A high-frequency analysis of the reflection and diffraction of well-focused electromagnetic Gaussian beams (GBs) by a perfectly conducting parabolic surface with an edge is presented for the two dimensional case. The fields are evaluated analytically via the physical optics (PO) approximation, and only the reflected field is expressed as a GB. The GB procedure developed here is expected to be highly efficient in applications involving large reflector antennas, since it avoids the conventional time-consuming numerical evaluation of the PO integrals. Some numerical results are provided to indicate the accuracy of the analytical expressions obtained. The three-dimensional case will be reported separately. ¿ American Geophysical Union 1995