Three-dimensional nanophotonics with spatially modulated optical properties

Implosion fabrication: 3D nanoprinting

The nanofabrication process we present in this paper, ImpFab, is depicted in Fig. 1. The approach combines top-down lithography for full control of the geometry, and bottom-up nanoparticle conjugation for the deposition and growth of various materials^28,29. A hydrogel scaffold serves as both the 3D matrix for the incorporation of functional materials, and as a scalable structure, capable of expansion and shrinkage, facilitating the achievement of truly nanoscale (~ 50 nm) features²⁸.

The process begins with the preparation of the hydrogel composed of a solution of sodium acrylate, acrylamide, and bisacrylamide²⁸. Weight concentrations of each component are optimized for a volume shrink ratio of 1000 x (10 x per side). The gel is then washed in water (dH₂O) to reach full expansion. Subsequently, the gel is immersed in a solution containing fluorescent Sulfo-Cyanine3 Amine (Cy3) dyes (250 μM) for 1 h, ensuring full diffusion of dyes throughout the porous hydrogel, see Fig. 1a. Next, a laser scanning microscope is employed to selectively photo-activate a chemical binding between the fluorescent dyes and the hydrogel backbone. Infiltrated dye molecules within the laser beam voxel (highest intensity volume) are covalently bound to the polymer matrix by two-photon excitation: see inset of Fig. 1a. Additional information about the photopatterning system can be found in the Supplementary Information Section S3. Upon completion of the patterning process, the gel is thoroughly washed in water to remove the unexposed dyes, leaving behind the optically patterned 3D structure composed of the fluorescent molecules with a functional group. We then proceed with a series of molecule-nanoparticle nanoconjugation steps to introduce desired optical functionality.

In the following, we describe the process for silver nanoparticles²⁸. This procedure can be generalized to a much greater library of materials of interest, including quantum materials, oxides, diamond, upconversion materials, and semiconductors²⁹. The gel is first washed in a solution of 100 μM N-hydroxysuccinimido biotin (NHS-Biotin) molecules, and subsequently immersed for > 8 h in a solution of streptavidin-fluoronanogold particles, see Fig. 1b. After each chemical process, the gel is thoroughly washed in deionized water (dH₂O) to minimize unintended particles in the gel background. After a wash in 50 mM ethylenediaminetetraacetic acid disodium salt dihydrate (EDTA) for 30 min, we follow with silver intensification through an oxidation-reduction reaction at the gold nucleation sites, see Fig. 1c. In addition to dH₂O, the gel is washed in 50 mM sodium citrate for 1 h. Finally, the gel is subjected to a controlled shrinking process, during which the embedded structures undergo an isotropic volumetric reduction, leading to the formation of the final 3D heterostructure with nanoscale features, see Fig. 1d. For the shrinking process, the gel is washed in a two-step salt solution of 0.1 M magnesium dichloride (MgCl₂) and 0.1 M calcium chloride (CaCl₂), each for about 20 min.

To experimentally validate the structural controllability and optical performance, we fabricated silver diffraction gratings with groove periods ranging from 520 nm to 1700 nm. Figure 2a shows an optical microscopy image of a representative grating with a period of 850 nm. Optical characterization using a custom-built Fourier microscopy system revealed distinct first-order diffraction under narrow-band illumination, as shown in inset of Fig. 2a. The measured diffraction angles closely match the expected theoretical predictions, confirming both the accuracy of the patterned periodicity and the isotropic shrinking process. Further details on the structural integrity and process optimization can be found in the Supplementary Information Sections S1 and S2.

The method described above offers unprecedented design freedom and material versatility²⁸, enabling the creation of complex 3D photonic devices for a wide range of applications. In particular, incorporating fluorescent dyes and metallic particles in combined structures enables the introduction of gain and lossy elements, an essential aspect of non-Hermitian photonics.

Modulated optical properties

We first demonstrate how the optical properties of the printed structures can be modulated through variations in printing parameters. We printed embedded square patches with an approximate thickness of 20 μm under different settings of laser power and scan speed. The left panel of Fig. 3a shows a fluorescence image of the hydrogels post-printing, where a clear gradient in the patterned molecule density can be identified. The activation of chromophores is maximized with increased laser energy, which is directly proportional to the laser power and printing dwell time. This correlation is translated to the silver density of the final structure, as observed by the pronounced contrast in the right panel of Fig. 3a, showing a wide-field microscope transmission image of the gel. This underscores our control over the optical properties of silver through adjustment of the printing parameters. Scanning electron microscopy (SEM), shown in Fig. 3b, revealed densely packed and interconnected gold nanoparticles, indicating efficient chromophore activation and uniform material deposition within the patterned regions.

A quantitative characterization of the final silver composition is obtained by reflection and transmission spectroscopy. To facilitate the characterization of the material properties, we printed a set of silver patches at the gel surface, exposing the silver-air interface. To ensure adequate area coverage, we printed four square patterns adjacent to one another (a visible stitch can be observed in the inset of Fig. 4a). The reflectivity was measured using a custom Fourier space microscope system. Figure 4a shows the measured absolute reflectivity of the printed silver under normal incidence across the visible spectrum, at its highest density. A mean absolute reflectivity of about 33% is measured, in contrast to the roughly 90% reflectivity of bulk silver. Using the expression for the normal reflection at an interface R = ∣(1 − n_eff)/(1 + n_eff)∣², we can estimate the effective refractive index of the printed silver as n_eff = 3.697 + 0.126i at a wavelength of 532 nm.

Furthermore, we can identify the volume fraction of silver in the fabricated devices by applying the Maxwell-Garnett effective medium model³⁰. This model describes the effective permittivity of a dielectric material with metallic inclusions using the formula ε_eff = ε_g[ε_g + 1 + 2f/3(ε_s − ε_g)]/[ε_g + 1 − f/3(ε_s − ε_g)]. Here, ε_g and ε_s are the bulk permittivities of the gel and silver, respectively, and f denotes the volume fraction of the silver particles. We find a volume fraction of f = 0.39, which suggests that a slightly higher volume fraction (up to ~ 0.74), and therefore reflectivity, is possible.

Additionally, Fig. 4b shows the measured relative reflectivity of square patches printed with different laser energies (60 nJ to 190 nJ), corresponding to laser power (75−120 mW) and scanning speeds (15−30 mm/s). The optical reflection is clearly affected by the printing energy, which allows us to control the relative reflection down to ~40%.

For low densities, losses become low enough to measure an appreciable transmission. Figure 4b shows the transmission for a low-density silver patch. A clear Fabry-Pérot interference pattern emerges from the silver thin-film. We estimate the effective index of the low-density silver for a narrowband spectral width \(T={(1-R)}^{2}/[{(1-R)}^{2}+4R{\sin }^{2}(\delta /2)]\exp (-\alpha {L}_{\mathrm{fi}lm})\), where \(R=[{({n}_{{\rm{gel}}}-{n}_{\mathrm{fi}lm})}^{2}+{k}_{\mathrm{fi}lm}^{2}]/[{({n}_{{\rm{gel}}}+{n}_{\mathrm{fi}lm})}^{2}+{k}_{\mathrm{fi}lm}^{2}]\) is the Fresnel reflection, δ/2 = ω/c₀n_filmL_film is the accumulated phase shift, α = 4πk_film/λ is the absorption coefficient, λ is the wavelength, L_film the silver patch thickness, c₀ the speed of light in vacuum, n_gel = 1.35 the gel index, and n_eff = n_film + ik_film the thin film complex index of refraction. Fitting for the index and thickness, we find n_eff = 2.14 + i0.0009 for a film thickness L_film = 21 μm. Having characterized the basic optical properties of nanomaterials fabricated with ImpFab, we now turn our attention to the realization of nanophotonic devices.

2D and 3D photonic crystals

In this section, we show how ImpFab can realize 2D and 3D photonic crystals formed by silver meta-atoms with various crystal lattices. Figures 5 and 6 show the fluorescence and optical microscope images of fabricated photonic crystals, alongside their corresponding diffraction patterns. The diffraction measurements were performed under narrow-band illumination at 520 nm, derived from a spectrally filtered supercontinuum laser.

Figure 5a left panel shows the fluorescence image of a fabricated 2D photonic crystal with square lattice, with periodicity a = 700 nm and width 0.5 a. The inset of Fig. 5a shows a bright field microscope image of a crystal structure consisting of silver cubes arranged in a lattice with periodicity a = 2.4 μm and width 0.4 a. The corresponding diffraction pattern is shown in the right panel of Fig. 5a, demonstrating a clear fourfold symmetry. This symmetry reflects the equidistant arrangement of meta-atoms along two perpendicular axes in the lattice. Diffraction peaks manifest at locations corresponding to the reciprocal lattice vectors, affirming the characteristic periodicity and integrity of the square lattice structure. The three-dimensional body-centered cubic (bcc) crystal shown in Fig. 5b yields a similar diffraction pattern, stemming from its three-dimensional nature and the specific meta-atom arrangement of the bcc structure. The right panel of Fig. 5b shows the diffraction pattern projected along the [001] plane.

Figure 6a shows a single-layer hexagonal lattice, displaying a sixfold symmetry in its diffraction pattern. This pattern offers a direct visualization of the inherent hexagonal arrangement of the meta-atoms within the lattice structure. The ImpFab method’s versatility and precision make it possible to create more complex structures such as twisted bilayer hexagonal “moiré” crystals. This is achieved by printing a stack of two separate hexagonal lattices with a twist angle. The interference of the two twisted layers effectively introduces a new length scale into the system, the moiré wavelength, giving rise to a larger superlattice moiré structure, seen in Fig. 6b. The moiré wavelength³¹ can be expressed as Λ_m = a/[2sin(θ/2)], where a is the lattice period and θ_m is the relative rotation between layers. The interaction between layers provides opportunities for complex band engineering, such as photonic flat bands³², as well as strong light localization and chirality^10,33.

The realized structure, shown in Fig. 6b, has a twist angle θ_m = 30^∘, a = 20 μm and z spacing of ~1 μm, resulting in a moiré wavelength of approximately Λ_m = 8.7 μm. For this angle, an intriguing phenomenon is observed: the diffraction pattern displays a twelve-fold symmetry, analogous to quasicrystals, materials known for their unique diffraction patterns and lack of periodicity^34,35. This is in stark contrast to the single layer shown in 6a. The additional Bragg peaks in the diffraction pattern originate from the second twisted layer and are positioned according to the inverse of the moiré wavelength, yielding the observed twelve-fold symmetry. The emergence of this quasicrystalline-like diffraction pattern from a bilayer system with crystalline layers demonstrates the fascinating possibilities presented by the control and manipulation of layered nanophotonic structures¹⁰.

Quasicrystals

Quasicrystals lack periodicity but do exhibit long-range orientational order. This unique property of quasicrystals, marked by non-repetitive patterns that still maintain a certain degree of order, poses a challenge for most conventional 3D fabrication techniques. However, ImpFab, with its nanoscale precision and flexibility of 3D structure and material density, is well-equipped to handle such complexity.

Figure 7 shows an optical Penrose quasicrystal, a canonical example of a 2D quasicrystal, consisting of an aperiodic two-tiling structure exhibiting fivefold rotational symmetry. Silver meta-atoms of distinct densities were placed at the center of each of the two tiles, as illustrated in the inset of Fig. 7. This serves as an example of an optical structure assembled from constituents with precisely controlled loss. In future experiments, using an optically patterned fluorescent dye, one could pump the dye to obtain gain within the same structure. By printing two sets of dyes, one set can be used as gain, while the other, with an overlapping spectral profile can be used as loss, effectively creating a non-Hermitian optical structure.

Figure 8 shows 2D projections of a fabricated 3D icosahedral quasicrystal along different symmetry axes (two- and five-fold), with characteristic spacing a = 1.4 μm and width 0.5 a. Such noncrystallographic symmetries naturally arise from the interpretation of quasicrystals as projections of higher-dimensional cubic lattices onto irrationally oriented hyperplanes, known as the cut-and-project method^36,37. The Penrose and icosahedral quasicrystals are projections from 5D and 6D cubic lattices onto 2D and 3D, respectively, with orientations related to the golden ratio, which introduces the fivefold rotational symmetry. Constraints in our printing system resulted in a periodic z-layer stack, necessitating artificial compression of the 3D fluorescence image along z to discern the symmetry patterns more efficiently.