Measurement of the strain-induced coefficient of permittivity of sapphire using whispering gallery modes excited in a high-Q acoustic sapphire oscillator

A low-loss monolithic sapphire has been developed for use as a novel transducer via the interaction between the electrical and mechanical resonances, with the intent of measuring the standard quantum limit in a macroscopic mass. This work has investigated the transductance mechanism due to the interaction between electrical and mechanical resonances in a low-loss electrical and acoustic resonator, which operates in the regime where parametric interactions dominate. High electrical and mechanical quality factors (Q-factors) are obtained at low temperatures (4.2 K) using high purity sapphire and single loop suspension vibration isolation. In deriving the displacement sensitivity of the monolithic sapphire transducer (MST), the acoustic mode shape and electromagnetic field distribution must be taken into account rather than the use of a simple mass–spring model. With the aid of this model we determine for the first time the strain-induced coefficient of permittivity for sapphire, both perpendicular and parallel to the c-axis. By comparison with other work, it has been determined that changes in the dielectric constant due to strain are approximately eight times smaller than changes caused by thermal expansion.