Capillary resonator as optical sensor for the measurement of the hydrostatic pressure. A theoretical study of its sensitivity

Abstract

We report the study of an optical device for the measurement of hydrostatic pressure in fluids. The device studied is a sensor based on a dielectric optical resonator in the form of a capillary that confines the light in its interior through the phenomenon of total internal reflection. For the analytical study of sensitivity, we have considered the solution of the Helmholtz scalar equation for the case of a resonant cavity in form of cylinder composed of three layers with different refractive index. During the study, the excitation of the Whispering Gallery Modes WGMs on a transverse plane along the axial axis of the cavity is studied and the equation of eigenvalues that has information of the wavelengths of resonances for the TE and TM modes were obtained from the resonance conditions. To determine the sensitivity of the device, the shift of the wavelengths of resonances as a function of the internal pressure in the cavity were analyzed. The results show that it is possible to increase the sensitivity of the microresonator when the wall thickness of the cavity is thin, and the maximum diameter is increased.