Mathematical Model for Electric Field Sensor Based on Whispering Gallery Modes Using Navier’s Equation for Linear Elasticity

Amir R Ali,Mohamed A Kamel

doi:10.1155/2017/9649524

Abstract

This paper presents and verifies the mathematical model of an electric field senor based on the whispering gallery mode (WGM). The sensing element is a dielectric microsphere, where the light is used to tune the optical modes of the microsphere. The light undergoes total internal reflection along the circumference of the sphere; then it experiences optical resonance. The WGM are monitored as sharp dips on the transmission spectrum. These modes are very sensitive to morphology changes of the sphere, such that, for every minute change in the sphere’s morphology, a shift in the transmission spectrum will happen and that is known as WGM shifts. Due to the electrostriction effect, the applied electric field will induce forces acting on the surface of the dielectric sphere. In turn, these forces will deform the sphere causing shifts in its WGM spectrum. The applied electric field can be obtained by calculating these shifts. Navier’s equation for linear elasticity is used to model the deformation of the sphere to find the WGM shift. The finite element numerical studies are performed to verify the introduced model and to study the behavior of the sensor at different values of microspheres’ Young’s modulus and dielectric constant. Furthermore, the sensitivity and resolution of the developed WGM electric filed sensor model will be presented in this paper.

Highlights

Optical cavities have been used for many sensory applications due their high quality factor and resolution [1, 2]
This paper presents and verifies the mathematical model of an electric field senor based on the whispering gallery mode (WGM)
Results of the 1st numerical studies are shown in Figure 2. dλ is plotted against the increasing electric field strength up to 1300 kV/m

Summary

Introduction

Optical cavities have been used for many sensory applications due their high quality factor and resolution [1, 2]. WGM based optical cavities are used to detect and measure the applied electric field. Any minute external disturbance on the sphere or its surrounding environment will be detected as shift in its transmission spectrum These cavities are used in many sensory applications by measuring the WGM shifts corresponding to the change in the measured phenomenon. When an electric field is applied on a dielectric microsphere, it induces surface and body forces across its body. Theses forces will deform the sphere changing it size, causing shifts in its WGM transmission spectrum, creating a WGM based electric field sensor. Where εsphere is the dielectric constant of the microsphere’s material; E is the applied electric field inside the sphere; and. The deformation of the microsphere needs to be calculated to get the WGM shift due to the applied electric field

Analysis

Results and Discussion

Conclusion