The emission transients of optically excited high-speed multiple quantum well laser diodes have been measured by up-converting the emission in a nonlinear crystal. From the gain-switched oscillation the intrinsic resonance frequency and damping factor are determined. The high temporal resolution allows us to observe additional short period oscillations with a frequency of about 170 GHz. Numerical solution of the traveling wave rate equations indicates that these high frequency oscillations arise due to inhomogeneous carrier injection