Alieva Krasheninnikova, TatianaBastiaans, Martin J.2023-06-202023-06-202005-06-150146-959210.1364/OL.30.001461https://hdl.handle.net/20.500.14352/51279© 2005 Optical Society of America. T. Alieva (talieva@fis.ucm.es) thanks the Spanish Ministry of Education and Science for financial support (Ramon y Cajal grant and projects TIC 2002-01846 and TIC 2002-11581-E). M. J. Bastiaans’s e-mail address is m.j.bastiaans@tue.nl.A Collins transformation maps an orthonormal set of Hermite-Gaussian modes into an orthonormal set of beams with a Gaussian envelope. Among these beams are Laguerre-Gaussian beams and the recently introduced Hermite-Laguerre-Gaussian beams. Compact expressions for the complex field amplitudes of these modes are derived. The results obtained are useful for description of the propagation of light through first-order optical systems, for the solution of the phase-retrieval problem by noninterferometric techniques, and for the design of mode converters and information processing systems.engjournal articlehttp://dx.doi.org/10.1364/OL.30.001461http://www.opticsinfobase.org/open access535Gaussian beamsHermiteÓptica (Física)2209.19 Óptica Física