Spectral shift of a Gaussian Schell-model beam beyond a thin lens

We give a comprehensive representation of the Wolf effect in propagation both in free space and after a lens for an outstanding class of partially coherent beams, namely Gaussian Schell-model beams. We characterize the correlation-induced spectral changes, throughout the whole space, by means of isoshift lines and transverse shift profiles. The maximum value of the frequency blueshift, occurring on the optical axis, is also calculated.