$ and 30° are shown in the inset of Figs. 4(c) and 4(d), respectively, and the corresponding band structures are calculated. The degenerate points at K in the first BZ open to form a pair of frequency extreme points (energy valley states) and form a complete bandgap (550–600 THz) in the green light band, as shown in the light blue band region. The waveguide constructed with the above structures may be applicable to topological transport and bring a new method for the manipulation of visible light. The unit cell with a three-level branch [Figs. 4(e) and 4(f)] is also simulated, and the results are similar to those previously described; however, the bandgap moves toward the red band. In depth, it can be regarded as a multilevel nested structure, which is conducive to adjusting the working frequencies. This finding indirectly responds to the intrinsic reason that the composite metamaterial PAMAM-Ag has a wide resonance wave band.

In summary, we have fabricated a visible light metamaterial covering a large area, by using the PAMAM-assisted metallic photochemical reduction approach. The 5G PAMAM-Ag, composed of Ag nanoparticles distributed in a multilevel netlike sphere, is highly transparent in the visible–near infrared wave band and can generate a negative GH shift and anomalous SHEL at resonant frequencies. Focusing experiments confirm that the 5G PAMAM-Ag flat lens focuses effectively at 750–1050 nm, and the maximum focusing light intensity increment reaches 128% compared with the nonfocusing condition. Moreover, the dendritic structures with a three-level branch and four-level branch are proposed to construct 2D valley–Hall PTIs, and the multilevel nest structure can be used for frequency modulation. This anomalous manipulation of light enables metamaterial to possibly be used in subwavelength super-resolution imaging and quantum optical information fields. Simplifying the expensive and time-consuming preparation process of metamaterials, our method merely requires the reduction of silver with the assistance of high-generation PAMAM regardless of the properties of the substrate, providing a new approach for developing larger-scale visible light metamaterials.