| A microring formed coaxially around an optical fiber is of interest because of the discovery that the microring supports a low threshold whispering gallery mode (WGM) laser, and hence suggests the prospect of integrating the microring directly onto optical fibers to form integrated pumping source for fiber amplifiers. In order to achieve a successful engineering design for the microring laser, one must establish a comprehensive description of the WGM laser in the microring as well as the coupling between the laser emission and the propagating modes of the fiber.;In this dissertation, a near rigorous theoretical treatment for the whispering gallery mode laser is developed for microrings with both circular and elliptical cross sections. Asymptotic methods are used to study the laser resonance and to compute fields in the microring. The coupling between laser field and the fiber mode by way of evanescent tunneling is analyzed, and a simplified aperture description is presented to formulate the coupling coefficient.;The coupling mechanism is investigated, and it is found that in order to achieve a coupling of microring laser into the fundamental mode of the fiber, one must disturb the orthogonality relation between the laser mode and fiber mode. When the microring and the fiber are of elliptical cross section, there exists controlable coupling. The coupling can be understood through characteristics of Mathieu functions that describe fields in elliptical waveguides. It is found that the coupling between the laser and the fiber can be controlled by the dimension of the microring, the eccentricity of the elliptical fiber, and the material contrast between the fiber core, cladding and the microring. |
