An analysis of coupling between a whispering gallery mode laser in an elliptical microring and the dominant mode in the coaxially oriented elliptical optical fiber

The problem of coupling a whispering gallery mode laser into an optical fiber is considered. The whispering gallery mode laser is generated in a polymer microring formed coaxially on the optical fiber. The focus of this paper is to determine factors that influence the coupling between the laser and the fiber around which it is formed. The coupling mechanism is analyzed and it is found that when the microring and the fiber are of elliptical cross section, there exists controllable coupling between the laser and propagation mode in the fiber. The coupling between laser mode and fiber mode is due to characteristics of Mathieu functions that describe the fields in elliptical waveguides. It is shown that the coupling between the laser and the dominant mode in the fiber can be optimized by the designing the dimension of microring, the eccentricity of the elliptical cross section, and the material contrast between fiber and microring.