Geometric design of antireflective leafhopper brochosomes

In nature, the sizes of brochosomes and their corresponding through-holes exhibit remarkable consistency across different leafhopper species, despite the varying body lengths of leafhoppers ranging from 3 mm to 9 mm (18, 19, 34). Specifically, the majority of natural brochosomes have diameters ranging from approximately 300 nm to 700 nm, while the through-holes measure around 100 nm to 280 nm in size (Fig. 1F). Furthermore, our analysis showed that the ratio between the through-hole size and the natural brochosome diameter consistently approximates 0.28 ± 0.04. This ratio closely aligns with the theoretical value of 0.29 for a buckyball model, or a truncated icosahedron model (SI Appendix, section 1). These observations indicate a remarkable precision and consistency in the formation of natural brochosomes. However, the relationship between their geometrical characteristics and the antireflection function remains an open question.

To investigate the geometrical effect of brochosomes on their antireflection performance, we utilized a two-photon polymerization 3D printing technique to accurately replicate their geometries (SI Appendix, Fig. S2). While state-of-the-art 3D printers like the Nanoscribe Photonic Professional can create objects with a resolution of 200 nm to 500 nm, the printing resolution falls short of replicating the nanoscale geometries of natural brochosomes (i.e., ~300 nm to 600 nm). To overcome this limitation, we employed a scaling model method, which was previously used in the studies of antireflection properties of nanostructured moth-eye surfaces using longer wavelengths of electromagnetic waves (2). Consequently, we fabricated microscopic synthetic brochosomes as a model system and examined their optical characteristics in the near-infrared (near-IR) and mid-infrared (mid-IR) ranges (Fig. 2 and SI Appendix, Fig. S3). Specifically, we designed synthetic brochosomes with diameters of approximately 20 µm and through-hole diameters around 5 µm to ensure that the printed structures were significantly larger than the resolution of the 3D printer. The 3D-printed synthetic brochosomes consist of 12 pentagonal and 20 hexagonal through-holes interconnected by a hollow core, mimicking the precise geometries of natural brochosomes (Fig. 2 B–D). As shown in Fig. 2A, the fabricated sample consists of an array of 20 by 20 synthetic brochosomes in a hexagonal close-packed (HCP) lattice, resulting in a particle packing density of approximately 91%. This arrangement emulates the close packing density of natural brochosomes observed on leafhoppers’ wings (Fig. 1 C–E). The brochosome array covers an area of approximately 400 µm by 350 µm. The shell thickness and through-hole wall thickness of the synthetic brochosomes is approximately 7% and 20% of the overall diameter D, respectively, closely mimicking the characteristics of natural brochosomes (18, 25) (SI Appendix, section 2). As a control sample, we also fabricated another type of synthetic brochosomes with the same topographical features as their natural counterpart but without through-hole structures (Fig. 2 E–G).

Using the microscale synthetic brochosomes as a model system, we performed specular reflectance measurements in the wavelength range from near-IR to mid-IR (i.e., 2.5 µm < $\lambda$ < 10 µm and 10 µm < $\lambda$ < 24 µm) using a micro-Fourier transform infrared (FTIR) spectrometer. It is important to note that the microscopic dimensions of our synthetic brochosomes minimize the plasmonic effect, as the angular frequency of the incident light in the infrared range is much lower than the typical plasma frequency of metals (~10¹⁵ Hz). To ensure that the materials of the synthetic brochosomes do not contribute to infrared absorption, we coated them with a 100-nm nickel layer, which is a highly reflective metal for infrared light (Fig. 3B). We confirmed the deposition of the nickel coating on the synthetic brochosomes using energy-dispersive X-ray spectroscopy elementary mapping analysis (SI Appendix, Fig. S4).

Our experimental measurements demonstrated that synthetic brochosomes with through-holes can effectively reduce specular reflection in the wavelength range from 2.5 µm to 24 µm by up to approximately 94% (Fig. 3). Specifically, we observed two distinct antireflection regimes by analyzing the reflection spectra of synthetic brochosomes with and without through-holes. In the first regime, when the wavelength of light is comparable to the diameter of synthetic brochosomes, D, (i.e., ~0.5 ≤ $\lambda /D$ ≤ ~1), but larger than the through-hole diameters, $d$, a broadband antireflection effect is observed. In this regime, both synthetic brochosomes with and without through-holes exhibit a reduction in reflection of approximately 80% compared to a reflective flat nickel surface (Fig. 3B). In the second regime, when the wavelength of light is smaller than or comparable to the through-hole diameter, $d$, (i.e., $\lambda /d$ < ~1.4), we observed an additional reduction in reflection of up to approximately 53% on synthetic brochosomes with through-holes compared to those without through-holes (Fig. 3E).

The broadband antireflection phenomenon in the first regime could be attributed to Mie scattering. Specifically, Mie theory indicates that broadband scattering of light dominates when the particle size is comparable to the wavelength of light (33) (Fig. 3A). Mie’s solution outlines that the light scattering efficiency of a spherical particle can be calculated based on the following expression (33, 35):

where the scattering coefficients $a_n$ and $b_n$ are defined by Bessel and Neumann functions, and their explicit expressions can be found in the literature (35). In particular, Eq. 1 predicts that the scattering efficiency is maximized when the ratio between the wavelength of light and particle diameter, $\lambda /D$, is around 0.1 to 3 (SI Appendix, Fig. S5). It is important to note that the above analytical relationship (Eq. 1) is developed based on a spherical particle model (33, 35). For more complex particle geometries, such as brochosomes, numerical simulations are necessary to understand their light scattering behaviors, in particular when the light-particle interactions involve multiple particles on a solid substrate (36).

To verify the light scattering process on brochosome arrays, we first conducted optical simulations using the finite-difference time-domain (FDTD) method and obtained a series of time-resolved simulation videos (Movie S1). A detailed illustration of the simulation set-up is presented in SI Appendix, Fig. S7. Our results showed that the light scattering intensity and patterns on the synthetic brochosome arrays, both with and without through-holes, are nearly identical to each other in the dimensionless wavelength range of ~0.5 ≤ $\lambda /D$ ≤ ~1.2. Time-lapse images of the light scattering process on brochosome arrays are shown in Fig. 3C and Movie S1. For completeness, we also performed FDTD simulations to illustrate Mie scattering on a single brochosome, both with and without through-holes (SI Appendix, Fig. S7B and Movie S4). Light is effectively scattered both on a single brochosome particle and brochosome arrays when the wavelength of light is comparable to the size of brochosome particles (~0.5 ≤ $\lambda /D$ ≤ ~1.2). These simulation results are consistent with the prediction from Eq. 1, demonstrating efficient light scattering on buckyball-shaped brochosomes in this range. Additionally, we observed that the incident light does not interact with the secondary through-holes within this wavelength range (Fig. 3C and Movie S1). This observation highlights the importance of matching the diameters of the brochosomes with the wavelength of light to facilitate the Mie scattering effect (36).

The additional reduction in optical reflection on brochosomes with through-holes could be attributed to the cavity absorption effect enabled by through-holes when the light wavelength is smaller than or comparable to the through-hole diameters (i.e., $\lambda /d$ < ~1.4) (Fig. 3D). We performed a theoretical analysis and found that these through-holes could serve as short-wavelength, low-pass filters to further reduce light reflection. Specifically, when considering light interacting with a brochosome, it can be approximated as light passing through a plane with through-holes. According to the classical theory of optics, light cannot pass through a hole whose characteristic size is smaller than the wavelength of light (37). In the 1940s, Bethe derived a simplified expression for the light transmittance of an ideal hole with an infinitesimal thickness (38):

where $d$ is the diameter of a through-hole and $\lambda$ is the wavelength of light. Eq. 2 shows that the light transmittance of a through-hole decreases rapidly as $d$ becomes smaller than $\lambda$. It has been shown that the light transmittance could be further attenuated for a through-hole when its thickness is increased (39). Recent studies based on Maxwell’s equations have demonstrated that when the thickness of a through-hole, h, is equivalent to the radius of a through-hole (i.e., $h=0.5d$), the critical cutoff wavelength, ${\lambda }_c$, above which the light transmittance exponentially attenuates, follows the relationship (40, 41) (SI Appendix, Fig. S6):

Eq. 3 indicates that when the wavelength of light is greater than 1.5 times the through-hole diameter, most of the light cannot be fully transmitted. Based on Eq. 3, we hypothesize that the critical wavelength would be approximately 1.5 times that of the through-hole diameter of brochosomes (i.e., ${\lambda }_c/d\approx 1.5$) as we found that the shell thickness of the majority of natural brochosomes is comparable to the average radius of their through-holes.

Our experimental measurements observed a notable reflection reduction on our synthetic brochosomes with through-holes compared to those without through-holes when the wavelength of incident light is shorter than the critical wavelength, ${\lambda }_c$ (Fig. 3E). To illustrate the geometrical relationship between reduced reflection and through-holes, we plotted the measured reflection spectra against the dimensionless wavelength, $\lambda /d$ (SI Appendix, section 1). As shown in Fig. 3E, the measured reflectance on brochosomes with through-holes ranges from approximately 5 to 18% within the dimensionless wavelength range of approximately 0.5 to 1.4 (corresponding to $\lambda$ = ~2.5 µm to ~7.2 µm). In contrast, the measured reflectance on brochosomes without through-holes is higher, varying from around 10 to 22% within the same range. Particularly in the dimensionless wavelength range of approximately 0.5 to 1.0, where the wavelength of incident light, $\lambda$, is smaller than the through-hole diameter, $d$ (i.e., $\lambda /d<1$), the reflection on brochosomes with through-holes is further reduced by up to 53% compared with those without through-holes, as shown in Fig. 3F. Notably, the measured critical wavelength is approximately 1.4 times the through-hole diameter (i.e., ${\lambda }_c/d\sim 1.4$), which is in good agreement with the theoretical value of 1.5 predicted by Eq. 3. These measurements indicated that the through-holes play an important role in reducing the light reflection on the brochosomes.

To further elucidate the optical absorption behaviors within the through-hole structures, we conducted optical simulations using the FDTD method on both individual brochosome particles and brochosome arrays to examine the light–brochosome interaction process in the short-wavelength range (Fig. 3G and SI Appendix, Figs. S7–S10). Fig. 3G shows the captured electrical field profiles obtained from the simulated light-brochosome interaction videos (Movies S2 and S3). We observed that when the wavelength of incident light is shorter than the critical wavelength (i.e., $\lambda <{\lambda }_c$), the light can enter the brochosomes by passing through the through-holes and resonates inside the cavities of brochosomes before being absorbed by brochosomes and dissipated as heat (Fig. 3 G, Top). This resonance effect prolongs the interaction time between the brochosomes and light, leading to enhanced light absorption below the critical wavelength ${\lambda }_c$. Conversely, when the wavelength of incident light is longer than the critical cutoff wavelength (i.e., $\lambda <{\lambda }_c$), the light cannot pass through the through-holes, and the reflection behavior on brochosomes becomes similar regardless of the presence of through-holes, as shown in Fig. 3H.

In addition to the time-resolved simulations, we also conducted simulations to analyze the total and specular reflectance spectra of brochosome arrays, both with and without through-holes, in the wavelength range of 2.5 µm to 10 µm (SI Appendix, Figs. S8 and S9 and section 6). This range corresponds to the same dimensionless wavelength range, from 0.5 to 2.0, as used in our experiments. The simulated spectra further supported our findings: When $\lambda /d$ is less than approximately 1.4, the reflection on brochosomes with through-holes is further reduced compared to those without through-holes (SI Appendix, Figs. S8 and S9). This result is consistent with both our experimental measurements and the theoretical prediction outlined by Eq. 3.

To further demonstrate that the reflectance reduction is due to enhanced light absorption by the through-hole effect, we simulated the absorption cross-section of brochosomes with and without the through-holes at the single particle level (SI Appendix, Fig. S10). Specifically, the absorption cross-section characterizes the ability of the studied particle to absorb light given the illumination condition of the incoming light. If the through-hole effect is present, then notable light absorption by the single brochosome below a certain wavelength threshold is expected. As demonstrated in SI Appendix, Fig. S10, a brochosome with through-holes exhibits a greater absorption cross-section than one without the through-hole structure when λ/d is less than or comparable to 1.5. This finding further supports the enhanced light absorption by brochosome with through-holes.

Our experimental and simulation results have demonstrated that the specular antireflective properties of brochosomes are contributed by two factors: 1) Mie scattering, resulting from the length scale matching between the diameter of brochosomes and the wavelength of incident light and 2) the through-hole absorption effect, occurring when the wavelength of incident light is smaller than or comparable to the diameter of the through-holes.

Our observations reveal that both the diameters of the brochosomes and their through-holes consistently fall within the range of hundreds of nanometers across different leafhopper species, showing weak dependence on leafhopper body length, as shown in Fig. 4. Importantly, we found that the ratio between the diameter of natural brochosomes (~300 nm to ~700 nm) and the wavelength of UV–visible light (~300 nm to ~700 nm), ranges from ~ 0.4 to ~2.3. This places them within the effective Mie scattering regime for UV–visible light, as depicted by Eq. 1 (Fig. 4A and SI Appendix, Fig. S5). Furthermore, we observed that the through-hole sizes (~100 nm to ~280 nm) fall within the range that can effectively reduce UV light reflection, as depicted by Eq. 3 (Fig. 4B). These findings suggest that the diameters of natural brochosomes and their corresponding through-hole sizes may have evolved to effectively reduce light reflection in both the visible (~400 nm < $\lambda$ < ~700 nm) and UV (~300 nm < $\lambda$ < ~400 nm) range.

To validate these analyses on biological samples, we measured the specular reflection on leafhopper wings, both with and without brochosomes (SI Appendix, Figs. S11 and S12), to gain qualitative insights into the antireflection performance. It is important to recognize that directly validating the geometry-induced antireflection mechanisms on biological samples could be complicated by the light-absorbing properties of the materials comprising the leafhopper wing and brochosomes, particularly when the wavelength of light is less than 300 nm (44). Our measurements show that the specular reflection on a leafhopper wing coated with brochosomes can be reduced by ~28 to ~86% in the UV range (i.e., ~300 nm < $\lambda$ < ~400 nm), and by ~28 to ~68% in the visible light range (~400 nm < $\lambda$ < ~700 nm), compared to a bare leafhopper wing without brochosomes (SI Appendix, Fig. S12). This degree of reflection reduction is comparable to that observed on moth wings with nano-pillars, which show an average reduction of approximately 69% compared to a bare moth wing without nano-pillars (SI Appendix, Fig. S12). In the case of the leafhopper wing, the observed reduction in broadband UV–visible reflection is consistent with our results derived from synthetic brochosomes, where the combined through-hole effect and Mie scattering significantly reduce UV reflection, and Mie scattering alone contributes to broadband anti-reflection in the visible light range.

In addition, natural brochosomes are typically found densely packed in a disordered arrangement (Fig. 1C). To understand how the packing density and disorderliness of brochosomes affect light reflectivity, we conducted further study using synthetic brochosomes. We found that the through-hole effect becomes more pronounced when the packing density exceeds the critical packing density ${\eta }_c$, which is approximately 58% (SI Appendix, Fig. S13). This effect is particularly noticeable when the gap distance between individual particles is smaller than the through-hole diameter. Additionally, we have also performed a disorder analysis to examine the robustness of the through-hole effect. We fabricated synthetic brochosomes, both with and without through-holes, and arranged them in a disordered array (SI Appendix, Fig. S14). Our experimentally measured specular reflectance reveals that the through-hole effect remains evident in a disordered arrangement (SI Appendix, Fig. S14).

How do antireflective brochosomes benefit leafhoppers? Antireflective surfaces are commonly found across the insect kingdom, with some of the well-known examples being the moth’s eye (2) and insect wings (45). It has long been hypothesized that these antireflective surfaces help insects by reducing mirror-like reflections, thus providing camouflage or decreasing their detectability to predators (46). Similarly, we hypothesize that leafhoppers consistently apply a dense coating of brochosomes on their wings, potentially maximizing the surface anti-reflectivity to avoid attracting predators with mirror-like reflected light. To maintain a high packing density, leafhoppers frequently secrete and distribute brochosomes across their body surfaces. They engage in anointing and grooming behaviors every few hours, ensuring a multilayered, dense, and evenly distributed brochosome coating on their bodies (47). These behaviors, observed in both nymphs and adult leafhoppers, persist throughout their lifespan (47).

The predators of leafhoppers, such as birds and lizards, possess tetrachromatic color vision, which enables them to perceive an extended range of colors, including UV colors (42, 48, 49). Plant leaves, which are a common habitat of leafhoppers, contain pigments that can absorb UV light, resulting in reduced UV reflection (50). Our results suggest that leafhoppers potentially utilize the through-holes on brochosomes to further decrease UV reflectance, thereby mimicking the low UV reflection of plant leaves. The combined effects of UV absorption by the through-holes and the scattering of visible light by the primary structures of brochosomes could synergistically aid leafhoppers in reducing their observability to predators. While this hypothesis remains to be tested in field studies, our results provide a physical basis for understanding why the size of brochosomes from various leafhopper species may have evolved within a size range on the order of a few hundreds of nanometers. These findings potentially suggest an evolutionary design strategy by leafhoppers, employing highly engineered, deployable optical materials as a means to evade their predators.

The leafhopper specimens were purchased from www.deadinsect.net. Silicon wafers were purchased from Addison Engineering Inc., USA. Photoresist IP-DIP was purchased from Nanoscribe GmbH & Co.

The optical image of the leafhopper was captured using a digital camera equipped with a macro lens (ILCE-7M2, Sony, Japan; Mitakon 20 mm f/2, Zhongyi Optics, China). The nanoscopic view of the insect surfaces was obtained using a field emission scanning electron microscope (Merlin, Zeiss, Germany) with a 5-kV acceleration voltage. To prevent electron charging on the non-conductive biological specimens, a 10-nm layer of iridium was sputtered.

The synthetic brochosomes were fabricated by a two-photon polymerization 3D printing method. The 3D computer-aided design files of synthetic brochosomes were designed using the software SolidWorks. The 3D printing process was carried out using a 3D printer (Nanoscribe Photonic Professional GT3D). To create the synthetic brochosome structures, a photoresist called IP-DIP (approximately 50 µL) was added onto a silicon substrate, and the photoresist was polymerized by a 780-nm laser beam. The synthetic brochosome structures were printed by moving the focus point of the laser beam in accordance with the 3D file instructions. Finally, the uncured polymer was removed by immersing the sample in SU-8 developer for 10 min, followed by rinsing with isopropyl alcohol for 2 min.

The 3D-printed synthetic brochosomes were conformally sputter coated with a layer of 100-nm nickel using e-beam deposition (Temescal FC-2000, Ferrotec, USA). The temperature of the samples during the deposition process was maintained around 16 °C.

The infrared reflection on synthetic brochosomes was measured using a micro-FTIR spectrometer system (HYPERION II, Bruker, Germany). To ensure measurement accuracy, a gold-coated flat mirror was used as the reference surface for calibration.

FDTD simulations of synthetic brochosome arrays were performed in Ansys Lumerical FDTD Solutions. In all simulations, brochosome (single particle or in arrays) is assumed to be made of nickel and supported by a silicon substrate coated with 100-nm-thick nickel. Permitivities of nickel and silicon in both simulations were acquired from the literature (51). The brochosome arrays were illuminated by a plane wave source positioned 45 µm above the arrays. Both the reflective spectra and the light–brochosome interaction processes were captured in the simulations. To obtain the total reflection spectra, the lateral dimensions of the simulation domain were set based on the size of brochosomes (~20 µm). The lateral boundary conditions in the x- and y-directions were set to be periodic to replicate a 2D infinite array. The boundary condition in the z-direction was set to be perfectly matched layers (PMLs) to absorb all outgoing waves and eliminate unphysical resonances. The total reflection spectra were captured by a 2D frequency-domain field and power monitor placed on the back side of the plane wave sources. To simulate the specular reflection spectra, similar simulation setup as the total reflection simulations was utilized, and the 2D electrical field captured by a frequency-domain field and power monitor is analyzed using the near-to-far field projection function of Ansys Lumerical. The angular distribution of reflected energy was acquired first and then integrated within a cone around the normal direction with a half vertex angle of 20°. The noises of the simulated specular reflection spectra were filtered using the moving average method with a filter window size of 2.5 to 5% of the total number of data points. The simulation videos were captured within one of the brochosomes of the infinite brochosome array. To capture the absorption cross-sections of single brochosomes, the total-field scattered-field source is used to illuminate the brochosome, and the absorbed power was captured and analyzed by “cross section,” a built-in module of Ansys Lumerical, to calculate the absorption cross-section. To capture the light–matter interaction videos of single brochosomes, the brochosome is illuminated by a plane wave source, and the interaction video is captured by a movie monitor located at the central cross-section of the brochosome. Boundary conditions are set to be PMLs to absorb all electromagnetic waves leaving the simulation domain to eliminate unphysical resonances.

L.W. and T.-S.W. designed research; L.W. and Z.L. performed research; L.W. conducted experimental studies and performed theoretical analysis; Z.L. performed simulation studies; L.W., Z.L., S.S., and T.-S.W. analyzed data; Z.L. and S.S. contributed to manuscript revision; and L.W. and T.-S.W. wrote the paper.

L.W., Z.L., S.S., and T.-S.W. are inventors on a patent application related to this work filed by the Penn State Research Foundation and Carnegie Mellon University.