Optical Resonance in Dielectric Micro-Sphere for Temperature Measurement

Abstract

We describe the effect of Transverse Electric (TE) wave propagation in dielectric micro-spheres for optical resonances based on Whispering Gallery Mode (WGM). TE waves are characterized both theoretically and experimentally by considering the fact that the size parameter (pi times diameter divided by wavelength of light) of the micro-spheres is very large at optical wavelengths. Asymptotic expressions have been developed based on electromagnetic theory derivations at the large size parameter limits. The developed expressions for optical resonance condition of TE wave are very simple and can accurately characterize resonances in dielectric microspheres. The theoretical development is mathematically robust and significantly less complicated than existing approaches based on quantum physics presented in the literature. The theoretical result of size parameter for consecutive morphology dependent resonance (MDR) peaks are validated by experimental data obtained via this study using a tunable semiconductor laser and from the literature. The comparisons are shown to be very accurate for large size parameters. The quality factor of experimental resonance spectra observed in the laboratory is calculated approximately in the order of 104 which is sensitive enough to detect micro or nano level temperature changes in the surrounding medium. The sensitivity of the MDR temperature sensor is wavelength change of 10−9 meter for one degree centigrade change in temperature. This sensor could potentially be used for nano technology, Micro-Electro-Mechanical Systems (MEMS) devices, and biomedical applications.