  The precise measurement of the gain lifetime at a specific wavelength holds
significant importance for understanding the properties of photonic devices and
further improving their performances. Here, we show that the evolution of gains
can be well characterized by measuring linewidth changes of an optical mode in
a microresonator; this method cannot be achieved using time-resolved
photoluminescence (PL) spectroscopy. We use an erbium-doped high-Q
whispering-gallery microresonator to show the feasibility of this method. With
the increase of time after the pump laser is turned off, the transmission
spectrum of a probe signal exhibits transitions from a Lorentz peak to a dip;
this indicates a decay of optical gains, and the corresponding lifetime is
estimated to be 5.1 ms. Moreover, taper fiber coupling is used to increase the
pump and collection efficiency. This method can be extended to other materials
and nanostructures.
