Fig. 5
From: Method for GHz optical helicity modulation by acoustic drum modes on a chip
Dispersion of cylindrical Lamb waves. Dispersion of rz-polarized Lamb waves in a cylindrical disk of sapphire of radius \(r_\textrm{film}\) with winding number \(n=0\) calculated assuming an isotropic elastic model for the sapphire substrate (cf. Eq. 2). The calculations were performed for a 425 \(\upmu\)m-thick substrate: due to the high mode density, not all modes are shown. The in-plane wave vector \(k_r\) is normalized to \(\pi /r_\textrm{film}\), where \(r_\textrm{film}\) is the radius of the ZnO island. The dashed lines indicate the dispersion of the pure longitudinal (\(v_\textrm{L}\), Eq. SM15), transverse (\(v_\textrm{T}\), Eq. SM15), Lamé (\(v_\textrm{T}\sqrt{2}\), Eq. SM25), and SAW modes (\(v_\textrm{SAW}\), Eq. SM17) determined for the sapphire substrate. The blue and purple dots show the dispersion of SAW modes determined for a sapphire substrate coated with a 700 nm-thick ZnO film (cf. Sect. SM2 B). The red asterisks are the corresponding experimental values for short period waves obtained from field maps (such as, e.g., those in Figs. 3 and 4).
