Projective Measurement of LG Modes via Refractive Beam Shaping

Rachel Sampson¹, Mohammad Mirhosseini², and Robert Boyd^2,3,4

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
³ Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
⁴SUPA, School of Physics and Astronomy, University of Glasgow, G12 8QQ, UK.

We describe an experimental technique for separating the orthonormal basis set of Laguerre-Gaussian (LG) radial modes. In this method, we exploit the orthogonality of the modes to use projective measurements to identify the radial modes. Theoretical results suggest this method is capable of correctly identifying LG radial modes, p=1-5, with about 80% efficiency and results in low cross-talk between modes. The ability to efficiently and accurately identify LG radial modes could have applications in increasing channel capacity in free-space communication and tolerance to eavesdropping attacks in quantum key distribution.

This research was supported in part by NSF award PHY-1156339.