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.