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We present a theoretical model for the propagation of non self-interacting atom laser beams. We start from a general propagation integral equation, and we use the same approximations as in photon optics to derive tools to calculate the atom laser beam propagation. We discuss the approximations that allow to reduce the general equation whether to a Fresnel-Kirchhoff integral calculated by using the stationary phase method, or to the eikonal. Within the paraxial approximation, we also introduce the ABCD matrices formalism and the beam quality factor. As an example, we apply these tools to analyse the recent experiment by Riou et al. [Phys. Rev. Lett. 96, 070404 (2006)].

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.