  A theoretical model for describing the emission spectra of microsphere
cavities is presented, and its prediction of detailed lineshapes of emission
spectra associated with whispering gallery modes (WGMs) of various orders in
ZnO microspheres (MSs) are verified experimentally by photoluminescence (PL)
spectroscopy. The interplay of Purcell effect, quality factor, and leaky modes
in spontaneous and stimulated emission spectra related to WGMs of all orders is
revealed. The key success of the theory is based on the expansion of the full
Green function of the MS in terms of all possible resonance modes in complex
frequency space, which allows incorporation of contributions from leaky modes,
stimulated emission processes, and Purcell effect. We show that the spontaneous
emission spectrum calculated according to Mie theory (without Purcell effect)
is dominated by the contribution of leaky modes, while the spontaneous and
stimulated emission enhanced by Purcell effect are responsible for the main WGM
resonance peaks observed experimentally. It is found that the stimulated
emission peaks are doubly enhanced by their respective mode quality factor Q:
one factor from the Purcell effect and the other factor from the photon number
derived from the rate equation. After combining all these effects the theory
can provide a quantitative description of fine features of both TE and TM modes
(including higher-order modes) observed in the PL spectra of ZnO MSs.
Surprisingly, it is found that for ZnO MS with diameter larger than 5 $\mu m$,
the PL emission spectrum is dominated by higher-order modes. The quantitative
understanding of the interplay of these emission mechanisms should prove useful
for optimizing the performance of light-emitting devices based on micro
resonators.
