SELF-IMAGING WITH FINITE-ENERGY

General solutions and conditions are presented for paraxial waves that image themselves with different scales through free propagation. Thes e waves, represented as superpositions of Gauss-Laguerre modes, have f inite energy and thus finite effective width. The self-imaging wave fi elds described by Montgomery [J. Opt. Sac. Am. 57, 772 (1967)], which possess a Fourier transform that is confined to a ring structure, are obtained as a specific limiting case of an infinite aperture. (C) 1997 Optical Society of America.