High-Q microspheres have attracted much attention as a useful and practical tool in various branches of optical science, particularly in laser frequency stabilization, selective optical filters, and a microcavity for lasers with quantum radiators such as quantum dots and single atoms. In this experiment, a prism-microsphere evanescent-wave-coupling configuration was used to measure the WGM cavity quality factors of homemade microspheres. An extended cavity diode laser (New Focus, Vortex 6000) of 780nm was used as a probe beam. The probe beam was focused under an optimal angle at the inner surface of a coupling prism. The microsphere fabricated by melting the end of an optical fiber was hold in a fiber chuck holder and positioned its equator next to the focal spot of the probe beam on the prisms surface. For an efficient coupling, the distance between the prism and the sphere was controlled in a step of about 0.1㎛ by a PZT positioner (Thorlabs, PE4). The WGM Q factors were measured from the reflectance spectrum obtained by scanning the wavelength of a probe laser. Cavity quality factors up to $4\times10^8$ corresponding to a linewidth of 1-2MHz, have been measured. This linewidth was mainly limited by the linewidth of the probe laser, limiting the highest Q value measurable in our experiment to be about $4\times10^8$. We also observed equally spaced WGM modes with about 2GHz spacing, which arises from the frequency splitting of different Z components of angular momentum due to slight eccentricity in microsphere. We also observed the dependence of coupling linewidth and amplidute of resonant dips on the distance between the prism and the microsphere. At about 0.5㎛, the amplitude of resonant dip was maximized, which was up to about 20% of off-resonance signal amplitude. As the distance decreased to a value less than 0.5㎛, the resonance transmission diminished. At this critical gap distance, the measured factor becomes a factor of 2 smaller than the intrinsic quality factor. As the distance decreased below $d_{crit}$, the linewidth of the modes were broadened exponentially as a function of the resonant-dip amplitude.
