Structural measurements on the liquid-crystal analog of the Abrikosov phase

High-resolution x-ray and optical studies were peformed on oriented samples of the recently discovered smectic-${\mathit{A}}^{\mathrm{*}}$ phase. We confirm that this phase exhibits smectic-A layers as well as a macroscopic helical strcucture with the helical axis parallel to the layer planes. Furthermore, we demonstrate that the observed scattering can be explained by a cylindrical structure factor that is, within our instrumental resolution, a δ function in the radial direction and a Gaussian in the transverse direction as predicted by Renn and Lubensky for the ‘‘twist grain boundary’’ phase.