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.
Highlights
Electromagnetic metamaterials are artificially structured materials for which the electromagnetic response is a function of their chemical composition and their structure.[1]
The Maxwell−Garnett effective medium theory is a poor model for the effective permittivity of the gyroid metamaterial, as it predicts a striking dip in reflectance at an effective Brewster’s angle of ∼60°, which is entirely absent in the measured data
The effective permittivity of multidomain gold gyroid metamaterials was estimated by comparing the results of three effective medium theories to measured specular reflectance spectra over a range of angles of incidence
Summary
Electromagnetic metamaterials are artificially structured materials for which the electromagnetic response is a function of their chemical composition and their structure.[1]. Gyroid metamaterials possess a range of optical properties not exhibited by the pure metal, including an unambiguous optical anisotropy.[8] Large individual domains exhibit a significantly decreased plasma frequency and linear dichroism, evidenced by the shift of the extinction peak by up to 100 nm upon rotation under linearly polarized light.[11] Both the plasma frequency and the linear dichroism are a function of the unit cell size, fill fraction, and dielectric environment.[12,13] much is known about the optical properties of gyroid metamaterials, suitable estimates of the effective material parameters remain elusive, thereby hindering a true appraisal of the metamaterial’s potential utility. It is of great interest to correctly identify the effective material parameters of gyroid metamaterials and to understand to what extent the ordered subwavelength structure continues to affect the optical response when the macroscopic order is not long range
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