Alieva Krasheninnikova, TatianaBastiaans, Martin J.2023-06-202023-06-202005-06-151. E. G. Abramochkin and V. G. Volostnikov, J. Opt. A, Pure Appl. Opt. 6, S157 (2004). 2. A. Wünsche, J. Phys. A 33, 1603 (2000). 3. A. A. Malyutin, Quantum Electron. 34, 165 (2004). 4. S. A. Collins, Jr., J. Opt. Soc. Am. 60, 1168 (1970). 5. R. K. Luneburg, Mathematical Theory of Optics (U. California Press, 1966). 6. R. Simon and K. B. Wolf, J. Opt. Soc. Am. A 17, 2368 (2000). 7. M. Abramowitz and I. A. Stegun eds., Pocketbook of Mathematical Functions (Harri Deutsch, 1984). 8. R. Simon and G. S. Agarwal, Opt. Lett. 25, 1313 (2000). 9. M. J. Bastiaans and T. Alieva, J. Phys. A 38, L73 (2005).0146-959210.1364/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