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We work out a simple, pulsed pump-probe measurement scheme to measure thehomogeneous linewidth of an atomic transition in an inhomogeneously broadenedspectral 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. Besideobtaining the homogeneous linewidth, we have estimated the populationrelaxation time as well.

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