Whispering gallery modes for 3D strain measurement

This paper deals with the use of Whispering Gallery Modes to measure the six components of an homogeneous strain tensor within a sphere undergoing a uniform strain field. The device is a silica sphere in which six WGMs resonate, describing six circles positioned on the sphere's surface in planes perpendicular to the normals of a dodecahedron. The direct model relating the strain to the resonant wavelength variation is established for one circle and then linearised in accordance with the intended application, i.e. the realisation of a sensor. The expressions are then generalised to six circles and inverse system computed to obtain an expression for the six components of the strain field as a function of six wavelength shifts of WGMs. Finally, the theoretical performances of the sensor are assessed. The study shows that using a conventional 1 pm resolution detector, the uncertainty on the strain components is, after correction of systematic errors, equal to 2 mu epsilon.

Automated summary

This paper investigates the use of Whispering Gallery Modes to measure the six components of a homogeneous strain tensor within a sphere. A direct model is established and linearized to obtain the relationship between the strain field and the wavelength shifts of the resonant modes. The expressions are then generalized to six circles, and an inverse system is computed to determine the six strain components. The theoretical performances of the sensor are finally evaluated, showing a high level of accuracy.