Sorting Laguerre-Gaussian Radial Modes Via Projective Measurements

Rachel Sampson¹, Mohammad Mirhosseini², and Robert Boyd²

¹Department of Physics and Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA
²The Institute of Optics, University of Rochester, Rochester, NY 14627-0186, USA

Laguerre-Gaussian (LG) orbital angular momentum (OAM) modes have received considerable attention recently because of their applications in free-space communication and quantum key distribution, radial LG modes have been largely overlooked though despite applications in the same technologies. Many of the technologies that utilize LG OAM modes require the different modes be properly sorted and identified.

In this project, we focused on sorting LG radial modes via projective measurements. Utilizing projective measurements, we imaged an LG radial mode onto its conjugate mode, producing a Gaussian beam, which we then couped into a single mode fiber. We created the LG radial modes and the phase masks to trnsform the beam using a hologram realized by a spatial light modulator. Using the Gerchberg-Saxton method of phase retrieval, we calculated theoretical sorting efficiencies of approximately 80% for p=1-5.Impementation of the experimental set-up is ongoing.