Cataglyphis bombycina is a highly heat-tolerant ant species living in desert areas with extreme insolation. Since they forage during the hottest hours of the day, they have to sustain temperatures that are close to their critical thermal limit [1]. For survival, this species has evolved several traits, including long legs, heat shock proteins, visual orientation, and a dense coverage with hair-like setae [1–3]. These setae have been shown to have amazing optical properties, helping the ant to deal with a wide spectrum of electromagnetic waves from sunlight. Nano-ribs on their upper surface in combination with a central canal efficiently scatter ultraviolet (UV) light [4]. The setae have cross sections in the shape of an isosceles right triangle with a hypothenuse of (3.4 ± 0.4) μm [4]. Because of this cross-sectional shape, they reflect visible light by total internal reflection [5, 6] and scatter light in the visible range by higher order Mie-resonances [4, 6]. In the mid infrared (MIR) the setae are suggested to form an antireflection layer, which enhances the radiative cooling of their body [6]. However, the size of the setae in that wavelength range is large enough to cause scattering due to low-order Mie-resonances [4]. Since the setae have an elongated shape, these resonances resemble resonances in optical wires. In optical wires these resonances are eigenmodes, that can be perfectly linked with Mie-resonances in dielectric structures [7]. These eigenmodes are also named leaky mode resonances (LMRs), since their electric field decays in the surrounding of the structure. Leaky modes determine optical properties of dielectric structures including absorption, scattering and emission. These properties can be engineered by changing, e.g., morphological details as well as substrate and superstrate [7]. In the natural system represented by the ant’s integument, the distances between the setae and the cuticle are small compared to the wavelength of the thermal radiation. In this case, near field effects may play a role for radiative cooling [8, 9]. Reid et al. showed that the radiative heat transfer between patterned and between un-patterned slabs increases by orders of magnitude if they are brought in close proximity, where d < λ T = ℏ c / k T [9]. For this thermal radiation region, Shi et al. suggested that the reflectivity of the ant body is reduced by a refractive index gradient of an effective medium layer formed by the setae, which enhances the emissivity according to Kirchhoff’s law, and thus enhances the radiative cooling of the ant body [6]. Since the setae, however, are spatially arranged with a defined distance from the underlying cuticle, the question can be raised whether effective medium theory is sufficient to explain the effects observed by [6]. Therefore, we experimentally characterized the arrangement of the setae and directly simulated the hemispherical emission of the system as a whole with finite difference time domain simulations (FDTD).

Since the setae of C. bombycina have a very anisotropic aspect ratio, it is still a challenge to simulate them with reasonable computational efforts. Therefore, the setae-cuticle system was assumed to extend infinitely along the setae’s long axis. The simulations can then be reduced to a 2D computation cell. Therefore, the emission can only be investigated along angles perpendicular to the setae’s long axes. In this study, hemispherical is thus defined only via the angle θ = − 90 ° ;   90 ° , as visualized in Figure 1. The emission was realized with a noisy material dispersion corresponding to the black body radiation at 53°C. This corresponds to a wavenumber range of [0–2,000 cm⁻¹]. Thus, the simulations consider the maximum body temperature the ants can tolerate (T = 326.15 K = 53°C) during their foraging periods in the natural habitat of this species [3].

The angle resolved emission was simulated for three different systems with increasing gap sizes between setae and cuticle (Figure 6). To demonstrate the effect of the setae on the emission, the three curves are normalized to a cuticle without setae (emission enhancement = 1). In the first simulated case the setae are directly attached to the cuticle without any gap (black dashed, gap = 0 µm). This already leads to an average increase in emission of about 3%. At small angles the emission enhancement is constant and only increases slightly at large angles. This mode of action corresponds to a classical anti-reflection surface [19]. In the second case the emission was simulated with a mean gap of 0.63 µm between setae and cuticle (orange solid) which corresponds closely to the geometry present in the ants with a mean distance of (0.68 ± 0.72) µm [determined by experimental measurements (Figures 2, 3)]. At small angles, the emission enhancement is almost like in the case without a gap, but at large angles it strongly increases. This results in an average emission enhancement of about 6%, which is almost twice as much as if there was no gap between setae and cuticle. If the gap is enlarged to more than double the size of the natural setup (blue dotted, gap = 1.56 µm), the overall average emission enhancement decreases to about 3%. This is a similar value as in the first case, but the curves show different trajectories in similar angle ranges. At small angles, the emission enhancement is lower and at larger angles [sin(θ) > 0.7] it is much higher and rises with an even larger slope than in case two. The enhanced emission at large angles in case two and three can be explained by much better outcoupling of evanescent waves than in case one.

The lower emission enhancement at small angles in case three shows that when the distance between setae and the cuticle would be too large, the setae would become a hindrance for the thermal radiation. This is also supported by the reflectance simulations under perpendicular incident light (Figures 4A, C).

The reflectance of the setup without a gap between setae and cuticle (dark blue; gap = 0 µm) is lower than that of the plain cuticle (dashed blue) over the full displayed wavenumber range for both polarizations. Thus, the zero-gap case shows the typical behavior of an anti-reflection coating [19]. The situation is different if a gap between cuticle and the setae is present. In those cases, resonances occur, especially at large wavenumbers (e.g., between 4,000–7,000 cm⁻¹). These resonances increase the reflectance of TM as well as TE polarized light (Figures 4A, C). In the spectral range below 2,000 cm⁻¹ however, the presence of setae results in a lower reflectance compared to a plain cuticle. Depending on the gap size between setae and cuticle, there is a spectral region where the reflectance is lower than if the setae were attached to the cuticle without gap. The larger the gap size, the narrower the respective region with low reflectivity. Additionally, the minimum in the reflectance is also shifted to lower wavenumbers. The larger the gap, the stronger is the influence of the absorption bands of chitin. They originate from the material dispersion included in the simulation, which is summarized in Table 1. The strongest ones occur between 1,500 and 2,000 cm⁻¹.

An opaque body with a higher reflectance has by Eq. 1 a lower absorption. By the reciprocity of light, a lower absorption also leads to lower emission. Thus, a higher reflectance would cause a lower emission for the ant. Therefore, all gaps between setae and cuticle reduce the emission enhancement in the spectral range between 4,000–7,000 cm⁻¹ (Figure 4B). In this range, all curves of the simulations with a gap show a higher reflectance and similar resonances. This indicates that these resonances are independent of gap size and the randomized spatial arrangement of the setae. Therefore, it is safe to assume that the resonances originate solely from the setae and correspond to their leaky modes (LMR) or Mie-resonances. Interestingly, deriving a Fabry-Perot thickness from the periodicity of these resonances leads to a value d ∼ 1.75 µm, which corresponds very well to the height of the setae [4]. The presence of similar resonances was confirmed before with experimental FTIR transmission measurements of single setae [4]. Since the Planck radiation of a black body at 53°C is almost zero in the wavenumber range of 4,000–7,000 cm⁻¹, the resonances in this region do not contribute to the thermal emission of the ant. For the thermal emission and resulting possible radiative cooling effects the range between 0–1,500 cm⁻¹ is much more relevant. In the range of 0–1,500 cm⁻¹, the reflectance for all gap sizes decreases below the reflectance of the hypothetical anti-reflection coating represented by the zero-gap case. In this spectral region the emission is strongly influenced by the distance between cuticle and setae. Increasing these gap sizes shifts the maximum of the emission enhancement towards smaller wavenumbers. This effect can be explained by near field coupling of the LMRs. Three examples of these LMRs of setae in different distances to the cuticle are illustrated in Figure 5.

Figure 5A shows the LMR TM₀₁ of a seta. Interestingly, it corresponds very well to the TM₀₁ of a cylinder, as demonstrated for a thin Germanium wire in [17]. Even the resonance frequency correlates very well to this literature example when considering the larger dimensions of the seta and the lower refractive index of chitin compared to the Germanium wire. Due to the lower refractive index of the seta, the leaky mode covers a broader wavenumber range (Figure 4) and extends further into the surrounding space. Therefore, the LMR can couple to the cuticle and to neighboring setae even if the gap between seta and cuticle becomes quite large. Similar coupling effects have been measured on Si-nanowires, too [20].

In terms of optics, enhancing the thermal emission of the ant for its survival is a problem which is comparable to maximizing the absorption in nanowire antennas for harvesting solar radiation, although different wavelengths are involved. Cao et al. showed that there would be better structures than triangular prisms for enhancing the absorption, at least at resonances of higher order than TM₀₁ [17]. To maximize the photocurrent inside their nanowires, they optimized the absorption of the TM₂₁/TE₁₁ resonances rather than TM₀₁, because these are less sensitive on illumination angle. The TM₀₁ LMR of silicon nanowires has a low absorption cross section (Q _abs) [17], which limits the absorption in the wires, a disadvantage that would lower the photocurrent. Cao et al. theoretically showed that the TM₀₁ LMR would have the largest potential to enhance the photocurrent compared to unstructured silicon with the same thickness, at least for certain illumination angles [17]. However, a wire that could use TM₀₁ LMR would require a diameter of around 10 nm, which is experimentally not feasible.

Despite the absorption bands in the MIR, which increase the refractive index of the chitinous setae, the optical nanowire antennas investigated by Cao have a much higher refractive index. Thus, the TM₀₁ LMR of the setae have an even lower Q _abs [4] compared to the nanowires. This turns into an advantage for the thermal emission problem of the ant. The setae cannot be treated as isolated antennas, since the underlying cuticle is an integral part of the body that always plays a role for the optical system of the ant. Thus, a large Q _abs is not necessary for the setae to enhance the outcoupling of the emitted thermal radiation of the cuticle. In this, the ant differs fundamentally from the nanowire antennas, where the substrate does not play an optical role. Therefore, near field heat transfer and near field coupling effects are much more relevant for the ant [9, 20]. For such coupling, the TM₀₁ of the setae is beneficial, because of its larger spatial extension compared to higher order resonances or to TM₀₁ resonances of high refractive index materials like Ge.

In this study, the TM₀₁ LMR was only investigated for angles of emission perpendicular to the setae’s long axis. However, for angles parallel to the long axis Cao et al. [17] experimentally characterized the LMRs of an isotropic nanowire and theoretically showed that there are only minor differences in the low order LMRs for nanowires of round, rectangular, hexagonal, and triangular cross-sectional shapes. The results in [17] show that the absorption cross section Q _abs is largest at normal incidence and decreases at larger angles of incidence. Especially the TM₀₁ resonance strongly decreases beyond 40° to normal incidence and disappears at parallel incidence. The incidence angle on the setae in the setae-cuticle system is limited by the angle of total internal reflection at the cuticle-air surface, which is about 40°; larger angles result in evanescent waves, which lead to parallel incidence on the setae. Since the TM₀₁ resonance of wire shaped objects (including objects with triangular cross sections like the setae of C. bombycina) is not excitable from these angles [17] the respective electric fields can no longer couple to the LMR. Thus, this scenario plays a minor role for the emission enhancement of the ant cuticle. Therefore, we focus on angles of emission perpendicular to the setae’s long axis, thus avoiding expensive 3D-simulations of the complex architecture of the natural setae-cuticle system and still gaining the most important information on its mode of action in the MIR. The LMRs of the triangular setae, illustrated in Figure 5A, are almost cylindrical even near the cuticle. Therefore, the TM₀₁ LMR is excitable over a broad illumination angle and the LMR can radiate into all the seta’s azimuthal angles in free space. Thus, the coupled LMR extends the angle of emission of the ant cuticle. Thereby, the thermal emission of the ant is enhanced by outcoupling of evanescent waves. The TM₀₁ intercoupling of the randomly arranged setae and its coupling to the cuticle causes the system to act like an array of low-Q optical antennas [20] that emit in the MIR and offload thermal radiation, which helps to keep the ant cool.

Figures 5B, C show the higher order resonances (TM₁₁ and TM₂₁). TM₁₁ corresponds well to simulations of triangular nanowires published by [17]. Since higher order resonances like TM₂₁ occur at shorter wavelengths, they are more confined to the seta. Therefore, they cannot couple that efficiently to the cuticle or neighboring setae like lower order resonances. Backscattering effects may occur and therefore the setae become a hinderance for the emitted radiation in these wavelength ranges. This is the reason why the emission depicted in Figures 4B, D decreases in these wavelength ranges compared to the zero-gap situation.

The simulations shown in Figures 4A, B reveal a certain wavenumber range where the near field-coupled TM₀₁ LMR have a lower reflectance than a classical anti-reflection coating. If the peak wavenumber of the Planck radiation at 53°C ( ν ∼ = 640 cm⁻¹) is plotted in the diagram (black dash-dot vertical line), it becomes clear that the reflectance of the TM₀₁ is minimal in that wavenumber range. This increases the emission of a black body at an emission angle perpendicular to the cuticle surface. However, the whole hemispherical emission at 53°C must be considered. This was done by a numerical integration over all angles within direct emission simulations (Figure 7A), where the resulting emission enhancement through the setae coverage for a series of gaps have been meticulously computed. In accordance with Figures 4B, D the maximum of the emission enhancement occurs at a mean gap size larger than 0 µm. The graph in Figure 7A reveals a maximum of the emission enhancement at a mean gap of 0.63 µm. Notably, this gap size aligns very well with the mean of the log-normal distribution derived from experimentally measured distances between setae and cuticle in the prepared cross section (Histogram Figure 3), at (0.68 ± 0.72) µm. The match between the dimensions of the natural system and the gap with highest emission enhancement is a strong indication for an evolutionary adaptation of the setae-cuticle system.

The dependence of the emission on the gap size suggests that it results from the coupling of the setae’s LMR to the cuticle. If this is the case, the trajectory of the curve in Figure 7A should be significantly influenced by variations in setae dimensions as this would shift the resonances and influence their coupling to the cuticle and between each other. Since the setae of C. bombycina are also adapted to reflect incoming sunlight [4–6], their dimensions are playing a crucial role in the visible and ultraviolet (UV) range [4]. Previous investigations have shown that the reflectance in the visible and the UV becomes better if the setae would be larger than their actual size [4]. The ability of the setae to enhance the emission in the MIR could be a possible evolutionary strain for their size restriction. To verify this, simulations of the emission of the setae-cuticle system were also done with varying setae sizes. This was done with a reduced number of simulations and only for a subset of gaps used for the data in Figure 7A to limit the computational effort. In Figure 7B the results of these simulations are summarized together with the curve from Figure 7A. The results indicate that the maximum enhancement for smaller setae (scaling factor = 0.5, blue dotted) would be localized at larger gaps, whereas for larger setae, the local maximum would be achieved at smaller gaps. At setae scaling factors of 2 (purple) and 3 (green) the emission enhancement decreases almost linearly with increasing gap size, similar to an anti-reflection coating, where the maximum of the emission enhancement is located at 0 µm gap size and leaky mode resonances play a minor role. This compellingly suggests that the setae-cuticle system represents an anti-reflection structure in the MIR through nearfield coupling resonant leaky-modes of the setae to the cuticle.

The detailed simulations presented in this paper lead to the conclusion, that the setae enhance the thermal emission of the ant in a more complex way then forming an effective medium. The setae not only form a Mie-resonant structure in the visible [4, 6], but also in the MIR. Thus, they do not only shield the ant from visible and UV-light, but also enhance their ability for radiative cooling. This is crucial for the survival of the animals in their extreme desert habitat, where the body of the ants is heated up by solar radiation and the surrounding sand and air. This heat radiates from the body to the environment. Without setae, the emission angle is limited by the total internal reflection inside the cuticle. This leads to evanescent waves that are trapped inside the body. Through the presence of the setae, these waves can now couple to the first order LMRs of neighboring setae, thereby radiating the energy to the full hemispherical angle range. This leads to a thermal emission enhancement of about 6% compared to the plain cuticle. Varying the setae’s size and their distances to the cuticle in our simulations shows, that the parameters realized by the ant are evolutionary optimized for enhancing the thermal emission. Considering the optical effects of the setae in the visible and UV range shows that dimensions, shape, surface structure, and average distance from the cuticle are evolutionary compromises to fulfill a large variety of functions that help this ant species to survive in its environment.

Although the optical functions described for visible and UV-light would be more efficient with larger setae [4], their actual size might be evolutionary restricted through their ability to enhance their thermal emission. The MIR effects are resonant-based, where the size is crucial and larger setae would become a hinderance for radiative cooling. LMRs in, e.g., nanowires have been shown to be an efficient way to enhance the absorption and the emission of light [7]. Radiative cooling does not require energy and is therefore a promising concept for a number of technical applications in the energy sector [21]. Here we show that a concept of radiative cooling based on near field coupled LMRs is realized in a biological system, which mainly differs from technical applications by consisting of low refractive index materials. Such systems can also combine high reflectance in the visible range with a high emittance in the MIR within a single structure. This type of structure has not been considered yet and might provide inspiration for new ways to use passive radiative cooling as a sustainable energy source.