Accurately identifying mode indices of Laguerre-Gaussian beams via weak measurements

We propose an efficient method to accurately identify two mode indices (p and l) of Laguerre-Gaussian (LG) beams simultaneously with weak value measurement (WVM). Concise relations between the spatial displacements from the WVM and two mode indices of LG beams have been obtained. Compared with the traditional measurements, the advantage of using our method is that LG beams with large p and l can be identified precisely. A joint spatial WVM with a looser approximate condition has been presented, which realizes better identification than the individual spatial WVM with correction terms or strict approximation. Furthermore, the signal-to-noise ratio (SNR) of the spatial WVM is also discussed.