Morizur, Jean-FrançoisNicholls, LachlanJian, PuArmstrong, SeijiTreps, NicolasHage, BorisHsu, MagnusBowen, WarwickJanousek, JiriBachor, Hans2016-05-242016-05-241084-7529http://hdl.handle.net/1885/101510Free space propagation and conventional optical systems such as lenses and mirrors all perform spatial unitary transforms. However, the subset of transforms available through these conventional systems is limited in scope. We present here a unitary programmable mode converter (UPMC) capable of performing any spatial unitary transform of the light field. It is based on a succession of reflections on programmable deformable mirrors and free space propagation. We first show theoretically that a UPMC without limitations on resources can perform perfectly any transform. We then build an experimental implementation of the UPMC and show that, even when limited to three reflections on an array of 12 pixels, the UPMC is capable of performing single mode tranforms with an efficiency greater than 80% for the first four modes of the transverse electromagnetic basis.This work was funded by the Centre of Excellence program of the Australian Research Council. It was supported by the Australian Research Council Discovery Project DP0985078 and the NCI National Facility at the Australian National University (ANU). We acknowledge the financial support of the Future and Emerging Technologies (FET) program within the Seventh Framework Programme for Research of the European Commission, under the FET-Open grant agreement HIDEAS, number FP7-ICT-221906.8 pages© 2010 Optical Society of America. http://www.sherpa.ac.uk/romeo/issn/1084-7529/ Author can archive pre-print (ie pre-refereeing) on author's personal website and institutional website (Sherpa/Romeo as of 19/12/2016) https://www.osapublishing.org/submit/review/copyright_permissions.cfm#posting One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited. (Publisher journal website 19/12/2016)unitary programmable mode converter (UPMC)spatialunitarytransformlightfieldfreespacepropagation2010-1110.1364/JOSAA.27.0025242016-06-14