  We study the propagation of a non-interacting atom laser distorted by the
strong lensing effect of the Bose-Einstein Condensate (BEC) from which it is
outcoupled. We observe a transverse structure containing caustics that vary
with the density within the residing BEC. Using WKB approximation,
Fresnel-Kirchhoff integral formalism and ABCD matrices, we are able to describe
analytically the atom laser propagation. This allows us to characterize the
quality of the non-ideal atom laser beam by a generalized M$^2$ factor defined
in analogy to photon lasers. Finally we measure this quality factor for
different lensing effects.
