1. Introduction

Naturally occurring composite materials with ordered, near-wavelength spatial variations in dielectric constant often demonstrate intriguing optical behavior, such as interference-based diffraction and etaloning, focusing, graded-index waveguiding, and beam shaping. In Nature, near-wavelength structural heterogeneity and periodicity provides evolutionary advantages in the form of vivid and often tunable coloration for communication (beetles, birds, butterflies), mimicry and crypsis (chameleons, squid, insects), and sensitive night vision (moths) [1–3]. Understanding the mechanisms governing such phenomena is a vital complement to determining their biological origins, as well as translating and implementing their design principles into technologically relevant venues. Moreover, the rarity of strict tolerances on pattern features and ordering in Nature does not preclude impressive functionality, and in many instances, feature disorder is responsible for a given effect [4]. For instance, patterned absorbers with positional disorder, e.g., reminiscent of biological structures such as butterfly wings, have been shown to enhance wide-angle light absorption in natural and synthetic material systems [5,6] to provide vivid coloration in amorphous colloidal glasses [7,8], and to support isotropic optical band gaps in correlated hyperuniform structures for Fourier-space meta-holography [9–11].

Marine diatoms, often referred to as the “glass menagerie” for their morphological diversity, possess quasi-periodic, siliceous exoskeletal valves known as frustules [12]. These porous, hierarchical structures have garnered decades-long academic interest in implementation and templating for molecular sieves, chemical sensing, heterogeneous catalysis, therapeutics, and photonic elements [13–18]. Many of these applications are best served by refined geometric control over the frustule, as well as coating, augmentation, replacement, or biochemical integration of the patterned siliceous materials with other dielectrics and metals [13,17,19–21]. Unfortunately, evolution and speciation pre-determine the diatom’s composition and structure, and systematically tuning geometric parameters by strategic selection of assorted diatom species is very challenging. Techniques to modify and improve process scaling of diatom-based materials, such as acid-promoted etching, wafer bonding, and fluidic assembly [22,23], have all been attempted, albeit with limited success. Ultimately, the small and curved nature of naturally occurring valves makes them difficult to integrate on-wafer, and the technological utility of any single species’ frustule geometry is likely serendipitous. As such, platforms for scalable and tunable artificial frustule analogues are a complementary and desirable technological goal.

Aside from mediating transmembrane nutrient and waste transport, the diatom’s patterned biosilica exterior has also been found to render useful optical functions, namely UV-scattering and visible-wavelength focusing, to reduce mutagenic irradiation and improve photosynthetic efficiency, respectively [24–26]. Recently, D’Mello et al. modeled the native Nitzschia filiformis frustule as a multi-component photonic circuit and showed significant light-harvesting efficiency in a photosynthetically active wavelength range [27]. Bright coloration and photonic bandgap formation in diatomaceous structures have also been reported in prior work, especially when bio-templating higher refractive index materials in and around them [19,28–30]; however, a systematic exploration of optical behaviors in frustule-like geometries has yet to be conducted with changes in material composition and structure. Herein, we computationally analyze the optical behavior and contributions of the key structural components comprising a perfect 2-D hexagonal pore array as a proxy for the centric diatom frustule lattice, select key configurations of surrounding environment and frustule material composition (i.e., refractive index contrast, Δn), and explore the effect of structural disorder on the resulting optical properties. By emulating naturally occurring geometries in a perfectly ordered, floating thin-film silica hole array membrane, a set of intense, narrowband Fano resonances were identified and attributed to coupling between the guided modes supported by the hole lattice and internal Fabry-Pérot etaloning sustained by the two membrane interfaces. This coupling intensifies in higher index contrast TiO₂ membranes, with near-unity reflectance taking the place of near-perfect transmission for the same geometrical parameters.

The resulting modal behavior revealed above was re-cast in terms of a dimensionless optical path length and a wavelength-normalized lattice period, allowing us to generalize the behavior to any lossless dielectric in the visible-IR wavelength regime. Higher-index nanomembranes were generally found to support tunable broadband reflection and transmission properties, in line with recent investigations of high-contrast gratings in the optoelectronics and photonics fields [31–34]. Finally, perturbing a perfectly ordered hexagonal pore array caused migration of the optical response from intense specular reflection to diffuse, wavelength-coherent scattering, suggesting the emergence of a partial bandgap similar to other correlated, disordered systems [9,10]. To validate these results and transcend the morphogenetic constraints of biotemplating, area-scalable colloidal masking was combined with standard nanofabrication to design and manufacture geometry-tunable, diatom-reminiscent TiO₂ nanomembranes showing distinct and non-iridescent coloration across the visible wavelength range.

2. Materials and methods

2.1 Optical simulations

3D finite-difference time-domain simulations (Ansys Lumerical) were conducted with three main structural layers (top foramen-containing slab, underlayer support, and thin cribrum or substrate material). Simulations were conducted in two specific configurations; for all configurations involving perfect hexagonal order, a single rectangular simulation volume containing two hexagonal unit cells was used, with x- and y-periodic boundary conditions (BCs) and absorbing, perfectly-matched layer (PML) BCs in the z-direction. A broadband white-light plane wave was injected downward onto the structure from the top of the simulation region, with a reflected-light electric field monitor positioned just above it. A transmission monitor was also introduced on the other side of the structure; both R and T monitors were positioned at least 1.5 microns away from the top and bottom interfaces of the structure. Owing to the lossless nature of the oxide materials and media under study in the visible and near-infrared spectral ranges, the reflectance and transmission were empirically observed to sum to near-unity in all considered cases. Accordingly, we have chosen to focus our discussion on only the reflectance and backscattering to illustrate modal behavior. Moreover, while both TE and TM polarizations were used for initial base case validation, it was observed that the modal behavior of all relevant simulations was equivalent under normal-incidence plane wave injection. Therefore, all simulation results shown were conducted with TE-polarized plane wave light sources.

For simulations of disordered surfaces, 72 hexagonal unit cells were used with full PML BCs, with varying degrees of uniformly distributed, random translational offsets in foramen positions from hexagonal lattice points, and/or offsets in pore diameter from an average diameter of 0.65 × (pore spacing). Each scattering result in this configuration was averaged over 3 distinct random configurations and subsequently analyzed with the Lumerical Grating Analysis package to extract specular reflectance and diffuse backscattering. This was achieved by binning angle- and wavelength-dependent power delivered to the far-field hemisphere in 10° polar-angle increments (azimuthally averaged). Effective-medium refractive indices for non-dimensionalization were calculated via the Maxwell-Garnett model, with solid medium permittivity ε_s and void fraction δ_v:

2.2 Nanofabrication

Briefly, a thin film of TiO₂ was sputter-deposited between two layers of sacrificial, low-density silicon deposited via physical vapor deposition on a silicon substrate. A pattern of mm-size square openings was defined via a lithography step, and the substrate was coated with a monolayer of silica nanoparticles. Upon resist stripping, particles were only left in the square regions. The particles were reduced in size with an isotropic plasma etch, whereupon a thin, nickel layer was evaporated over them, creating a hole-array mask. After lifting particles off with sonication, the hole-array pattern was transferred with a highly anisotropic reactive ion etch with a SF₆/O₂ gas mixture. Finally, the metal mask was removed and the sacrificial silicon was removed via a XeF₂ vapor etch. Please refer to Section 3.4 below and prior published work for further details of the nanofabrication process [35].

2.3 Optical characterization

Diffuse reflectance was measured via a solarization-resistant collection fiber positioned approximately 1 cm from the sample and mounted on a customized variable-angle goniometer with fiber-coupled, collimated deuterium-halogen white light illumination (∼300 μm spot diameter). A BaSO₄-coated surface was used as a diffuse scattering reference. Spectra were collected via an Ocean Optics USB2000 + spectrometer. Spectra of the fiber-coupled and Lambertian-scattered light source are provided in Supplement 1 (Ref. [36]).

3. Results and discussion

3.1 Analyzing diatom frustule optics

Centric diatom frustules distinctively feature a single over-arching structural motif of correlated, micron-sized chambers (areolae) and pores (foramina) embedded in a curved biosilica membrane, as shown in micrographs of two representative species, Thalassiosira eccentrica and Coscinodiscus sp., in Fig. 1(a). The exterior of the Coscinodiscus sp. structure (left panels in Fig. 1 (a)) is capped with a fine meshwork of ∼40 nm pores known as the cribellum, immediately followed by a perforated layer containing 200 nm diameter pores known as the cribrum. Finally, at the opposite interface of each areola is a foramen, roughly 1150 nm in diameter, facing into the diatom’s interior, that is clearly visible in the SEM images shown. FFT insets of this correlated pore structure reveal isotropic, highly correlated global order and even approach crystalline order in isolated sections of the frustule. In the case of T. eccentrica, the exterior valve surface contains foramina with diameters of roughly 850 nm arranged in a quasi-ordered hexagonal array that conforms to the spacing of the underlying wall support. The lower valve layer (cribrum) contains an ensemble of fine, hexagonally arranged nanometer-sized pores approximately 40 nm in diameter [37]. In the present work, we focus our discussion on the T. eccentrica structure given its slightly simpler constituent geometry relative to Coscinodiscus sp., a slightly more cylindrical areolar profile, and more well-defined, planar silica slab regions near the top and bottom interfaces of the entire membrane.

 

Fig. 1. (a) Scanning electron micrographs of the interior surface of Coscinodiscus sp. (left) and exterior surface of Thalassiosira eccentrica (right) diatom frustules. The scale bar in the Coscinodiscus image is a best-faith approximation, and corresponding insets are two-dimensional Fourier transforms of the images. Left images are adapted from [37], and right images are reproduced from [20] with permission. (b) Schematic depiction and optical simulation configuration of a supported, perfectly periodic slab with pore spacing p, pore radius r₁, thickness t, underlayer support thickness h, and underlayer pore radius r₂, approximating the structure in (a).

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To clearly identify fundamental optical resonances and pragmatically assign interactions with visible and infrared light, several idealized simplifications were made to the natural morphology of the T. eccentrica frustule, which is shown in Fig. 1(b). First, we assume the areolar arrangement is perfectly ordered on a lattice with a characteristic period, p, and foramina are modeled as air cylinders of radius r₁ embedded in a slab of thickness t. Second, given that the cribrum has a low void fraction with feature periodicity (40 nm) that is significantly smaller than visible wavelengths (350-750 nm), and that patterns are localized to minority regions within an otherwise solid layer, the cribrum layer was simplified to a thin, solid biosilica slab. The interior supporting walls in the intermediate layer (of thickness h, areolar radius r₂) are also air cylinders made distinguishably wider than the foramina-containing top layer, as illustrated in the SEM image. We also neglect the gradual curvature of the frustule (with the radius of curvature greatly exceeding both p and t) and additional scattering events by other cellular components as light propagates within the diatom. The finite difference time domain (FDTD) simulation configuration employed for perfectly ordered frustules is also shown in Fig. 1(b), highlighting the stacked reflectance monitor and downward-injecting plane wave source onto a single diatom unit cell.

FDTD optical simulations (Lumerical) were conducted on an idealized diatom frustule comprised entirely of silica in an air environment, as well as on selected portions of the structure to elucidate modal contributions by comparing normal-incidence reflectance spectra. The specific geometry used in calculating optical response was chosen to approach naturally occurring T. eccentrica frustules, and is as follows: p = 950 nm (actual p for T. eccentrica is 1.2 μm), r₁ = 310 nm, r₂ = 380 nm, t = 400 nm, h = 500 nm. The “lower” slab comprising the cribrum was set to a constant 50-nm thickness. Results of these simulations are shown in Fig. 2. Starting with the spectrum of an isolated foramen-containing silica slab in air (panel (a), dashed blue), additional auxiliary components are sequentially added or replaced, modifying the optical response. The single-slab spectrum is quite simple, displaying one prominent reflection mode at ∼920 nm, which approaches p. Evidently, the upper and lower slabs do not appreciably interact (panel (a), orange curve, fine dashes), with reflectance curve overlays highlighting the negligible modification of the original spectrum, in part owing to the thinness of the lower plate relative to the wavelength range considered. Introducing the areolar supports instead of the cribrum (panel (b), dashed green curve) modifies the prominent 920-nm mode, shifting the central mode to ∼850 nm and lowering its reflectance slightly, presumably by enhancing transmission (aided by minimal visible-light absorption in silica). Two sharp, lower-intensity side modes remain around the original mode wavelength observed in the isolated slab, once again clustering in the near-infrared region, presumably dictated by p. The fully assembled frustule structure (panel (c), solid red) is a hybrid of the previous two cases, intensifying the two side modes but also recovering and red-shifting the original prominent mode sustained by the top frustule layer, settling at 880 nm.

 

Fig. 2. (a-c) Normal-incidence reflectance curves of a deconstructed, perfectly periodic diatom frustule in air, starting with an isolated top frustule slab in panel (a) (blue, coarse dashes) and sequentially added auxiliary frustule components. (d) Approximate T. eccentrica frustule geometry (p = 950 nm, r₁ = 310 nm, r₂ = 380 nm, t = 400 nm, h = 500 nm) modeled with three scenarios: in water, dried in air, and dried with top layer replaced by TiO₂. (e) Electric field enhancement maps for the three configurations in (d), sampled at λ = 550 nm and a second, highly resonant wavelength for each configuration. For clarity and contrast, the color maps are re-scaled commensurately with increasing field confinements.

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Having identified the importance of the foramina-containing layer in the frustule’s normal-incidence optical response, one might wonder what would occur with an increase in the refractive index contrast of the structure (Δn). Three cursory combinations of surrounding environment and top slab layer material were thus simulated, with increasing Δn: water-silica (live diatom frustule), air-silica (dried frustule), and air-TiO₂ (biomimetic construct). The full frustule geometry was initialized with a fixed SiO₂ underlayer structure below the top slab, yielding reflectance spectra and cross-sectional electric field (|E/E₀|²) maps that are shown in Figs. 2(d,e). Owing to the relatively low refractive index contrast between the exoskeleton and cytoplasm/surrounding water (Δn ≤ 0.1), the live-diatom case shows little to no reflectance across the wavelength range considered. This is also evidenced by the incoupling and weak confinement of the incident electric field within the structure, and significant down-welling of the electric field is observed at 550 nm. This is likely beneficial to the diatom, enabling efficient transit and overlap of photosynthetically useful light with photoactive harvesting organelles in its interior. As identified in the discussion above, the dried frustule (Δn ≈ 0.4) supports several intense, narrow-band resonances that prominently emerge from a low-intensity, gradually varying spectral background. Finally, in the case of the silica-supported TiO₂ membrane surrounded by air (Δn ≈ 1.3), a rich modal resonance profile emerges, surpassing the silica-air configuration in intensity and breadth. Most remarkably, a broader, high-intensity (>98% R) asymmetric mode emerges at 1140 nm, compared to near-zero % R in the analogous air-silica case. The corresponding |E/E₀|² map suggests the mode originates from intense field confinement within the frustule foramina. Further, the field distribution inside the TiO₂ layer at 550 nm indicates confinement of secondary, higher-order thin-film resonant modes.

3.2 Generalizing effects of frustule geometry on optical behavior

Sharp, well-defined optical resonances are highly sensitive to the geometry that sustains them; given the intense modal response of the foramen-containing layer shown in Fig. 2, changing the layer’s thickness, t, is expected to significantly modulate optical behavior. Figure 3 shows the evolution of spectrally resolved normal-incidence reflectance with changing thickness in the top, foramen-containing layer (p = 550 and 950 nm, constant r₁/p ratio of 0.325) for the three configurations depicted in Fig. 2. In the present case, one might also expect significant changes in optical properties with a change in the pitch, p. We note that the p = 550 nm case departs from any naturally occurring diatom morphology. A set of broad, low-intensity resonances that vary linearly with top layer thickness can be discerned (yellow dash-dots), which comprise the thin-film interference background sustained by the top and bottom interface of the foramen-containing upper slab. For a given slab thickness (t) and homogeneous wavelength-dependent effective index (n_eff), the peak locations, λ_FP, of thin-film Fabry-Pérot reflected orders (j) at normal incidence (i.e., with incident k-vector k_z,m at grating order m = 0) can be obtained with the following resonance condition:

The Fabry-Pérot background is barely discernible in the live-diatom case; however, as the refractive index contrast increases, the index mismatch at the interface between the supporting wall and top slab causes the thin-film interference fringes to intensify. In the silica-air case (panels (b) and (e)), narrow, intense, and single modes appear to overlap or displace these fringes, and reverse polarity with changing thickness. Moreover, the wavelengths around which these dramatic reflectance oscillations occur scale roughly with the characteristic areolar pitch p. These are in fact isolated, uncoupled Fano resonances that exist, one at a time, within the structure. In the TiO₂-air configuration, increasing vertical electric field confinement allows two Fano modes of opposite polarities to couple and interact, introducing a warped “checkerboard” pattern. This type of resonant behavior has been noted in optoelectronic and photonics literature with photonic-crystal membranes or high-contrast gratings that have a near-wavelength, periodic, and unusually high refractive index profile [30–33]. Hence, strong thin-film interference (vertical confinement) couples to two resonant waveguide modes, adding strong lateral confinement within the high-index (TiO₂) and low-index (air) regions of the structure. Strategic choice of material thickness tunes the phase difference of light propagating in the two media to yield coherent, nearly perfect reflection (or transmission) at normal incidence for a broader set of design wavelengths [30–33].

 

Fig. 3. (a-f) Normal-incidence reflectance contour maps for naturally occurring frustule structures (areolar spacing, p = 550 nm (a-c) and 950 nm (d-f)) with increasing foramen layer thickness in (a,d) water and (b,e) air, as well as (c,f) a silica-supported TiO₂ slab layer in air. Yellow dashed lines represent Fabry-Pérot resonance orders. White dashed lines and stars represent the top slab thicknesses (400 nm) and mode locations sampled for the electric field maps shown in Fig. 2, respectively. (g) Rescaled versions of (c) and (f) are recapitulated in dimensionless form, showing the similarity of the two reflectance landscapes despite different areolar spacing.

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Given the fundamental role of geometry in the aforementioned optical behaviors, key structural features were tuned and then normalized to generalize and inform wavelength-independent design. For phenomena involving thin-film interference, we introduce an effective optical path length, given by the product of t and n_eff. Whereas thickness influences thin-film interference, the lateral period p determines the energies of the discrete, Bloch-like modes present and informs the wavelength-dependent phase behavior; accordingly, the optical path length was normalized by p. The wavelength axis was also normalized by the period to yield a fully dimensionless parameter space. These spaces are depicted in Fig. 3(g) for the p = 550 and 950 nm TiO₂-air reflectance contour maps. While the exact modal locations and intensity profiles differ, the sharp Fano-resonant delineations and Fabry-Pérot fringes of the two maps readily align in the dimensionless reflectance landscape. In essence, this construction represents the phase offset of the few low-order propagating modes in the structure and highlights the regime where perfect transmission and reflection are broadest (highest constructive and destructive interference, respectively). Assuming one operates within the regime of low absorption loss, the resulting parameters aid in informing and engineering modally specific optical responses in ordered frustule-like structures of any size.

3.3 Disorder-mediated, non-iridescent color

Diatom valves are believed to form via the delivery and aggregation of siliceous macromolecules mineralized in the interstitial space between pore-forming proteins enclosed by a vesicle, after which the valves are extruded to the diatom’s exterior [12,21,39]. As seen via microscopy, this delicate process will likely stray from (and perhaps advantageously avoid) perfect hexagonal order when subjected to the perturbations of hydrodynamic, interfacial, and chemical forces in the cellular environment. Several primary, foreseeable perturbations can be captured in the form of diameter polydispersity (distributed r₁, r₂) and unequal areolar spacings (broad distribution of p), both of which can be observed in the SEMs shown in Fig. 1. To probe the effect of this type of disorder on the optical behavior of our set of simplified, perfectly ordered models, the simulation size was expanded to 72 unit cells. The two disorder types were allowed to each act independently, and then simultaneously. Figure 4 shows reflectance contour maps for the silica-air and TiO₂-air configurations from above with p = 550 nm, and varying slab thickness for five different cases: (a) perfectly ordered top slab, (b) ordered, full structure, (c) pore (diameter) polydispersity (PD) only, (d) translational offset only (i.e., imperfect hexagonal lattice), and (e) both pore PD and translational offset. Translational offset of pores in the top slab was also extended coaxially into the intermediate areolar support.

 

Fig. 4. Effects of structural disorder in frustule-like nanostructures on optical response. Paired normal-incidence reflectance contour maps of a diatom frustule are shown, with a variable-thickness top slab comprised of SiO₂ (left panels) and TiO₂ (right panels). Maps are presented for the (a) perfectly ordered floating slab, (b) perfectly ordered full frustule, (c) full frustule exhibiting up to a 15% hole diameter polydispersity (PD), (d) translational pore displacement (up to 10% of the lattice pitch), and (e) combined translational hole offset and PD cases. Lowest-order Fano contours are represented by dashed yellow outlines. Shaded, semi-transparent white areas in the disordered frustule plots depict total diffuse (off-normal) backscattering, binarized with intensity thresholds to best depict the spectral scattering profile (thresholds of 9% and 27% of incident source power for SiO₂ and TiO₂, respectively).

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The floating slab in (a) exhibits exclusively normal-incident, Fano-resonant behavior, as the changing thin-film interference background from the slab layer (only the first two FP orders are well shown) couples to guided modes set by the pore spacing (single-mode in the case of SiO₂, multi-mode in the TiO₂ case). By outlining the first several Fano resonance orders with dashed yellow contours, we track their modification and evolution with added disorder. Upon introducing the silica support under the SiO₂ slab (panel (b), left color map), a second Fabry-Pérot background emerges, and the low-order Fano resonance at ∼550 nm is repartitioned into finer modal structure as a result. A similar repartitioning also occurs with the TiO₂ slab in the 500-600 nm range, where both regions of previously broad, high-reflectance behavior are now truncated and de-tuned; this is most evident at a top slab thickness of 200 nm.

The effects of pore diameter disorder on optical behavior were evaluated by spectrally resolving both normal-incident specular reflection and total diffuse backscattering. Diffuse scattering responses were overlaid onto the specular reflectance by binarizing the response and making it semi-transparent atop the existing specular color map (hence the darker and lighter regions in the red/blue contours), where the reflectance color scale remains the same. As seen in Fig. 4(c), perturbing only the pore diameter distribution barely affected the normal-incident modal profile and intensity, with some minor off-axis scattering visible to the left of the delineated Fano modes (between 400-500 nm) in thinner slabs. A more striking change to the spectral landscape occurs when translational pore disorder (uniformly random, up to 10% of the lattice pitch) is introduced, yielding a significant reduction in specular reflectance. In contrast to the exclusively specular and diffractive response of the perfect grating structure, intense wavelength-specific diffuse backscattering was observed. In the all-silica case, backscattering occurs primarily in the UV/blue wavelength range and is relatively weak, comprising less than 10% of the wavelength-resolved source power. In the TiO₂ case, the scattering intensity increases by more than threefold, and occurs at the crossing of Fano-resonant contours at 475-525 nm and 640 nm. We conclude that the two sets of adjacent, interacting Fano resonances that gave rise to broadband reflectance within the perfectly ordered TiO₂ slab decouple due to hole disorder. Accordingly, the diffuse scattering is spectrally located at the centroids of each of the two modes, arising from a distribution of local resonant phase differences between neighboring quasi-ordered unit cells that lose coherence with each other in the near-field, and thus radiate over a wide angular range into the far field. Notably, the lowest-order Fano modal crossings in high-reflectance contours mark the points of maximum backscattering intensity.

Surprisingly, a combination of translational pore offset and diameter polydispersity (panel (e)) appeared to have less impact on specular reflectance intensity than translational offset alone. While less pronounced overall, the diffuse scattering originates at similar mode locations to those in panel (d). Moreover, translational offset appears to be the more dominant contributor to diffuse scattering intensity (see Figure S1 in Supplement 1 for simulated scattering intensity versus the degree of disorder in both SiO₂ and TiO₂ structures).

Given this emergent diffuse scattering behavior, our above efforts to non-dimensionalize perfectly ordered frustule optics also aids in designing diffuse scattering of any color. In particular, the dimensionless coordinates that maximize structural color near the target design wavelength (i.e., low-order Fano contour crossing) are at $\left\{ {\frac{\lambda }{p},\frac{{t{n_{eff}}(\lambda )}}{p}} \right\} \approx {\; }\{{1.2,{\; }0.65} \}$. Thus, for a TiO₂ diatom slab layer to appear a vivid green color (λ_peak ≈ 530 nm), we would select a pitch of $p = \frac{\lambda }{{1.2}} = 442$ nm and a thickness of $t = \frac{{0.65\cdot p}}{{{n_{eff}}({\lambda \; = \; 530\; nm} )}} \approx $ 160 nm. Longer-wavelength, non-iridescent structural color (e.g., yellow, orange, and red) is unique and rarely observed in nature, owing to high-order resonances which overwhelm or detract from color saturation of the contributing low-order modes [8,38]. The system considered here is no exception; the designed slabs sustain broadband reflection by coupling two or more Fano modes, one of which augments the color rendering of the other. Possible routes to selectively suppress the high-order mode can involve the presence of absorbing materials, and/or strategically allowing multiple scattering events within the structure [40]. Finally, it is worth noting that the exact parameters for a given wavelength also depend on the ratio of hole diameter to lattice spacing (or duty cycle, DC), which was set at a constant of 0.65 for this study. Varying the DC tunes the effective refractive index within the top frustule slab, bringing additional changes in bandwidth and modal position. In perfect hole arrays, increasing air fraction has been observed to narrow and blueshift the broad reflectance behavior featured here (see Fig. S2 in Supplement 1 for DC-dependent reflectance behavior); however, higher-DC structures become less straightforward to fabricate due to shrinking critical dimensions, and any resulting resonances are therefore prone to greater variability through lower fabrication tolerances.

3.4 Synthetic, frustule-like TiO₂ membranes

To validate the design principles described above, a fabrication process for synthetic diatom analogues was realized. Colloidal particle monolayers and vacuum thin-film deposition were used in place of pore-directing proteins and silica-forming vesicles to create specific structure patterns and thickness dimensions. The full fabrication procedure for these structures can be found in prior work [35]; briefly, diatom-inspired TiO₂ frustules were fabricated by dip-coating a jammed colloidal monolayer onto a photoresist-masked, multi-layer dielectric stack, shadow deposition of a metal mask, and reactive-ion etching, followed by XeF₂ vapor exposure to clear the sacrificial silicon surrounding the oxide materials. Three TiO₂ diatom-like surfaces were fabricated with average pitches of 404, 507, and 690 nm (duty cycles of 0.59, 0.72, and 0.75, respectively) and were supported by a porous Si/SiO₂ underlayer. TiO₂ layer thicknesses were scaled with the pitch to maintain a near-constant optical path length for all design wavelengths (t = 132, 180, and 235 nm, respectively) by consulting the dimensionless plots generated above (cf. Figure 3(g)). Figure 5 shows an abridged process schematic, as well as imaging and optical characterization of the resulting structures.

 

Fig. 5. (a) Abridged processing schematic for diatom frustule-inspired TiO₂ membranes, based on colloidal dip-coating and size reduction, metal mask deposition, pattern transfer, and XeF₂ vapor etching. (b) Characterization and simulation of the designed and fabricated TiO₂ diatom-inspired membranes. Scanning electron micrographs and corresponding 2D Fourier transforms of the low-magnification images, high-magnification images, and photographs of each surface are shown. Experimentally measured diffuse reflectance spectra are plotted for normal-incidence illumination and variable-angle collection (40-80° off-normal), along with computed scattering spectra for 45° collection in dashed black. Color swatches represent apparent color from the measured spectra, calculated by mapping to the CIE XYZ color space. Curves are offset for clarity.

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Morphological similarity of synthetic TiO₂ frustules with diatom frustules was assessed with scanning electron micrographs, which revealed a highly correlated pore structure in the TiO₂ layer, and corroborated by radially symmetric, sharply concentric 2D Fourier projections of the high-resolution, low-magnification images. Magnified and cross-sectional SEMs reveal sharply defined pores and thin underlying supporting walls (see Figure S3), resembling those found in centric diatoms. The relationship between disorder and off-axis scattering is well illustrated by the distinctly sharper FFT profile of the yellow (p = 507 nm) surface, and correspondingly lower peak scattering intensity (∼5% of source power) relative to the other two surfaces (20-30%). Surfaces with increasing pitch appeared light blue, yellow, and red-orange, respectively, with the apparent color nearly invariant to viewing angle. Angle-resolved scattering measurements (with corresponding CIE color-mapped swatches above each curve) were performed at normal-incidence illumination to confirm non-iridescence; minimal shifts of the scattering peaks contributing to apparent color were observed, further highlighting the precision of their Fano-derived modal origins.

Simulated scattering spectra (black dashes, normal-incidence illumination, 45° collection) were found to be in excellent agreement with experimental measurements. Top-view and cross-sectional SEM imaging informed the precise structural parameters of each sample (thickness, duty cycle, underlayer air fraction, degree of disorder), which were input as simulation parameters to predict optical response. Simulations determined that a nontrivial amount of residual silicon was present in the underlayer of the 507- and 690-nm samples, which suppressed the high-order Fano mode and improved color saturation [8,40]. The 404-nm sample was especially devoid of sacrificial Si remnants, which allowed the higher-order Fano mode to feature prominently at ∼400 nm in the diffuse reflectance spectrum.

Extending the diatom’s structural motifs to unnaturally high index contrasts provides exciting opportunities for further applied and fundamental optical studies, especially in the venue of tailoring disorder to further understand and control the spatial and spectral properties of light propagation. For instance, one may envision further increasing pattern disorder without compromising field confinement, allowing access to the weak and strong (Anderson) localization regimes, wherein optical modes can yield incredibly high Q-factors [41–43]. Moreover, emissive high-index materials such as III-V semiconductors could benefit from disordered structuring with improvements in extracting spontaneous emission or enhanced local |E|² confinement for lasing [43].

4. Conclusion

We have explored the optical behavior of approximated centric diatom frustules and their synthetic analogues, specifically demonstrating that rich optical modalities can be obtained for refractive index contrasts that are inaccessible to diatoms via natural biochemical processes. In doing so, we have highlighted a wavelength-tunable platform for broadband reflection, transmission, and, through introduction of geometric disorder, non-iridescent color. Informed by these findings, the TiO₂ structures we designed and fabricated showed angle-independent, saturated coloration that aligned favorably with computationally outlined modal contours. The saturation and color purity of yellow- and red-appearing surfaces were aided by the residual Si material in the supporting underlayer, which suppressed high-order Fano modes. Through simple changes in colloid size and processing, we have shown the possibility of transcending the morphogenetic constraints on pore and structure geometries of particular diatom species. Moreover, accessing a wider palette of constituent materials promises to extend diatom-inspired photonics to many other venues, e.g., photocatalysis, sensing, and optoelectronics, as well as exotic epsilon near-zero phenomena, nonlinear optics, and meta-optics.