Multi-layered resonators for optimized electric field detection

Abstract

In this study, we carry out an analytical investigation to determine the efficacy of multi-layer dielectric micro-sphere resonators as high-resolution electric field sensors. The use of a large number of layers with different electrical and mechanical properties allows for optimum dielectric constant and elastic modulus gradients within the sphere to optimize sphere resonator’s sensitivity to external electric field. The external electric field applied to a dielectric sphere induces an elastic deformation of the resonator (electrostriction effect), leading to shifts in its whispering gallery optical modes (WGM). The non-uniform distribution of the dielectric constant leads to a gradient in the electric field within the sphere. This in turn induces non-uniform body force on the sphere when subjected to an external electric field. By also appropriately varying the elastic modulus of the layers, the electrostictive deformation of the sphere can be optimized. In this paper we present a mathematical model describing the effect of the electric field on the WGM shift of layered micro-spherical resonators.