An extended family of perforated submicrometer hollow or core-shell plasmonic particles as antireective synthetic brochosomes

We investigated different biomimetic structures inspired by natural brochosome powders which appear on the bodies and wings of leafhoppers (insects from the Cicadellidae family). All structures we analyzed are roughly spherical, with diameters 200 nm to 1000 nm, with a core and a shell made of different materials and the core perforated with subwavelength holes with diameters of the order of tens of nanometers. We extended the range of possible designs, geometries and materials of synthetic brochosomes, inspired by their natural counterparts found as powders secreted by various species of leafhoppers. We performed simulation of the optical properties of the structures using the nite element method. We found out that our approach ensures the design of highly ecient omnidirectional ultra-antireective diffractive powders with subwavelength apertures. The reectivity of 600 nm diameter holey spheres does not exceed 0.02% in 500-600 nm range. We showed that planar arrays of plasmonic-based articial brochosomes exhibit a rich optical behavior, including effective refractive index below unity and even below zero at longer wavelengths. Such metamaterial-like behavior contributes to the multifunctionality of our synthetic brochosomes which can already serve as antireective, superhydrophobic and highly porous structures controllable by design. This kind of versatility shows potentials for numerous practical uses. A major part of the novel functionalities stems from the use of nanocomposites containing free-electron conductors (plasmonic materials). Thus we arrived at a toolbox for the design of highly customizable antireective layers. Potential elds of use include photodetectors, photoelectrochemistry, photocatalysis and general microoptoelectromechanical (MOEMS) systems.


Introduction
Antire ective (AR) properties and cloaking are of crucial interest in many optical and photonic devices and systems. They are indispensable for the performance improvement of various photodetectors and nd their application everywhere where it is necessary to increase the input light ux (Raut et al. 2011;Jakšić 2014).
There is a plethora of different approaches to decreasing re ection and increasing absorption.
Historically, the oldest method is the use of interference ultrathin lms that may be single-or multilayered (Macleod 2010). The next large group are various diffractive antire ective surface pro les. With the advent of plasmonics and metamaterials, new highly e cient structures appeared, mostly based on subwavelength diffractive elements utilizing metamaterials -the superabsorbers (Aydin et al. 2011). A typical metamaterial superabsorber has its top plasmonic surface structured -e.g. riddled with holes and has a bottom metallic layer, divided from the top by a dielectric spacer. Another family of synthetic antire ective structures includes the bioinspired ones (Han et al. 2016), the basic function of many of these overlapping in a certain degree with the diffractive antire ective surface pro les. One of the earliest examples that caught the attention of the scienti c community were the so-called moth-eye structuresperiodic diffractive structures mimicking the antire ective relief found in the eyes of moths (Clapham and Hutley 1973).
In 2017 a new approach to bioinspired antire ective structure has been proposed, based on plasmonics and metamaterials: the use of synthetic brochosomes as omnidirectional ultra-antire ective diffractive structures (Yang et al. 2017). It immediately attracted the attention of researchers and a number of papers appeared dealing with the various practical applications of synthetic brochosomes -e.g. (Ding et al. 2019;Lei et al. 2020;Hua et al. 2021;Li et al. 2021).
Natural brochosomes are submicrometer hollow spherical submicrometer particles usually consisting of proteins and lipids, their surfaces riddled with nanoscale apertures. They were rst described as early as in 1950ties (Tulloch and Shapiro 1954) and were studied in depth by Rakitov and collaborators (Rakitov 1995;Rakitov 2000;Rakitov 2004;Rakitov and Gorb 2013). They are produced by some insects (e.g. leafhoppers -Hemiptera: Cicadellidae) and cover them as integumental powders. They simultaneously perform a role of superhydrophobic protection against sticking the insect to plants sap (Rakitov and Gorb 2013) and serve as antire ective coatings in the visible to reduce observability by predatory species (a natural cloaking device) (Yang et al. 2017).
A procedure for the microfabrication of synthetic brochosome-like structures was described by Yang et al (Yang et al. 2017). They deposited sacri cial nanospheres on the plasmonic shells of core-shell submicrometer particles at various depths and then etched them, leaving round holes in the surface.
Other works dealing with the micro/nanofabrication of synthetic brochosomes include (Sukamanchi et al. 2017;Borja 2018;Ding et al. 2019;Lei et al. 2020;Shih et al. 2020;Li et al. 2021). Most of these make use of the fact that when fabricating synthetic brochosomes one is not limited by the materials appearing in the natural structures, which ensures a wider range of available properties and thus extended possibilities for practical utilization.
The experimental applications of synthetic brochosomes proposed so far show their true multifunctionality and include not only omnidirectional antire ective layers (Yang et al. 2017;Borja 2018;Lei et al. 2020;Shih et al. 2020;Li et al. 2021) but also superhydrophobic and superoleophilic particles and surfaces (Sukamanchi et al. 2017), electrochromic materials (Hua et al. 2021), omnidirectional surface-enhanced Raman scattering substrates (Ding et al. 2019), photoanodes for photoelectrochemical hydrogen production (Pan et al. 2019), etc. At that, this research eld is only in its nascence, the rst paper about the fabrication being published a few years ago (Yang et al. 2017). Thus it is reasonable to assume that new applications will continue to appear for at least some time. The variety of the practical implementations described so far con rms the multifunctionality of synthetic brochosomes and an obvious real-life interest for them.
In this work we rst consider various alternative designs for synthetic brochosomes, both those found in nature and those only loosely inspired by the biological ones. We used free and open-source computer graphics environment Blender to design and render our structures. We modeled their electromagnetic properties like scattering parameters (transmission and re ection coe cients) of interest for their antire ective behavior using nite element method (FEM). We also extracted the effective optical parameters of the synthetic brochosomes from the simulated complex transmittance and re ectance.

Some Designs Of Synthetic Brochosomes
We present here two groups of designs for synthetic brochosomes. One group are more or less replicas of the natural structures secreted as integumental protective submicrometer particles by leafhoppers. Another large group are the synthetic brochosomes that do not exhibit a direct correspondence with the natural ones. Instead of it, they share a number of general properties, being hollow or dielectric-lled (core-shell) sphere-like shells with subwavelength apertures on their surfaces. Among examples of such alternative designs are the structures designed, modeled and fabricated by (Yang et al. 2017). We may say for the members of the latter group that they draw the basic inspiration from nature, but the exact geometries and materials will vary wildly and the departures from the natural structures may be quite signi cant. In other words, these synthetic structures are inspired by their natural counterparts, some more loosely than the others.
For the both groups we generated appropriate 3D models in the free and open-source software package for computer graphics Blender ver. 2.82. Some chosen examples of the investigated structures are further described. Figure 1 represents a simpli ed synthetic analogue of the natural brochosomes secreted by e.g. the species Paraulacizes irrorata and Oncometopia orbona (Rakitov 2004). Similar shapes are actually ubiquitous among leafhoppers and are encountered in a majority of the integumental powders of various Cicadellidae. Their dimensions in nature (diameter) may vary between 200 nm and 600 nm, but some larger specimens even reach up to 5 mm. The left part of Fig. 1 shows the templating that would be necessary to synthesize the shapes as shown in Fig. 1 right. The white sphere represents the core which is either lled with dielectric or hollow, the pink shapes with trapeze-like cross-section are actually truncated hexagonal pyramids that serve as sacri cial structures, while light blue part represents a conductive plasmonic layer deposited after the sacri cial structures. The nal synthetic brochosomes have their extruded parts (plasmonic material "walls") similar to a honeycomb, while its layout is icosahedral, not unlike the fullerene (buckyball) shape. Obviously, such templated structures with nanometer-scale details would be extremely di cult to fabricate, albeit their effectiveness is already proven in nature. Thus instead of these shapes, we consider much simpler geometries, easier to produce using conventional microfabrication and nanofabrication by sacri cial nanoscale spherules in a manner akin to that presented in (Yang et al. 2017). Figure 2 shows a relatively simple synthetic brochosome structure that can be obtained in a manner quite similar to that described by Yang et al (Yang et al. 2017).
As in (Yang et al. 2017), templating can be done using nanoscale sacri cial spherules densely packed on the surface of a larger sphere. The nal shape after etching has a cratered appearance, its hemispherical pits being scattered across the plasmonic core-shell surface in a rather random manner. Very similar shapes are found in nature in large brochosomes used for egg powdering in Oncometopia genus leafhoppers, an average diameter of a powder particle being about 1 mm.
We further consider some synthetic brochosomes which actually represent variations of the one shown in Fig. 2. Several possible forms are shown in Fig. 3. Basically, each of the particles is a submicrometersized plasmonic shell with holes of varying diameters templated by sacri cial spherules of different sizes and placed at different depths.
The number of possible combinations is literally endless, even when one considers holey core-shell geometry variations only. Even natural structures are encountered in a lot of different forms and sizes, a majority of which is not even mentioned here. A review of some of numerous shapes and kinds of brochosomes can be found in (Rakitov 2004). In addition to that vast diversity, novel properties are also obtained by choosing building materials outside the nature toolbox, like in our case (as far as the authors know, there are no known plasmonic biological structures).

Results And Discussion
We simulated the optical properties of our proposed synthetic brochosomes by FEM using the Comsol Multiphysics software package -RF Module. We calculated the spectral dispersion of scattering parameters (coe cients of transmission and re ection) and the spatial distribution of the electromagnetic eld intensity. The holey plasmonic shell was illuminated from the top (the case of normal incidence of the light beam). We assumed that the plasmonic material was gold. In order to obtain more realistic results, its optical parameters were modeled using experimental data from literature (Rakić et al. 1998) rather than using the idealized Drude model that deviates in a certain degree from the reality. We assumed that the dielectric core within the particles was air (i.e. refractive index n = 1).
We rst considered the scattering parameters of the shapes shown in Fig. 3 top. In order to check if the antire ective properties appear even for the simplest cases, we performed our simulations for a shell with 6 holes, an opposing pair on the x, y and z axis each. The shell diameter was 600 nm, the wall thickness was 20 nm and the hole diameter was 160 nm. We considered a 2D square array of holey shells, the distance between two neighboring shells being 200 nm. The transmission and re ection coe cient are shown in Fig. 4. In Fig. 4 left one can see that there are two bands with very low re ection coe cients, at 500-600 nm (green-yellow light) and above 1100 nm (near infrared). Fig. 4 right is an extract from Fig. 4 left, shown in the 500-700 nm range and in logarithmic scale to stress the low values of the re ection coe cient at the lowest wavelengths (even reaching below 0.02% between 500 nm and 600 nm). The re ection drop in near infrared (the rightmost part of Fig. 4 left) is due to the plasmonic particles starting to behave as an effective medium mostly consisting of dielectric (air) -the well-known arti cial dielectric effect (Brown 1953;Mendis et al. 2016) -thus decreasing their absorption with wavelength and becoming transparent. Since this phenomenon does not contribute to increased absorption, it is of no immediate interest for us here.
The spatial distribution of the electric eld is shown in Fig. 5 for a square array of perforated hollow particles and on the surface of a single particle from that array. Two operating wavelengths of interest were considered, 550 nm and 680 nm.
The propagating waves are coupled to the golden spheres through nanoaperture scattering, similar to that rst described by Ebessen and coworkers in their seminal paper on extraordinary transmission hole arrays (Ebessen et al. 1998). The difference is that in our case, due to the speci c geometry of the structures, the increase of the wavevector of the incident waves results in generation of localized surface plasmons polaritons (SPP) on the plasmonic shells. This effect can readily be observed in Fig. 5 at 550 nm (bottom) where a distinct dipole radiative pattern is observed around the nanoaperture. Inside the sphere scattered eld couples with quadrupole resonant mode of the shell which in turn couples with adjacent particles resulting in leaky modes (weak con nement). On the other hand, at 680 nm the shell material (gold) has a much higher refractive index, resulting in much more con ned spatial eld distributions. Nanoaperture scattering results in highly localized "pockets" of EM radiations due to increased eld penetration into the structure. At the end of the process the localized SPP are absorbed in the highly absorptive metal of the shell both from outside and from within the sphere. The result is a large drop of the re ection coe cient in the 500-600 nm range as seen in Fig. 4.
We further performed extraction of the effective optical parameters for our planar arrays of holey spheres. We calculated the complex values of the effective relative dielectric permittivity (ε), effective relative magnetic permeability (µ) and effective refractive index (n). To this purpose we used the approach of Smith and coworkers (Smith et al. 2002) and applied it to our simulated complex transmittance and re ectance. Fig. 6 shows the extracted effective parameters.
The extraordinary spectral behavior of the extracted optical parameters of the planar array of synthetic brochosomes is readily noticed in Fig. 6. Remarkably, their values mostly remain below unity. In the 500-600 nm range both the real and the imaginary part of the effective refractive index remain relatively close to zero, never exceeding 0.1, but are always positive. However, in the range above 1 µm the real part of the effective refractive index drops below zero, meaning that the array behaves as a double negative metamaterial. Such rich behavior of the spectral dispersion points out to numerous potential practical applications of plasmonic synthetic brochosomes.

Conclusion
In this work we proposed some extensions and generalizations to bio-inspired geometries of synthetic brochosomes containing plasmonic holey shell. We simulated the electromagnetic parameters of the structures using the FEM approach. We succeeded in obtaining very low re ection coe cients in a wavelength range of interest (especially yellow and green part of the spectrum). We showed that even in a very simple case of just 6 subwavelength holes the planar arrays of plasmonic-based arti cial brochosomes show a rich optical behavior, including effective refractive index below unity and even below zero at longer wavelengths. Such metamaterial-like behavior, together with their multifunctionality (they can serve as antire ective, superhydrophobic and highly porous structures with parameters controllable by design) points out to a versatility that may prove itself convenient for numerous microoptoelectromechanical (MOEMS) systems. In our further work we intend to extend our investigations to other geometries and plasmonic/dielectric material pairs. Figure 1 Biomimetic core-shell submicrometer powder miming the brochosomes of the leafhopper tribe Proconiini and generally Cicadellidae family. Left: schematics of templated synthesis of the biomimetic core-shells. Blue annulus: plasmonic shell. Pale pink trapezes: sacri cial structures to be etched, leaving the holey shell. White: core, either hollow or lled with dielectric. Right: 3D CG render of biomimetic core-shells.

Figure 2
Biomimetic core-shell microscale powder miming the brochosomes of the leafhopper genus Oncometopia. Left: schematics of templated synthesis of the biomimetic core-shells. Blue annulus: plasmonic shell. Pale pink spheres: sacri cial structures to be etched, leaving the holey shell. White: core, either hollow or lled with dielectric. Right: 3D CG render of biomimetic core-shells. 3D CG renders of biomimetic core-shell submicrometer powders consisting of hollow metal cores riddled with nanoscale apertures. Templating is done in a manner identical to that in Fig. 2, but with various sizes of spherules at different depths. Top: largest holes, middle: mid-sized holes. Bottom: smallest holes.

Figure 4
Spectral dependence of scattering parameters of synthetic brochosomes arranged in a square array of holey golden shells (shell diameter 600 nm, wall thickness 20 nm, hole diameter 160 nm, 6 holes in total). Left: spectral re ection, transmission and absorption coe cients, linear scale. Right: Finer view of the same dependence as shown left, 500-700 nm range, logarithmic scale.