Effects of defects and surface roughness on high-Q modes in ZnO microspheres

The interest in WGMs can be traced back to a century ago when Lord Rayleigh studied the sound propagation in a gallery with a curved surface [1]. In 1989, Braginsky and coworkers demonstrated that silica microspheres can support optical resonant modes with high quality (Q) factor [2]. Since then, silica microspheres have been considered as the key element for making modulators and sensors in fiber communication. For spherical resonators with size much larger than the wavelength of light, the WGM resonant frequencies can be predicted by using geometric optics [3]. The Q-factor of a WGM mode is defined as the ratio of the resonant frequency to the peak width, which is proportional to the energy dissipation rate of the mode [4]. To determine the Q-factor of individual WGM mode, it is better to use wave mechanics to find the solution to Maxwell equations for the wave function that satisfies the boundary condition of a dielectric sphere and find the complex root for the resonance frequency as illustrated by Little [5]. The imaginary of the complex root then describes the width of the resonance peak, which can be used Photoluminescence (PL) spectra of high-Q ZnO microspheres of various degrees of inhomogeneity are studied. Multiple sharp resonance features with distinct patterns associated with whispering gallery modes (WGM) of these microspheres are observed. Relative WGM peak strengths in these PL spectra are found to be closely related to defects and the surface roughness of the microspheres. A theoretical model based on Mie theory and Green's function method is used to simulate the optical emission spectra of these microspheres. The effects of defects and surface roughness can be characterized by a frequency-dependent external quality factor (Qex) with a prefactor. By adjusting the prefactor in Qex and a parameter describing the contribution of stimulated emission in the PL spectra, we can fit the observed PL spectra well. Through this study, we gain a better understanding of the relation between the diffusive scattering and the lineshapes of spectral features in PL.