Rodrigo Martín-Romo, José AugustoAlieva Krasheninnikova, TatianaCalvo Padilla, María Luisa2023-06-202023-06-202007-03-051094-408710.1364/OE.15.002190https://hdl.handle.net/20.500.14352/51043© 2007 Optical Society of America. Spanish Ministry of Education and Science is acknowledged for financial support, project TEC2005-02180/MIC.In this work we formulate the main properties of the gyrator operation which produces a rotation in the twisting (position-spatial frequency) phase planes. This transform can be easily performed in paraxial optics that underlines its possible application for image processing, holography, beam characterization, mode conversion and quantum information. As an example, it is demonstrated the application of gyrator transform for the generation of a variety of stable modes.engjournal articlehttp://dx.doi.org/10.1364/OE.15.002190http://www.opticsinfobase.org/open access535Orbital Angular-MomentumOptical-SystemsGaussian BeamsÓptica (Física)2209.19 Óptica Física