Circular dichroism of pseudo-two-dimensional metal nanostructures: Rotational symmetry and reciprocity

Circular dichroism (CD) spectra for pseudo-two-dimensional chiral nanomaterials were systematically investigated and analyzed in relation to the rotational symmetry of the nanomaterials. Theoretically, an ideal two-dimensional chiral matter is CD inactive for light incident normal to the plane if it possesses threefold or higher rotational symmetry. If the matter has two- or onefold rotational symmetry, it should exhibit CD activity, and the CD signal measured from the back side of the matter is expected to be inverted from that measured from the front side. For pseudo-two-dimensional chiral gold nanostructures fabricated on glass substrates using electron beam lithography, matter with fourfold rotational symmetry is found to be CD active, even when special care is taken to ensure that the optical environments for the front and back sides of the sample are equivalent. In this case, the CD signal measured from the back side is found to be almost exactly the same as that measured from the front side. It is revealed that the observed chiro-optical behavior arises from three-dimensional chiral characteristics due to differences in the surface shape between the front and back sides of the structures. For matter that is two- or onefold rotationally symmetric, the CD signal measured from the back side is not coincident with that from the front side. For certain wavelength regions, the CD signals measured from the front side and back side are observed to be similar, while at other wavelengths, the inverted component of the CD signals is found to dominate. The observed CD spectral behavior for reciprocal optical measurement configurations is considered to be determined by a balance between the in-plane isotropic and anisotropic components of the chiral permittivity.