Homogeneous linewidth of the I_11/2--I_15/2 optical transition of erbium in LiNbO_3:Er^3+

We work out a simple, pulsed pump-probe measurement scheme to measure the homogeneous linewidth of an atomic transition in an inhomogeneously broadened spectral line in a solid state environment. We apply the theory to the I_11/2 -- I_15/2 optical transition of erbium in LiNbO_3:Er^3+ crystal. Beside obtaining the homogeneous linewidth, we have estimated the population relaxation time as well.