Gyroid Optical Metamaterials: Calculating the Effective Permittivity of Multidomain Samples

Abstract

Gold gyroid optical metamaterials are known to possess a reduced plasma frequency and linear dichroism imparted by their intricate subwavelength single gyroid morphology. The anisotropic optical properties are, however, only evident when a large individual gyroid domain is investigated. Multidomain gyroid metamaterials, fabricated using a polyisoprene-b-polystyrene-b-poly(ethylene oxide) triblock terpolymer and consisting of multiple small gyroid domains with random orientation and handedness, instead exhibit isotropic optical properties. Comparing three effective medium models, we here show that the specular reflectance spectra of such multidomain gyroid optical metamaterials can be accurately modeled over a broad range of incident angles by a Bruggeman effective medium consisting of a random wire array. This model accurately reproduces previously published results tracking the variation in normal incidence reflectance spectra of gold gyroid optical metamaterials as a function of host refractive index and volume fill fraction of gold. The effective permittivity derived from this theory confirms the change in sign of the real part of the permittivity in the visible spectral region (so, that gold gyroid metamaterials exhibit both dielectric and metallic behavior at optical wavelengths). That a Bruggeman effective medium can accurately model the experimental reflectance spectra implies that small multidomain gold gyroid optical metamaterials behave both qualitatively and quantitatively as an amorphous composite of gold and air (i.e., nanoporous gold) and that coherent electromagnetic contributions arising from the subwavelength gyroid symmetry are not dominant.

Controlling Self‐Assembly in Gyroid Terpolymer Films By Solvent Vapor Annealing

“…Block copolymer (BCP) self‐assembly is a particularly promising route to fabricate functional nanomaterials over macroscopically large areas . For many applications, long‐range order on the millimeter length scale is required, e.g., for 1D and 2D nanolithographic templates, and 3D optical metamaterials . Producing BCP films with such high degrees of order requires an annealing process, and it is often advantageous to utilize solvent vapor annealing (SVA).…”

Metasurfaces Atop Metamaterials: Surface Morphology Induces Linear Dichroism in Gyroid Optical Metamaterials

“…Alternative “bottom up” approaches overcome these limitations and allow efficient fabrication of otherwise inaccessible 3D nanoscale structures. One successful method employs self‐assembling triblock terpolymers, and results in optical metamaterials with a single gyroid morphology . The chemical dissimilarity between the different “blocks” of the terpolymer (i.e., the constituent polymer chains) leads to microphase‐separation into various morphologies on the nanometer length scale.…”

“…The single gyroid structure is a chiral, cubic, and triply periodic geometry found in a variety of natural and synthetic self‐assembled systems . Its unique morphology imparts a range of optical properties to gyroid‐structured optical metamaterials that are dependent on the unit cell size, volume fill fraction, surrounding refractive index, and degree of order . Intriguingly, gyroid optical metamaterials give rise to a linear and circular dichroism (i.e., a variation in the optical properties as a function of azimuthal orientation of linearly polarized light and handedness of circularly polarized light, respectively), both of which are sensitive to the structure of the metamaterial .…”

“…However, this optical anisotropy is only readily observable (e.g., by standard optical microscopy techniques) when the metamaterial possesses long‐range order, whereby domains of the self‐assembled template span at least tens of micrometers. If the metamaterial possesses only short‐range order, its anisotropic optical properties are masked and it responds similarly to disordered nanoporous gold …”

An Overview of Materials with Triply Periodic Minimal Surfaces and Related Geometry: From Biological Structures to Self‐Assembled Systems

“…Metamaterials are artificial materials that enable magnetism to be achieved at optical frequencies not found in nature and are famous for potential applications such as cloaking devices and superlenses . In addition to materials with both negative permittivity and permeability, the strong chirality in the SG structure can lead to cross‐coupling between electric and magnetic dipoles, breaking the degeneracy between two circularly polarized waves to give a negative refractive index …”