Colloids are simply particles [1–12]. More specifically, the term colloid refers to particles within a fluid that can disperse well without settling due to gravity. Colloidal suspension denotes a fluid in which these colloidal particles are well dispersed. Traditionally, the fields of optics and photonics overall have been less interested in soft matter like colloids and colloidal suspensions for the development of optical and photonic structures (henceforth collectively referred to as soft manufacturing) [13–20]. Instead these fields have predominantly relied on top-down manufacturing, precisely developing structures from hard materials like polymers, metals, metal oxides, and semiconductors through lithography [21–58] This aligns well with the pursuit of theoretical blueprinting and experimental testing of predictable physical phenomena from precisely defined structures, which characterizes the main research streams of modern optics and photonics. In contrast, colloids are materials randomly dispersed within a fluid; structuring them into precisely controlled geometries and patterns is achievable only through self-assembly, which is an error-prone manufacturing method [2, 14, 18, 59–61]. Typically, self-assembled structures of soft matter intrinsically possess undesired structural complexity and defects. As a result, such unconventional soft manufacturing has not aligned well with the traditional academic and practical pursuits of optics and photonics mentioned above.

However, Michael Faraday (a renowned physicist in the fields of electromagnetism, optics and photonics) surprisingly focused on the optical properties (reddish color) of colloidal gold nanoparticles (Au NPs) [62] dispersed in a solution and elucidated the underpinning mechanism (Mie scattering). Moreover, plasmonics (a significant part of nanophotonics) demonstrated how colloidal Au NPs painted onto the surface of ancient Roman Lycurgus cups could induce wavelength-selective scattering, and the resultant color [63]. Similarly, stained glass windows in medieval cathedrals used metallic colloids to induce visible-light scattering, therefore maintaining their vibrant colors for a long period, because such color depends on the scattering by colloids rather than the intrinsic absorption of molecules such as organic dyes [64, 65]. This old knowledge of scattering-based color due to NPs laid the foundation for modern mass production and utilization of paint.

While their undesired structural complexity and defects has diluted academic interest in colloids concerning modern optics and photonics, their practical utility has greatly exceeded that of lithographic structures, permeating both current and past human civilizations. This is because the unique soft fluidity of colloids provides a nonlithographic, full-solution route for scalable and cost-effective manufacturing of optical and photonic structures. In addition to this easy-to-craft feature, recent advances in self-assembly (e.g. templated or confined colloidal assembly) have pushed our structural control over colloidal assemblies to an increasingly deterministic level [20, 66, 67], making them more compatible with the traditional academic perspectives and practical pursuits of optics and photonics. For example, a real metallic nanogap of a few nanometers (or even subnanometer), enabling light squeezing at the picoscale in volume [19, 68–71] has become manufacturable over a large area solely through colloidal synthesis [72–78] and assembly [79] since device-quality placement of individual colloids has become available via templated self-assembly [80, 81].

In this review we would like to emphasize that it is time to expand the scope of optics and photonics, by introducing the last three decades of research efforts to translate colloidal materials and their structuring models to the academic and practical perspectives of modern optics and photonics. To achieve the objectives of this review, it is necessary to first discuss the available shapes and sizes of colloids, and how their self-assembly has led to the formation of optical and photonic structures and devices, ranging from wavelength-scale photonic crystals [13, 82–113] to subwavelength-scale plasmonics and metamaterials [38, 39, 114–160].

2.1. Ceramic, Polymer, and Semiconductor Colloids

The method of uniformly synthesizing colloidal particles made of dielectric materials such as ceramics, polymers, and semiconductors has a long research history. Notably, silica colloids were synthesized using the Stöber method, a technique developed in the 1960s [161]. Other ceramic materials including titania (TiO₂) and zirconia (ZrO₂) were found to be challenging, in terms of controlling the size and shape uniformity of their colloids; therefore, silica has long been a main ingredient for ceramic colloids. The subsequent advancement of emulsion polymerization methods led to the uniform synthesis of polymer colloids, including commodity polymers like polystyrene (PS) and poly(methyl methacrylate) (PMMA) [162]. Even if these ceramics and polymers can be massively and well synthesized into a colloidal platform, their available refractive index (RI) is generally limited to about 1.4–1.5. This relatively low RI restricts the available optical mode of each colloid to nonresonant Rayleigh scattering at optical frequencies. This is why silica or polymer colloidal suspensions appear to have a whitish color, as shown in Fig. 1(a). A colloidal suspension with such low RI may not be very useful in and of itself for optics and photonics. However, as will be discussed, even low-RI colloids can become highly advantageous when it comes to the formation of 3D crystals (photonic crystals) [91, 93, 163–169] or amorphous assemblies (photonic glasses) [14, 170–172].

Figure 1. Dielectric colloids and their assemblies for optics and photonics. (a) Macroscopic image (left panel) and dark-field optical microscopy image (right panel) of a silica colloidal suspension (200-nm diameter). (b) Electric field profile at electric and magnetic resonant modes of a silicon colloid with 200-nm diameter. (c) Macroscopic epitube images (left panel) and extinction spectra (right panel) of a Si colloidal suspension. Reproduced with permission [176] Copyright © 2023, American Chemical Society. (d) Colloidal crystals and corresponding Si-air inverse opals with on-chip integration (upper panels) and embedded cavities (lower panels). Reproduced with permission [164, 166] Copyright © 2001 and 2007, Macmillan Magazines Ltd. and Springer Nature. (e) Self-assembled photonic Janus balls with black and structural-color regions. Reproduced with permission [167] Copyright © 2008, Wiley-VCH.

To further expand the design space for colloidal optics and photonics, a RI higher than 1.5 could be beneficial; This need can be addressed by using semiconductor colloids, made of for example silicon, with an RI of 2.5–4.5. Although metal oxides such as TiO₂ and ZrO₂ retain a high RI beyond 2.0, it is challenging to synthesize these colloids with sufficient uniformity, as mentioned above. As shown in Fig. 1(b), an increase in RI (e.g. with Si) can endow a colloid with resonant scattering modes (all-dielectric Mie resonance), spanning fundamental electric and magnetic dipoles (EDs and MDs) [173–175]. As a result, a Si colloidal suspension can exhibit a distinct color, resulting from resonant light scattering [Fig. 1(c)] [176]. Even higher-order resonant modes, including electric quadrupole (EQ) and magnetic quadrupole (MQ) modes, also become available for a relatively large-sized, high-RI colloid [Fig. 1(b)] [173–175]. As such, high-RI colloids themselves can play the role of scattering colorants, resulting from such all-dielectric Mie resonances. Also, the interplay between electric and magnetic resonances of high-RI colloids can impart angular momentum to a nanoscale optical mode (i.e. optical helicity) [176], which constitutes a crucial technical foundation for spectroscopy and enantioselective sensing of chiral molecules [177].

Note that such optical magnetic resonances cannot be attained with naturally occurring materials; thus colloidal suspensions exhibiting unnatural optical magnetism have been conceptualized as the distinct field of optical metafluids [16, 176, 178–181]. Metallic plasmonic colloids can also induce such optical magnetism [16, 178–180, 182–188]. However, unlike high-RI dielectric colloids, they require the clustering of at least three colloids to form a ring inclusion (denoted as plasmonic metamolecules) [173–176]. The manufacturing complexities of these plasmonic metamolecules inevitably lead to reduced throughput, which has been a contributing factor to their limited usage, since in addition to the synthesis of uniform colloids, confined self-assembly of colloidal clusters should be carried out. More critically, the Q-factor of a plasmonic metamolecule’s resonance is far lower than that of a single high-RI colloidal resonance, due to the intrinsic lossy plasmonic features.

Nevertheless, so far the chemical synthetic route for uniform Si colloids unfortunately relies on extremely high temperature (800 ℃) and pressure (10,000 psi, 69.0 MPa), which excludes them from commodity usage [174–176]. Very recently the mechanical crushing of macroscopic silicon monoxide (SiO) lumps into a mesoscale, crystalline Si colloid with high uniformity has been suggested. In particular, lump SiO was thermally disproportionated and subsequently etched by hydrofluoric acid, and crushing this SiO lump yielded crystalline Si spheres [176]. However, this mechanical manufacturing has yet to be widely utilized, owing to its dependence on highly trained personnel (indeed, as of Aug. 2023 it seems that only one research group worldwide is currently employing this method and reporting it in papers) [176, 181]. On the other hand, selenium (with an RI of 2.5–3.5) can be chemically synthesized into colloids under benchtop conditions, at ambient pressure and mildly high temperature (60 ℃) [189, 190]. As for Si colloids, Se colloids and their suspensions can show strong optical magnetism, pointing to their potential for all-dielectric soft metaoptics [189, 190]. However, Se colloids (with a relatively low glass transition temperature of around 60 ºC) are predominantly obtained in an amorphous phase, implying that their mechanical properties are quite weak, which limits their use in solid-state devices. Se colloids deteriorate even due to the heat generated by optical resonances. Other semiconductors, such as germanium and gallium arsenide, have yet to be exploited for colloidal chemical synthesis.

Despite the ability to induce strong all-dielectric Mie resonance, such practically limited options for materials and synthetic routes have relegated semiconductor colloids to an underutilized toolset for dielectric colloids. This research trajectory has also been influenced by the distinct characteristics of the field of colloids, as follows: colloid research has mainly been pursued in the fields of chemical engineering, chemistry, and materials science and engineering, rather than in physics or electrical engineering. Researchers in the former fields have shown relatively limited interest in meta-optics, in which unnatural optical magnetism has been of important interest. Instead, they have primarily focused on developing photonic crystals [91, 93, 163–169] and photonic glasses [14, 170–172, 191], in which naturally diffractive or diffusive scattering can be induced. As a result, the development of methods for semiconductor colloid synthesis has progressed relatively slowly. Overall, silica and polymer colloids are still the only commodity options for dielectric-based colloidal optics and photonics.

2.2. Colloidal Photonic (diamond) Crystals

Since Yablonovitch and John [82, 83] modernized the concept of photonic crystals in 1987 (interestingly, it was 100 years earlier in 1887 when Lord Rayleigh [192, 193] first elucidated photonic crystals), it has remained a highly significant research topic overall in optics and photonics [13, 82–113, 163–169]. In the early 1990s the experimental verification of photonic band gaps, theoretically proposed in the initial stages of photonic crystal research, was mainly conducted at low frequencies (microwave and terahertz) [194–196]. This was partly due to the relatively large structural sizes required, which could be fabricated easily using conventional semiconductor processes. However, to realize photonic crystals operating at optical frequencies, crystal structures with mesoscale periodicity are necessary. Until the late 1990s and early 2000s, it was challenging to address this need through any means other than electron-beam lithography (EBL) [197–199], alongside conventional manufacturing. Despite its exotic success in the creation of 1D and 2D photonic crystals, EBL (and also other conventional lithographies) is not intrinsically compatible with 3D structuring. Similarly, metamaterials were initially realized at low frequencies due to versatile processibility (e.g. common PCB printing and photolithography), and the related research gradually progressed towards higher frequency ranges [116, 200, 201].

Such technological challenges have been addressed by colloidal and polymeric self-assembly [91, 93, 163–169] or holographic lithography [21, 26, 47, 58, 95, 103, 202]. The mixing of more than three coherent beams can generate a 3D interference pattern, such that using visible light as a beam source allows holographic lithography to generate a mesoscale 3D pattern [26, 95, 103, 202]. More critically, full control over 14 3D Bravais lattices is possible, by adjusting the polarizations and wave vectors of the beams to be mixed [26, 95, 103]. However, despite research efforts over the past 20 years, the holographic realization of mesoscale 3D crystals with controlled lattices remains very limited. This is due to various technical challenges, including the difficulty of setting up an optical system that interferes with more than four beams; the sensitivity of interference patterns to mechanical vibrations, humidity, and temperature, which leads to structural errors; and the thermal instability of photoresist resin under beam exposure, which results in poor reproducibility and controllability of holographic lithography. Particularly for processes involving centimeter-scale or larger areas, more such challenges arise, and the infrastructure (e.g. cleanroom facilities) that can mitigate the abovementioned factors hindering process reproducibility becomes increasingly important. Additionally, thick resists are difficult to process, due to structural collapse caused by the capillarity effect during the development process. As a result, the diffractive properties (diffractive color) of 3D photonic crystals created through holographic lithography have not been comparable to those of their self-assembled counterparts.

Mesoscale 3D photonic crystals, self-assembled from block copolymers (BCP) and colloids, are obviously easy to craft because they depend fully on solution processes, without state-of-the-art infrastructure or trained personnel. For instance, spin coating of BCP and subsequent thermal annealing at 100–200 ℃ and ambient pressure are sufficient for developing self-assembled crystals [203, 204]. Solution-based entropic packing [3] and dip coating [168] provide a robust platform for the 3D crystallization of colloids. This versatile processibility of BCP and colloidal self-assembly in turn promotes the large-scale (generally wafer-scale) and cost-effective production of 3D photonic crystals, for experts and nonexperts alike. However, in the overall field of soft optics, colloidal self-assembly has been more widely used than BCP self-assembly for fabricating mesoscale 3D photonic crystals. This is because the 3D periodicity achievable through BCP self-assembly is generally below 100 nm [203], making it more suitable for implementing photonic crystals primarily below the visible-wavelength range (and note that 1D visible Bragg stacks can be well implemented using such sub-100-nm-scale BCP photonic crystals) [204].

As mentioned, colloids are primarily synthesized at the mesoscale. Thus the self-assembly of these colloids into 3D crystals can produce mesoscale 3D photonic crystals operating at optical frequencies. Alongside the colloidal synthesis described above, the discovery of mesoscale colloidal self-assembly (entropic packing) in the late 1980s [3] aligned well with the demand for the fabrication of such mesoscale 3D photonic crystals. Over the 1990s and 2000s, in addition to entropic packing [3], various and robust colloidal crystallization techniques (e.g. dip coating and entropic packing in photocurable resin) were proposed [165, 168], facilitating the broader utilization of 3D colloidal photonic crystals. Indeed, colloidal self-assembly began to be used to fabricate 3D photonic crystals in the mid-to late 1990s; Since then, this has led to two major research trends. (i) In traditional optics and photonics (from physics and electrical engineering), development has focused on the on-chip integration of colloidal crystals [Fig. 1(d)] for waveguide- and nanolaser-integrated devices operating at communication wavelengths [164, 166]. As a 3D photonic crystal with a complete photonic band gap (PBG) can act as an omnidirectional microscale mirror, its on-chip integration could dramatically expand the degrees of freedom in terms of chip-scale molding of light flow. (ii) In the fields of chemical engineering, chemistry, and materials science and engineering, the focus has been more on practical applications, such as structural color [Fig. 1(e)] [167]. In particular, structural color has drawn much attention, as it can cover a wide range of immediate practical applications such as sensors [205], anticounterfeiting materials [206], and displays [207]. However, the research direction (i) has diminished since the mid-to late 2000s. Alternative yet more competitive strategies for on-chip nanophotonic devices, including plasmonics [117, 120], metasurfaces [132, 135], and topological photonic crystals [38, 89, 95, 97, 112, 145], have been suggested and deterministically integrated on chips via lithographic approaches. In contrast, the research direction (ii) has continued up to the present day, because the prospects of the aforementioned colorization could be uniquely envisioned with colloidal crystals.

In particular, the crystals that could be obtained from colloidal self-assembly at that time were limited to the face-centered cubic (FCC) lattice, and are often referred to as opals. Due to the relatively small RI contrast between colloids and air, there were limitations in significantly expanding the complete PBG in 3D space. Subsequently, polymer and silica opals were used as templates to coat high-RI materials (e.g. Si, Ge, and GaAs), using methods like atomic layer deposition (ALD) and chemical vapor deposition (CVD). Selective removal of the opal template allows for the production of inverse opals with much higher RI contrast than standard opals [164, 169]. This approach successfully expanded the width of the PBG within 3D space. However, this multistep process resulted in reduced structural fidelity and process reliability. Moreover, structural defects commonly observed in self-assembly processes further reduced the efficiency of on-chip integration processes. Compared to the lithographic capability to deterministically develop and integrate 1D and 2D semiconductor photonic crystals for on-chip nanophotonic devices, the rationale for using colloidal photonic crystals became less compelling. This trend was accelerated by rapid advances in (i) plasmonic and metamaterial nanophotonic devices in the 2000s [38, 39, 114–160] and (ii) optical metasurfaces and topological photonic devices after the 2010s [38, 89, 95, 97, 112, 132, 135, 145], both of which can be well and reliably addressed via conventional manufacturing [EBL and deep-ultraviolet (DUV) photolithography]. Here, note that conventional photolithography has also evolved toward scalable and reliable manufacturing of mesoscale structures, even if it is still limited to 1D or 2D features (e.g. DUV and extreme-UV lithography). As a result, the practicality of on-chip applications using colloidal crystals has essentially faded.

In the fields of chemical engineering, chemistry, and materials engineering, however, colloidal photonic crystals have still remained attractive for practical applications such as structural color and visible-light sensors, and research in this area has continued actively, as mentioned. Even in these material applications, though, the need for a completely opened 3D PBG was critical, yet remained a challenge due to the intrinsic limitations of FCC crystals, prompting this question: Why does an FCC crystal retain a limited width of PBG? This is mainly due to the fact that a high volume fraction (vol%) of colloid in an FCC crystal (up to 74 vol%) dilutes the RI contrast. The width of the PBG is generally proportional to the RI contrast of a photonic crystal. In other words, the RI of polymer or silica is unable to completely open the PBG of an opal, in that an inverse opal made of a high-RI material needs to satisfy a complete 3D PBG. Then, we are once again faced with the question: are the crystals obtained through colloidal self-assembly limited to only FCC structures? The answer is mostly yes, if the colloidal shape is restricted to a sphere.

Most of the common dielectric colloids mentioned above have been synthesized mainly in spherical rather than polyhedral forms, with a size range from 100 nm to a few micrometers (from mesoscale to microscale) [162]. This is because the synthetic route for such polymeric, ceramic, and semiconductor colloids is oriented toward amorphous condensation of precursors. Crystallizing atoms form facets to maximize enthalpic reduction and overcome entropic penalty, leading to the synthesis of polyhedral colloids [72, 73, 76]. As will be mentioned later, the chemical synthesis of metallic colloids can be achieved through this process. In contrast, amorphous dielectric materials tend to be condensed into the spherical geometry of colloids, which can yield the lowest possible surface energy at interfaces [162, 189, 190].

The lattice of a 3D colloidal superstructure (e.g. a colloidal crystal) is defined by the shape of the unit colloid. In particular, individual colloids tend to maximize coordination number (the number of nearest neighboring particles); this behavior is spontaneous, because it maximizes enthalpic reduction and minimizes free-energy change during the self-assembly of colloids. This thermodynamic understanding in turn can be extended to rationalize the fact that higher coordination numbers in general lead to more mechanically stable colloidal assemblies. An FCC crystal can endow the maximum coordination number to each sphere (i.e. 12) [16, 164]. Therefore, it would be challenging to achieve a crystal other than an opal via the self-assembly of spherical colloids. Actually, almost all of the colloidal crystals reported thus far for 3D photonic crystals have been opals or inverse opals [163–169].

Of course, opals might be sufficient for practical uses, including structural colorants and their applications to sensors and security materials. In fact, over the past two decades research on colloidal opals and using them for the above applications has been actively pursued, aiming for easier and mass-producible approaches. Methods involving optofluidic synthesis of spherical opals (also called photonic supraballs) [167] and photolithographic patterning of opals [206] can be considered representative research directions. However, these research trends have been constrained by the inability to easily and robustly assemble crystal structures other than opals. Despite significant developments in the structural coloration of opal colloidal crystals, this restricted assembly has in turn led to performance limitations, including angle-dependent colorization [206]. This is because silica and polymeric opals are unable to open a complete PBG. While photonic glasses, achievable also by spherical-colloid assembly [14, 170–172, 191], enable angle-independent structural coloration, they suffer from reduced color purity [171]. This raises questions about whether there exists a lattice structure that can achieve a complete PBG beyond FCC, and whether it can be implemented through self-assembly of a low-RI spherical colloid.

In 2004, Maldovan and Thomas [208] reported crucial research to this end, where they theoretically elucidated that diamond crystals could achieve a complete PBG with the lowest RI contrast [Figs. 2(a)–2(b)]. Since then, diamond lattices have been referred to as champion photonic crystals. In particular, Maldovan and Thomas proposed two architectures of diamond crystals, achievable by connecting the ends of rods or a sphere’s surface in a tetravalent geometry [Fig. 2(a)]. However, the challenge lies in the difficulty of self-assembling diamond lattices. To create colloidal diamond lattices, the bonds between the unit colloids need to possess tetravalency, but most synthesized dielectric colloids are spherical, as mentioned, and can bond in all directions. Therefore, during entropic crystallization or dip-coating crystallization, they self-assemble into mechanically stable FCC structures with the highest number of isotropic bonds (12). FCC structures can achieve a colloidal vol% of up to 74, ensuring sufficient mechanical stability. On the other hand, the colloidal vol% for a diamond lattice must be below 40 [Fig. 2(b)], compromising its mechanical stability and making it difficult to achieve through conventional colloidal self-assembly. Meanwhile, it is obvious that the lower vol% of the diamond lattice than that of FCC can further improve RI contrast in photonic crystals, lowering the required RI of colloids for opening a complete PBG [Fig. 2(b)]. As mentioned, the 74 vol% of the FCC lattice inevitably dilutes the possible RI contrast.

Figure 2. Strategy for realizing a complete photonic band gap (PBG) with diamond crystals. (a) Arranged dielectric spheres (left panel) and connected dielectric rods (right panel) for a diamond lattice for the complete PGB. (b) PBG of diamondlike lattice structures. (a), (b): Reproduced with permission [208] Copyright © 2004, Springer Nature. (c)–(e) Binary Laves phase for the experimental realization of diamond crystal structures. (c) Self-assembled tetrahedral clusters in a pyrochlore structure. (d) Diamond structure generated by placing colloidal particles within the lattice vacancies of the pyrochlore structure. (e) Laves crystal structure consisting of pyrochlore and diamond structures. Reproduced with permission [211] Copyright © 2007, Springer Nature.

Although, as an exception, rod-shaped colloids that possess tetravalency can be synthesized using DNA origami, as will be explained later [209], the manufacturing of mesoscale diamond crystals using DNA origami is still limited to a theoretical proposal [208]. The possibility of implementing diamond crystal structures through holographic lithography has been also suggested, but its experimental realization has not yet been achieved [210]. Is there no way to materialize mesoscale diamond crystal structures using spherical colloids? Once again, it should be emphasized that, from a practical point of view, we are limited to having only spherical colloids, except for DNA origami. Could we start by exploiting the possibility of avoiding the prevalent shape of colloids (i.e. the sphere)?

Surprisingly, the answer to that question was addressed quite some time ago by Blaaderen et al. [211]. In 2007, they theoretically proposed a method for obtaining diamond crystals through self-assembly solely with spherical colloids. To achieve a diamond crystal, as mentioned, tetravalency needs to be conferred to the colloidal interactions. The Blaaderen group aimed to satisfy this requirement by arranging four spherical colloids closely packed in an isotropic cluster [Fig. 2(c)]. In 2003, Manoharan et al. [212] had demonstrated the self-assembly of isotropic colloidal clusters within water droplets through capillary forcing. For instance, when four spherical colloids are present inside a water droplet, the capillary forces resulting from droplet evaporation can induce the self-assembly of a colloidal cluster with a symmetric tetrahedral geometry. This colloidal cluster can be viewed as a polyhedral shape, granting tetravalency, in contrast to spherical colloids. Crystals in which these tetrahedral clusters are three-dimensionally crystallized with tetravalency are referred to as having the pyrochlore structure [yellow balls in Fig. 2(c)].

However, the challenge lies in the fact that the pyrochlore structure has a low colloidal vol%, which can compromise its mechanical stability. In the pyrochlore structure, distinct vacancies are visible between the tetravalent colloidal clusters. The Blaaderen group suggested a strategy to address this problem by placing single colloidal particles, of comparable size to the tetravalent colloidal cluster, within the lattice vacancies [reddish balls in Fig. 2(d), corresponding to the diamond lattice], enabling the robust formation of diamond crystal structures using solely spherical colloids. This 3D superstructure is denoted the Laves phase [Fig. 2(e)]. Note that (i) the yellow tetrahedral clusters forming the pyrochlore structure and (ii) the red individual colloids within the Laves phase respectively establish independent tetravalent bonding, contributing to the formation of the mechanically stable diamond lattice.

To achieve the Laves phase, two key conditions must be met. First, the colloidal sizes for the assembly of the pyrochlore structures (yellowish clusters) and for completing the Laves phase (reddish single colloid) should differ from each other. Second, there must be a specific interaction between the tetrahedral colloidal cluster’s facets and the surface of the individual colloidal particle. Notably, one of the facets of the tetrahedral colloidal cluster needs to selectively or directionally bond with the surface of the individual colloidal particle. This specifically programmable interaction is crucial for achieving the desired assembly. However, this complex set of colloidal interactions had been extremely challenging to achieve with a commodity dielectric colloid, and was out of reach until the 2010s.

To reiterate, the formation of colloidal diamond lattices necessitates adjusting the geometry of inter-particle bindings (e.g. endowing tetravalency) while concurrently imparting programmability to these bindings. These two conditions can be simultaneously satisfied by inducing selective binding between tetrahedral colloidal clusters’ facets and similarly sized spherical single colloids. As of today, DNA remains the sole material capable of highly accurate control over selective binding. While other programmable matter like proteins or RNA can engage in molecular-level selective interactions, their control precision cannot be compared to that achievable with DNA. In 2017, Pine’s research group [213] reported partial success in realizing Laves phase with DNA. In particular, they sequentially (i) pre-clustered four individual spherical colloids [Fig. 3(a)], (ii) slightly fused these clustered spherical colloids to moderately adjust the overall geometry of clusters while maintaining tetravalency, and (iii) coated the surfaces of preassembled clusters with single-stranded DNA (ssDNA) chains [Fig. 3(b)]. Additionally, larger spherical colloids coated with ssDNA, which can complementarily bind to the ssDNA on the preassembled clusters were prepared separately. These separately prepared, DNA-coated clusters and the larger individual colloids were then mixed, facilitating their programmable self-assembly through the DNA’s complementary binding between them, and eventually, the Laves phase was partially obtained [Fig. 3(c)]. In 2020, as shown in Fig. 3(d), the Pine group optimized this approach to successfully obtain Laves-phase diamond crystals with long-range order on a macroscopic scale [214]. After more than two decades of effort, they achieved the benchmark feat of obtaining champion 3D photonic crystals through the self-assembly of spherical colloids.

Figure 3. Experimental realization of the Laves phase, toward the formation of colloidal diamond lattices. (a) Polystyrene (PS) tetrahedral clusters for pyrochlore-structure assembly. (b) Red tetrahedral clusters are coated with single-stranded DNA that is complementary to the DNA on green colloidal particles, creating the Laves phase. (c) Fluorescence microscopy image (left panel), scanning electron microscopy (SEM) image (middle panel), and confocal microscopy images showing successive planes (right panel) of the assembled Laves phase. (a)–(c) Reproduced with permission [213] Copyright © 2017 Springer Nature. (d) SEM images of the [111] plane of a colloidal diamond lattice with tetrahedral patchy clusters. Reproduced from [214] Copyright © 2020, M. He et al., under exclusive licence to Springer Nature.

However, experimental validation of a complete PBG has not yet been achieved. This is due to the inability to selectively remove either the clusters or individual particles in the Laves phase. Furthermore, the colloidal clusters used in this case were of microscale size, resulting in 3D photonic crystals with relatively large periodicities that could not operate effectively at optical frequencies. The manufacturing of such microscale 3D photonic crystals can be deterministically achieved with fewer structural defects using interference lithography and 3D printing (two-photon lithography) [26, 56]. As a result, the justification for utilizing colloidal self-assembly diminishes, especially for manufacturing 3D photonic crystals with larger-scale periodicities.

2.3. Colloidal Photonic Glasses

By regulating the thermodynamic conditions, these meso/microscale spherical colloids can be spontaneously assembled into amorphous glass as well as 3D crystals, and colloidal 3D crystals and glasses can be used as 3D photonic crystals [91, 93, 163–169] and photonic glasses [14, 170–172, 191], respectively. In particular, the reaction-limited assembly in the equilibrium state allows the colloid to crystallize, whereas the diffusion-limited fractal growth of colloids in the non-equilibrium state leads to random aggregation [2]. Each material system provides a different molding of light flow: (i) diffractive light scattering (photonic bandgap) for photonic crystals, and (ii) resonantly diffusive light scattering (Anderson localization) for photonic glasses [Fig. 4(a)] [14, 171]. For both, a relatively low RI in ceramic and polymeric colloids is still enough to induce these types of light management. Colloidal photonic glasses have received less attention than photonic crystals; however, as mentioned, the drawback of angle-dependent coloration in opals can be completely resolved by using photonic glasses. This daunting potential of colloidal photonic glass highlights its continued significance in the field of colloidal optics and photonics.

Figure 4. Colloidal photonic glasses for structural color. (a) Schematics illustrating light scattered by a colloidal photonic crystal and an inverse opal (left panel), compared to colloidal photonic glass and inverse photonic glass (right panel). (b) Macroscopic image (left panel) and transmission spectra (right panel) of a colloidal photonic glass without well-defined short-range order. d indicates the diameter of the colloidal polystyrene (PS) spheres. Reproduced with permission [14] Copyright © 2010, Wiley-VCH. (c) Transmission spectra of photonic glasses with well-defined short-range ordering. Reproduced with permission [215] Copyright © 2012, Optical Society of America. (d) Reflection spectra of colloidal glasses of poly(methyl methacrylate) (PMMA) particles with different diameters. Reproduced with permission [216] Copyright © 2014, American Physical Society. (e) Colloidal photonic glass of hollow silica spheres and infiltrated inverse photonic glass. Reproduced with permission [218] Copyright © 2017, American Chemical Society.

Before the 2010s, 3D colloidal glasses primarily exhibited strong broadband scattering, resulting in a whitish appearance [Fig. 4(b)] [14]. However, since then it has become possible to induce specific color scattering in colloidal random assemblies, by appropriately imparting short-range order [Fig. 4(c)] [215]. To achieve resonantly diffusive light scattering in colloidal photonic glasses that effectively results in specific colors, two key factors must be well-controlled [171, 172]. The first is the scattering from a single particle, known as the form factor; the second is the scattering resonantly induced due to the short-range order of colloidal aggregates, known as the structural factor.

Due to their low RI, individual silica or polymer colloids can induce Rayleigh scattering only, implying that at shorter wavelengths scattering becomes stronger (i.e. form factor). In other words, regardless of their size, mesoscale dielectric colloids exhibit a stronger form-factor-driven scattering at shorter wavelengths. Thus, a form factor acts as broadband background scatter (whitish background) [171]. On the other hand, the wavelength of the structural-factor-driven scattering is directly related to the scale of the short-range order of photonic glasses. This is because structural-factor-driven scattering can be resonantly enhanced via diffusion of scattered light selectively along the short-range order of colloidal aggregates. Given a form-factor-related whitish background, a structural factor, which has been achieved by a precise regulation of thermodynamic conditions for colloidal aggregation, defines an available scattering color.

In other words, the purity of such structural color of photonic glasses is generally ruined by a form factor. This drawback becomes clear particularly for greenish and reddish structural colors, because the form and structural factors are spectrally detached in these colorations [Fig. 4(d)][172, 216]. In contrast, bluish coloration can benefit from the synergistic interplay between the spectrally coincident form and structural factors. Thus, adding a broadband light absorber (e.g. carbon-black particles) has been suggested to reduce whitish background colors and enhance the prevalence of greenish and reddish scattering [217]. However, the presence of broadband light absorbers inevitably dilutes the structural factor as well. Recently, the importance of inverse colloidal photonic glasses has been raised, as it can selectively remove a form factor while preserving a structural factor [Fig. 4(e)] [218].

3.1. Libraries for Metallic Colloids

On the other hand, the synthesis of metallic colloids has been developed and advanced more recently than that of dielectric colloids. The progress of the nanochemistry field, which gained momentum in the early 1990s, has led to research focusing on the controlled reduction of metal ions and the subsequent nanoscale crystallization of the reduced metallic atoms. This crystallization of metallic atoms can diversify the accessible polyhedral shapes of metallic colloids (e.g. cube, rhombic dodecahedron, truncated ditetragonal prism, cuboctahedron, concave cube, tetrahexahedron, and octahedron), in stark contrast to polymeric, ceramic, and semiconductor colloids.

Particularly, during this period the synthesis of Au nanorods commenced [219], laying the foundation for the attempted synthesis of uniform spherical and polyhedral metal colloids; Its culmination was achieved in the early 2000s, as follows: in 2002, the group of Xia [220] succeeded in synthesizing polyhedral metallic colloids, including silver nanocubes, with relatively uniform shapes and sizes. This breakthrough served as a catalyst for the remarkable development of numerous synthesis methods, ultimately leading to the synthesis of various metallic polyhedral colloids, represented by Au and Ag, with extremely high uniformity of size and shape [Fig. 5(a)] [73]. Especially, the precise control over the surface energy of growing colloids has become possible via adjusting the species and densities of organic ligands, which in turn allows for elaboration of the polyhedral shapes of metallic colloids [73, 75, 76]. However, these synthetic characteristics imply that the synthesis of spherical metal colloids is much more challenging. Instead the method of coating Au onto the surfaces of pre-synthesized spherical silica colloids to obtain spherical Au colloids has been available [126], but in this case, the achievable core-shell colloids are relatively large, around 200 nm in size. More importantly, the surface of silica-core, Au-shell colloids is relatively rough, reducing the scattering cross section.

Figure 5. Libraries of polyhedral metal colloids. (a) Polyhedral gold colloids with well-defined facets and edges. Reproduced with permission [73] Copyright © 2014, American Chemical Society. (b), (c) Scanning electron microscopy (SEM) images, (b) and circular dichroism spectra (c) of plasmonic chiral Au nanoparticles synthesized using L-cysteine and D-cysteine. Reproduced with permission [222] Copyright © 2018, Macmillan Publishers Ltd., part of Springer Nature. (d) Transmission electron microscopy (TEM) image of Au nanoprisms. Reproduced with permission [227] Copyright © 2005, American Chemical Society. (e) TEM images of aluminum colloids with controlled facets and edges. Reproduced with permission [229] Copyright © 2018, American Chemical Society. (f) Optical properties (left panel) and SEM images (right panel) of Al nanocubes with sharp corners. Reproduced with permission [228] Copyright © 2019, American Chemical Society.

In 2014, the synthesis of uniform metallic colloidal spheres, which was unattainable before then, was eventually addressed [73]. In particular, the addition of Au ions (using gold chloride) was phenomenologically found to induce the selective etching of the vertices and edges of the uniformly growing Au polyhedral colloids; Consequently, blunt-ended Au colloids with high uniformity could be achieved. In this case, the higher numbers of vertices and edges of Au polyhedral (e.g. concave rhombic dodecahedra) to be etched likely lead to more spherical shaping of uniform Au colloids [73, 76]. Repetition of this selective etching and growth of polyhedral could increase the uniformity and spherical features of Au colloids. This is referred to as the iterative growth and etching method, which was found to be effective also for Ag [73, 76, 78]. These ultrasmooth, spherical Au colloids can be used as seeds for further growth of polyhedral Au colloids; using this seed-growth method allows for better uniformity, compared to directly performing growth [221].

Furthermore, it is important to note that such controlled crystallization of metallic ions enables otherwise impossible shaping of colloids. In 2018, Nam et al. [222–225] found that the chirality of the peptides to be attached to achiral, symmetric Au colloids gives rise to the chiral growth of Au colloids [denoted plasmonic helicoid; See Fig. 5(b)]. Their chirality matched with that of the peptide. This programable atomic growth of chiral features enables nanoscale inscription of chiral topology onto each facet of polyhedral Au colloids, so that a strong chiral resonance benefitting from the chiral metallic nanogap-concentrated LSPR mode on each helicoidal surface evolves [strong circular dichroism (CD), as shown in Fig. 5(c)]. This pioneering work has been further diversified via changing the chiral ligands and growth conditions [226].

For Au, as mentioned above, well-established methods for synthesizing both spherical and polyhedral colloids, including helicoids with geometrical isotropy, are available presently. Also, their sizes can be precisely controlled within the range of 100 nm or less [73]. In addition to isotropic colloids, various shapes of anisotropic Au colloids (nanoplates), including nanoprisms, can be obtained [Fig. 5(d)] [227]. However, for Ag the achievable shapes and uniformity are still limited, compared to Au. This is due to the high susceptibility of Ag colloids to oxidation under ambient conditions, leading to its less frequent use in plasmonic studies, compared to Au. Consequently, the development of synthesis methods for Ag colloids has been less advanced in this aspect (e.g. helicoidal growth has yet to be translated to Ag). Since the interband transition of Au primarily occurs at wavelengths below 500 nm, the advancement of Ag-colloid synthesis is crucial to shift the plasmon resonance into the shorter-wavelength region. For the same reason, the synthesis of aluminum colloids is also critical. Al colloids can induce plasmon resonances in the UV range, whereas Au and Ag cannot. However, Al colloids have only recently been controlled in terms of shape and uniformity, by Halas’s research group [228, 229], and they are not as common as Au and Ag colloids in terms of availability and level of control [Figs. 5(e) and 5(f)]. As with Ag, Al is vulnerable to oxidation, preventing Al colloids from deterministic and reliable chemical synthesis.

Such widened libraries of Au colloidal shapes can diversify the resonant modes of Mie scattering, driven by localized surface plasmon resonance (LSPR). Unlike dielectric colloids, the accessible size of metallic colloids was predominantly limited to the nanoscale (sub-100 nm). In general, individual metallic colloids in this size range can retain only ED resonance (LSPR), in contrast to high-RI dielectric colloids. However, the exotic LSPR of such metallic colloids enables otherwise impossible near-field enhancements, opening up a new horizon for molecular spectroscopy [surface-enhanced Raman spectroscopy (SERS)] [69], nanophotonic optoelectronics (e.g. solar cells and light-emitting diodes) [230–232], plasmonic photothermalization (plasmonic heating) [233, 234], and plasmonic hot-electron-driven catalysts (plasmonic catalysis) [235, 236].

Certainly, metal particles can also be patterned using photolithography or EBL. Additionally, the crucial structural part of LSPR-based field enhancement, the metal nanogap, can be structured through lithography as well [e.g. bowtie nanoantennas, as shown in Fig. 6(a)] [237–240]. However, the chemically synthesized Au colloids and their use for the fabrication of metal nanogaps afford several advantages that would be challenging with lithography. First, chemically synthesized Au colloids have exceptionally smooth surfaces at the atomic level, and they can retain single-crystalline Au atoms within the colloid, which is difficult to achieve in deposited metallic films [241]. This implies that the Q-factor of LSPR and the resultant scattering cross section is significantly stronger for nanostructures from Au colloids, compared to those from lithographically defined nanostructures on deposited film [241]. In particular, the structural fidelity and possible near-field enhancement from bowtie nanoantennas, which are lithographically defined on a synthesized Au nanoprism, outperformed those from the deposited-film counterparts [Fig. 6(b)] [241]. Second, the process of creating a metal nanogap using Au colloids is much easier and can be carried out on a smaller scale than lithography. For instance, as Au colloids are typically surrounded by organic ligands 1 nm or less in thickness, simply putting them on a flat Au surface can complete the formation of a metallic nanogap of 1 nanometer or less. This is known as the metal nanoparticle-on-mirror (NPOM) cavity, which has been a promising avenue for plasmonic molecular spectroscopy and quantum sensing over the last decade [68–70]. Third, these metal nanogaps enable the deterministic positioning of quantum emitters with the assistance of DNA origami or cucurbit molecules, promoting the coupling between the molecules and the plasmonic cavity [Figs. 6(c) and 6(d)] [68, 242].

Figure 6. Key advantages of metallic colloidal optics and photonics. (a) Lithographically fabricated metal nanogap for electric field enhancement. Reproduced with permission [237] Copyright © 2009, Springer Nature. (b) Scanning electron microscopy (SEM) images (left panel) and photoluminescence-signal map (right panel) of the single-crystalline and polycrystalline metal nanogap. The nanostructures on the upper left Au flakes correspond to single-crystalline metal nanogaps. Reproduced with permission [241] Copyright © 2010, Springer Nature. (c) Nanoparticle-on-mirror (NPOM) cavity containing a dye molecule. The molecule is positioned inside of the cavity, guided by a cucurbit molecule. Reproduced with permission [68] Copyright © 2016, Springer Nature. (d) DNA-origami-guided plasmonic nanocavity with a single quantum emitter. The single molecule was positioned in the NPOM gap by the programmable hybridization of DNA. Reproduced with permission [242] Copyright © 2017, American Chemical Society.

In this review, we will not discuss deeply such LSPR-based plasmonic applications of metallic colloids, because those topics have already been covered extensively in a variety of reviews [19, 79]. Instead, we aim to introduce recent research trends in ensemble optical properties that can be induced from Au colloidal clusters and superlattice structures (metamaterials and metasurfaces).

3.2. Assembly of Metallic Colloids for Optical Magnetism

Unlike dielectric colloids, the accessible size of metallic colloids was predominantly limited to the nanoscale (less than 100 nm). This limitation arises due to the higher density of metals than that of dielectric materials, causing them to be more prone to the loss of colloidal-suspension stability when particles exceed 100 nm in size. Suspension instability disables deterministic colloidal self-assembly. However, this size limitation in turn has proven advantageous in terms of metamaterial and metasurface applications, because metallic colloids of such dimensions can themselves function as meta-atoms that satisfy effective-medium theory [146, 243].

In the 2000s, in addition to photonic crystals, metamaterials emerged as a significant research topic in optics and photonics. Particularly, the importance of controlling the magnetic properties of light, as proposed by Pendry et al. [244–246] in the late 1990s, gained profound attention. This extended beyond just controlling permittivity via naturally occurring materials and included the extraordinary control of permeability, leading to the prominence of negative refraction. To achieve this, the artificial induction of magnetism became a crucial research challenge, and split-ring resonators (SRRs) were proposed as suitable resonant structures for this purpose [Fig. 7(a)] [244]. In relatively low frequency ranges, such as microwave and terahertz, SRRs could be readily fabricated using photolithography accessible even via university-level infrastructure, because their required structural size is easy to access, from millimeters to tens of micrometers [Figs. 7(b) and 7(c)] [200, 247]. By the middle of the 2000s, negative refraction had already been demonstrated in these frequency ranges; The next challenge was transitioning to optical frequencies, including the visible regime. The structural demands of the required optical SRRs, with dimensions of 100–200 nanometers or smaller, were difficult to meet using conventional lithography methods available at that time.

Figure 7. Strategy for realizing unnatural optical magnetism through the assembly of metallic colloids. (a) Split-ring resonators (SRRs) for unnatural induction of magnetism. (left panel) Plane view of split rings comprised of two sheets of metal. (right panel) Unit cell of SRR structure in a 3D array, and its corresponding permeability. Reproduced with permission [244] Copyright © 1999, IEEE. (b) Macroscopic photograph of a SRR array operating at gigahertz frequencies (left panel), and the corresponding index of refraction (right panel). Reproduced with permission [200] Copyright © 2001, The American Association for the Advancement of Science. (c) Scanning electron microscopy (SEM) image of chiral metamaterials for unnatural magnetism (left panel) and corresponding permittivity at terahertz frequencies (right panel). The black and gray lines correspond to the real and imaginary parts, respectively. Reproduced with permission [247] Copyright © 2009, American Physical Society. (d) Spherical Au colloid clusters for unnatural magnetism at optical frequencies. Schematic representation (left panel), electric field distribution (middle panel), and normalized magnitude of electric and magnetic polarizabilities (right panel), for single Au colloids (upper panels) and Au colloid clusters (lower panels). Reproduced with permission [184] Copyright © 2009, Optical Society of America.

In 2006–2009, Alù and Engheta [182–184] proposed a radical idea to overcome these limitations. Their idea involved the materialization of optical SRRs through the clustering of spherical metal colloids. The isotropic clustering of more than three metallic colloids (much like the aforementioned confined self-assembly of colloids within a droplet) can form a ring inclusion, which is essential for driving magnetism. As shown in Fig. 7(d), a ring inclusion made of spherical Au colloids can yield current circulation and resulting magnetism, when illuminated.

Due to the individual sizes of Au colloids being around 50–100 nm, their clusters can satisfy homogenization conditions at optical frequencies, allowing them to act as metamolecules [16, 182, 183]. Furthermore, the metal nanogaps between the colloids are only 1–2 nm, maximizing capacitive coupling between the metallic colloids and enhancing current circulation, which amplifies optical magnetism. Through the self-assembly clustering of spherical metallic colloids, it becomes possible to achieve SRRs operating at optical frequencies without resorting to lithography. Initially 2D metamolecular motifs were suggested (e.g. trimers); later they were extended to 3D, to make their magnetism isotropic regardless of incident angle [Fig. 7(d)]. Alù and Engheta [182] not only demonstrated the enhancement of optical magnetism through metallic colloid clustering, but they also theoretically confirmed that such meta-atoms, when dispersed at high concentrations (over 60 vol%) within a host medium, can lead to an effective RI below zero according to effective-medium theory. Overall, the potential for achieving negative-RI metamaterials through colloidal self-assembly was theoretically established.

Following the theoretical proposal by Alù and Engheta, relevant research aimed at experimental verification of metamolecules through colloidal self-assembly and spectroscopic verification of optical magnetism has been actively pursued. However, there were challenges in experimental realization, primarily due to the absence of a reliable synthetic method for highly uniform spherical Au or Ag colloids at that time (2007–2009). Also, simultaneously, research efforts extended from the creation of self-assembled metamolecules to their optical characterization. A notable technique conceived then was dark-field optical microscopic spectroscopy, which successfully confirmed the scattering spectrum selectively from individual Au colloids [248–250].

In 2010, a breakthrough was achieved by successfully self-assembling metamolecules through colloidal self-assembly and experimentally verifying optical magnetism [185]. Given the difficulty in synthesizing uniform metallic colloids, the approach in this work involved coating spherical silica colloids with an Au shell, followed by self-assembly of these silica-core, Au-shell (silica@Au) colloids into clusters (trimers), as shown in Fig. 8(a). Additionally, dark-field optical microscopic spectroscopy was used to analyze the scattered signals selectively from the assembled trimers, and experimentally evidenced optical magnetism. Subsequently, not only molecular motif-based clusters [185, 186, 251–253] but also Au nanorod dimers [Fig. 8(b)] [180] and raspberry-type [Fig. 8(c)] [179] colloidal clusters were synthesized experimentally, and their strong magnetism was confirmed in solution (optical metafluids) or the solid state. However, achieving negative-RI metamaterials using these colloidal metamolecules remains a pipe dream so far.

Figure 8. Experimental realization of metamaterials through the self-assembly of metal colloids. (a) Transmission electron microscopy (TEM) image (upper left panel), numerically calculated electric field distribution (lower left panel), and scattering spectra (right panel) of trimeric silica-core, Au-shell colloidal clusters. Reproduced with permission [185] Copyright © 2010, American Association for the Advancement of Science. (b) Optical properties of Au nanorod assemblies in solid (left panel) and solution (right panel) states. Reproduced with permission [180] Copyright © 2016, Springer Nature. (c) TEM image (left panel), solid-state scattering spectra (middle panel), and angle-resolved scattering spectra from bulk fluids (right panel) of raspberry-type colloidal clusters. Reproduced with permission [179] Copyright © 2013, American Chemical Society. (d) Unnaturally high-refractive-index metasurface achieved through entropic packing of Au colloids. (left panel) TEM image of the metasurface, with macroscopic image. (middle and right panels) Refractive index of the Au colloidal metasurface. Reproduced with permission [260] Copyright © 2020, American Chemical Society.

The failure to achieve negative-RI metamaterials using colloidal meta-atoms can be attributed to several reasons. Alù and Engheta proposed that effective parameters, including permittivity and permeability, would fall below zero when implementing metamolecules for optical magnetism at a concentration of 50 vol% or higher. However, achieving such high concentrations of colloids, especially in clusters, is extremely challenging in experiment. While 50 vol% concentration might be attainable for individual particles, achieving it for clusters has proven to be elusive.

In suspensions with a vol% greater than 50, colloids undergo entropic packing (or crystallization), if the interactions between colloids can be ignored (hard-sphere model) [3, 16]. The regularly arrayed metamolecules should experience electric or magnetic interactions between each other. However, Alù and Engheta’s theoretical analysis [182] assumed an effective-medium theory, without electric and magnetic interactions between metamolecules. Subsequent theoretical results suggested that electric and magnetic interactions between metamolecules lead to spectral detachments between electric (permittivity) and magnetic (permeability) resonances [16]. To achieve negative RI, both effective parameters need to be simultaneously pushed below zero in the same wavelength range.

Another challenge is the extreme sensitivity of the optical magnetism of colloidal self-assembled metamolecules to tiny variations in the metallic nanogap, which is at the scale of 1–2 nm [251]. Even such small structural errors at the nanometer scale can lead to significant changes in optical magnetism. For instance, in a tetrahedral configuration, if one of the four metal nanogaps increases by just 1 nm, the symmetry of the ring inclusion becomes broken, resulting in Fano resonances where electric and magnetic resonances destructively interfere [251].

Overall, while the theoretical concepts proposed by Alù and Engheta were promising, the practical implementation has faced challenges in achieving the necessary high colloidal concentrations, accounting for interactions, and maintaining structural precision at an extremely high level. These obstacles have limited the realization of negative-RI metamaterials using colloidal self-assembled meta-atoms.

3.3. Ultrahigh Refraction via Colloidal Metasurfaces

Indeed, the achievement of negative-RI materials holds significance not only because it enables the realization of superlenses [245], but also because it allows us to explore the realm of RI that has been inaccessible. In this context the concept of negative RI carries meaning because it allows us to attain RI values that were previously beyond the reach of natural materials. Conversely, positive RI, particularly the realization of very high RI values that have not been achievable with natural materials, can contribute to enhancing the spectral completeness in terms of RI. Furthermore, the pursuit of high RI has practical implications in various fields, including optoelectronics (e.g. solar cells) [254] and other optical applications relying on light-matter interactions [255, 256]. Overall, the quest for negative- and high-RI materials goes beyond theoretical curiosity, presenting possibilities for unprecedented optical and photonic phenomena and promising applications in diverse technological domains.

The RI is defined as the square root of the product of permittivity and permeability. If one or both are increased, RI increases. As mentioned, inducing strong magnetism at optical frequencies is very challenging, so most research on unnaturally high-RI metamaterial has focused on drastically increasing permittivity, through electric resonance [146, 243, 257–259] As mentioned, chemically synthesized Au colloids are coated with organic ligands that are around 1-nm thick. Therefore, even by simply allowing entropic packing of these Au colloids, one can obtain over a large area a 2D array of electric meta-atoms with metallic nanogaps of a few nanometers (i.e. metasurfaces with unnaturally high RI). This achievement surpasses what can be accomplished even with state-of-the-art photolithography, such as EUV lithography. Through this approach, an RI of 6.2, outperforming the natural limit of 4.0–4.5 at optical frequencies, has been reported in Fig. 8(d) [260]. Also, BCP templated Au half sphere packing enabled the achievement of a high RI at the optical frequencies [261].

Mesoscale dielectric and nanoscale metallic colloids can play the roles of scatterers at the wavelength and subwavelength scales respectively. When chemically synthesized, these colloids have smoother surfaces at the atomic level, compared to lithographically patterned particles. In particular, these metallic colloids can exhibit strong scattering cross sections due to their ability to impart single-crystallinity, enabling them to achieve significant scattering even in the liquid state. As a result, they have gained attention as paintlike liquid optical materials, with historical relevance extending from ancient times to the present. Over the past 30 years, research efforts have shifted their focus from these general applications to contribute to the scientific goals and practical applications of optics and photonics, such as photonic crystals, plasmonics, and metamaterials and metasurfaces. While the application of colloids in chip-scale photonic crystals eventually faced challenges, they continued to serve as important optical and photonic materials for the realization of 3D photonic crystals and glasses, and for use as colorants. Advancements of microfluidics [262–272] and DNA nanotechnologies [10, 273–288] greatly expanded the accessible motifs of colloidal crystals and clusters. Notably, mesoscale diamond crystals, often referred to as champion photonic crystals, were realized after two decades of research efforts [214]. This achievement stands as a representative milestone in colloidal processes for optical and photonic structures that were deemed impossible through conventional manufacturing methods. However, limitations such as the yet-to-be-confirmed complete PBG in colloidal diamond crystals within the visible-light range, and the need for templating with high-RI materials, remain as future challenges. Colloids have also made significant contributions in various topics in plasmonics, particularly in the realization of real metallic nanogaps and molecular spectroscopy based on them [68, 69]. Furthermore, while unsuccessful in achieving negative-RI metamaterials [16], the realization of extremely high-RI optical metamaterials and metasurfaces has been achieved solely through self-assembly of metallic colloids [260, 261].

Overall, through the research trends of the past three decades, the competitive strengths and challenges to be addressed in colloidal optics and photonics can be summarized. Colloids can make considerable contributions in optics and photonics areas that demand nanoscale and 3D structural complexity (e.g. diamond crystals). However, their contributions may be limited in areas that require precise, deterministic control over nano-, meso-, and microscale structural accuracy and defects.

4.1. Still Optical Metafluids?

Future prospects should further emphasize the aforementioned advantages and address the drawbacks. For instance, the benefits of forming complex 3D structures like diamond crystals and the ease of scalability and solution-applicability, as compared to lithography, need to be highlighted even more. Although the potential of optical metafluids with optical magnetism was explored, the issue of significant changes in optical magnetism due to even slight structural errors in plasmonic metamolecules (even 1-nm structural deviation) has hindered their widespread use [251, 289]. However, this issue can be overcome by high-RI dielectric colloid-based optical metafluids. Unlike plasmonic metafluids, high-RI dielectric colloids can induce both electric and magnetic resonances in the dispersed state of single particles in solution, eliminating the need for self-assembly such as clustering [176, 181, 189, 190].

Indeed, the associated research efforts have started to conceptualize all-dielectric optical metafluids using actual Si and Se colloid dispersions [176, 181, 189, 190], aiming to use them in applications like molecular sensing [176, 290]. Aside from negative refraction, inducing electric and magnetic resonances and coupling them can greatly enhance optical helicity [291, 292], which is advantageous for chiral-molecule spectroscopy [177]. The practical applicability of resonance-based negative refraction is questionable, as the imaginary part k in RI = n + ik becomes large, resulting in substantial loss. Additionally, traditional concepts of metamaterials have somewhat diminished in importance due to the prominence of metasurfaces. However, this transition requires more facile mass synthesis of high-RI semiconductor colloids, including Si and Se, which necessitates further advancement in the chemical synthesis of semiconductor colloids.

For implementing solution-based optical and photonic materials using metallic colloids, there are still new possibilities to explore. Toward this end, we need to discover plasmonic motifs that can maintain robust optical characteristics, even in the presence of structural errors or randomness at the nanoscale or even mesoscale. The research group led by Chanda [293, 294] has provided a good example in this direction: they demonstrated that Al nanoparticles self-assembled onto dielectric/metal layered stacks can absorb specific wavelengths of visible light, due to plasmonic resonances in metal-insulator-metal (MIM) configurations [Fig. 9(a)] [283, 294]. Even with randomly dispersed Al nanoparticles, this MIM plasmonic resonance can lead to strong, uniform structural color, regardless of the angle of incidence. Moreover, these MIM layered structures formed through sequential deposition can be mechanically fractured into particulates and dispersed well in solvents. This fluidic platform for plasmonic colorants offers new possibilities for the development of mass-producible nanophotonic paints, whose color hues, visibility, and durability can go far beyond what can be achieved via conventionally commercialized paints that depend on organic dyes and dielectric scatters [Fig. 9(b)] [294]. Overall there are novel avenues to be explored in the realm of solution-based optical and photonic materials using metallic colloids [283, 294].

Figure 9. Colloidal optics and photonics for device-level applications. (a) Schematic (top panel) and scanning electron microscopy (SEM) images (lower panel) of a self-assembled metal-insulator-metal (MIM) configuration for structural color. Insets in lower panel show the macroscopic images of the self-assembled plasmonic paint. Reproduced from [293] Copyright © 2020, D. Franklin et al. (b) Plasmonic paint composed of MIM-configured color flakes. (top panel) Macroscopic image of the color flakes dispersed in solution. (lower panel) An artistic butterfly, painted with plasmonic paint. Reproduced from [294] Copyright © 2023, P. Cencillo-Abad et al. (c) SEM image (left panel) and optical-helicity-density (h_sca) profile (right panel) of a chiral Au colloidal array assembled through templated colloidal assembly (TCA). Reproduced from [177] Copyright © 2022, R. M. Kim et al., under exclusive licence to Springer Nature Limited. (d) Shape-directed assembly of Au colloids into 2D lattices with controlled positions and orientations. Reproduced from [81] Copyright © 2020, National Academy of Science.

4.2. Can We Develop a Device-quality Colloidal Array?

The aforementioned drawbacks of error-prone manufacturing are indeed challenges that pertain to all self-assembly fields involving colloids. The research effort to precisely arrange randomly dispersed colloids onto solid substrates in desired lattices, patterns, and positions at micro- or nanoscale accuracy is essential for the immediate practical application of colloidal solid-state devices. Over the past 20 years, significant research efforts have been dedicated to achieving this goal. Among these, one of the most remarkable achievements has been templated colloidal assembly (TCA) [66, 67]. TCA involves placing colloidal particles into prepatterned micro- or nanoscale line/hole arrays using capillary forces. Depending on the shapes and geometries of the patterns, various types of colloidal assemblies can be obtained on a large scale. Single colloidal particles or colloidal clusters can be assembled within hole patterns, while linear colloidal arrays can be assembled within line patterns. This approach has been utilized to create practical colloid-based optical and photonic components, such as coupled waveguides [295] and chiral metasurfaces [e.g. helicoidal arrays, as shown in Fig. 9(c)] [177, 296]. Until the mid-2010s, TCA was mainly limited to assembling spherical colloidal particles into symmetric structures [66] but recent advancements have allowed for the assembly of polyhedral single particles into any desired position, with arbitrarily controlled orientations [Fig. 9(d)] [81]. This advancement implies that TCA can achieve colloidal assemblies with complexity comparable to that of typical, lithographically defined metasurfaces.

4.3. Can DNA Nanotechnology be the Unsung Hero for Colloidal Optics and Photonics?

Not only TCA, but also DNA nanotechnology can enhance the structural accuracy of colloid self-assembly. In particular, DNA origami, developed by Rothemund [275] in 2006, has made significant contributions to the advancement of colloidal optics and photonics [20, 186, 252, 253, 277, 281, 282, 284, 285, 289]. DNA origami can be attained by folding long ssDNA (spanning over 8,000 bases) at desired locations to synthesize DNA colloids [275]. Treating ssDNA as a kind of polymer, DNA origami can be thought of as folding and controlling colloidal shapes, much like drawing with a single stroke. By folding polymers to control colloid shapes, molecular-level accuracy can be achieved in DNA colloidal shaping, benefitting from the complementary base pairing of DNA. Furthermore, much like drawing any desired shape with a single stroke in the macroscopic world, DNA origami enables the creation of virtually any desired shape.

DNA origami itself lacks optical utility. Typically, its lateral dimensions reach around 100 nm, and for this lateral dimension its thickness is only about 2–2.5 nm. Additionally, its RI is relatively low (1.4). Such structural features and low RI of DNA origami result in negligible scattering characteristics at optical frequencies. However, DNA origami possesses the capability to position ssDNA molecules on its surface with nanometer accuracy. Leveraging this feature, DNA origami enables the programmable self-assembly of nanoscale metallic colloids, quantum dots, and organic dyes, each equipped with complementary ssDNA strands for specific binding [20, 186, 252, 253, 277, 281, 284, 288].

Due to the typical size limitation of DNA origami to around 100 nm, as metioned, only nanoscale colloids can be self-assembled on DNA-origami surfaces. Exceptionally, there have been reports of programmable clustering of micrometer colloids, which was achieved by attaching DNA-origami plates in a 1D belt configuration and wrapping them around microscale polymeric colloids or emulsions [297]. However, this research direction has not been widely adopted, owing to the limited experimental accessibility arising from multistage procedures. Overall, DNA origami can function as a pegboard that can integrate nanoscale optical colloidal elements with molecular-level accuracy. Despite lacking intrinsic optical properties, the exotic ability of DNA origami to orchestrate the precise assembly of optically functional colloidal elements on its surface holds great potential for creating sophisticated optical and photonic structures and devices.

Actually, in 2012, DNA origami began to be employed in the field of optics and photonics. A notable example involves the chiral integration of Au colloids below 20 nm onto DNA-origami nanotubes [Fig. 10(a)], enabling strong CD responses [277]. Subsequent work has efficiently realized plasmonic metamolecules [186, 298] and integrated quantum emitters [20, 299] through DNA-origami-enabled programmable self-assembly. These optical structures remain in a dispersed colloidal form in solution. Arranging solution-dispersed DNA origami onto solid-state substrates has been actively pursued over the past decade, and is known as DNA-origami placement (DOP). In 2016, Gopinath, Rothemund et al. [282] presented astonishing DOP achievements. In particular, they demonstrated that individual DNA origami could be placed at any desired position on the surface of numerous (about 68,000) 2D Si photonic crystal cavities, patterned using EBL. This illustrated how DNA origami could be efficiently integrated on a solid-state substrate with device quality. In 2021, even more advanced results were announced, showing not only precise control of DNA-origami position but also complete control over the orientation of DNA origami through the DOP process [285]. This marks a significant advancement with which to arrange DNA origami colloids on a macroscopic scale in a perfectly controlled manner, in terms of both their orientations and positions [Fig. 10(b)].

Figure 10. DNA-guided self-assembly of colloids. (a) Integration of Au colloids (~20 nm in diameter) into chiral helices, using DNA nanotubes as a template. (left panel) Transmission electron microscopy (TEM) image of the assembled left-handed chiral structures. (middle panel) Circular dichroism of the left-handed (red lines) and right-handed (blue lines) structures. (right panel) Transmission microscopy images revealing the optical-rotatory-dispersion activity of the assembled chiral structures. Reproduced with permission [277] Copyright © 2012, Springer Nature. (b) DNA-origami placement (DOP) on a 2D surface with controlled position and orientation. (upper left panel) Model DNA origami with offset holes and DNA-binding fluorescent dye molecules. (upper right panel) Atomic force microscopy (AFM) and averaged AFM images of the DNA origami placed on a disk-shaped patchy array. (lower panel) A 2D rhomboidal array consisting of DNA origami with spatial and orientational order. Reproduced from [285] Copyright © 2020, A. Gopinath et al.

So far, only organic dyes have been integrated into such DNA origami arrays arranged in a device-quality manner, and practical applications in optics and photonics have not yet been fully exploited with DOP technology. However, these research achievements have opened up new possibilities for the practical application of colloids in optics and photonics as solid-state devices. In the future, if plasmonic or dielectric colloids and quantum dots can be deterministically integrated into these DNA origami arrays, it is anticipated that advanced optics and photonics materials and components that have not been achieved thus far could come to the fore.

National Research Foundation (NRF) grant (NRF-2022M3H4A1A02074314 and NRF-RS-2023-00272363); Samsung Research Funding & Incubation Center for Future Technology grant (SRFC-MA2301-02); the KIST Institutional Program (Project No.: 2V09840-23-P023); a Korea University grant.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

No data were generated or analyzed in this study.