Exploiting Colloidal Metamaterials for Achieving Unnatural Optical Refractions

Abstract

homogenization theory. [1-3] Additionally, in this case, metaunits need to be coupled with each other through ultrasmall gaps (e.g., those of a few nanometers), while simultaneously satisfying 2D or 3D structural complexities (e.g., 3D chiral split rings and stacked fishnets). [4-21] Monolithic lithography, such as photo, electronbeam (e-beam), and focused ion beam lithography, has effectively addressed such challenges; nevertheless, scaling down through these lithographic methods is still limited to tens of nanometers (especially at the university level). [22-24] Furthermore, true 3D structuring is difficult to achieve through such monolithic lithography. These challenges have motivated the use of colloidal self-assembly as a toolset for the development of optical metamaterials. [25-63] By benefitting from the recent advances in synthetic strategy, the diversified shapes of metallic and dielectric colloids spanning from 5 to 1 µm in size have come to the fore with sufficiently high yield; [64-91] at the moment, these subwavelength-scale nanoparticles can serve as optical meta-atoms with controlled electric and magnetic responses. [37,51-61,67,85,86,88-90,92-94] For example, merely by dispersing subwavelength-scale metallic colloids within the medium, effective electrical parameters such as effective permittivity (ε eff) and the resultant refractive index (n eff) at optical frequencies can be broadly enhanced beyond the naturally available regimes. [37,94] The colloidal dispersion of dielectric nanoparticles with strong Mie-resonances can unnaturally modulate the effective magnetic parameters including effective permeability (μ eff) and the resultant n eff. [95-99] Thus, metallic and dielectric colloids can be considered, respectively, as electric and magnetic meta-atoms at optical frequencies. It is also noteworthy that their self-assembly into well-defined clusters and superlattices, acting as optical metamolecules and metamaterials, respectively, has substantially progressed over the past two decades. [25-63] The close-packing of at least three metallic colloids into clusters can form a geometry of ring inclusion, which enables boosting the circulating displacement current. As such, unnatural magnetism at optical frequencies can be obtained from such plasmonic metamolecules according to Lenz's law. [25-48,100-103] This optical magnetism is essential for achieving unnaturally negative and near-zero n eff. [25-27,35-38,41-43] Aside from lowering n eff , the regularly arrayed superlattice of metallic colloids can squeeze the incoming optical waves into The scaling down of meta-atoms or metamolecules (collectively denoted as metaunits) is a long-lasting issue from the time when the concept of metamaterials was first suggested. According to the effective medium theory, which is the foundational concept of metamaterials, the structural sizes of meta-units should be much smaller than the working wavelengths (e.g., << 1/5 wavelength). At relatively low frequency regimes (e.g., microwave and terahertz), the conventiona...

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