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Optics Express

Experimentally measuring the mode indices of Laguerre-Gaussian beams by weak measurement

Zhu Jing, Pei Zhang, Feiran Wang, Yunlong Wang, Qichang Li, Ruifeng Liu, Jinwen Wang, Hong Gao, Fuli Li

Published Jan 28, 2021• 13 citations
Publisher

Abstract

As a special experimental technique, weak measurements extract very little information from the measured system and does not cause the measured state to collapse. When coupling the Laguerre-Gaussian (LG) state with a well-defined pre- and post-selected system of a weak measurement process, there will be an indirect interconnection between the expected value of coordinate operators of the final state and the mode indices of the measured LG state. The mode of the light is impacted very slightly after the weak measurement. Based on this we propose an experiment scheme and have managed to experimentally measure the mode indices of LG beams spanning from l = -6 to l = +6, p = 0 to p = +8 accurately with the final intensity distributions approximatly at their origin.

DOI
10.1364/oe.416671

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As a special experimental technique, weak measurements extract very little information from the measured system and does not cause the measured state to collapse. When coupling the Laguerre-Gaussian (LG) state with a well-defined pre- and post-selected system of a weak measurement process, there will be an indirect interconnection between the expected value of coordinate operators of the final state and the mode indices of the measured LG state. The mode of the light is impacted very slightly after the weak measurement. Based on this we propose an experiment scheme and have managed to experimentally measure the mode indices of LG beams spanning from l = -6 to l = +6, p = 0 to p = +8 accurately with the final intensity distributions approximatly at their origin.
Here, joint spatial weak measurements with higher-order Laguerre-Gaussian (LG) point states are investigated experimentally. From the intensity patterns of the final LG point states, two dimensional position operators 〈X〉 and 〈Y〉 as well as high-order position operators 〈XY〉, 〈X2 − Y2〉, 〈X3〉, and 〈Y3〉 are extracted simultaneously, from which both the complex weak values and joint weak values of two non-commuting observables can be obtained. The enhancement of joint weak values by the postselection state are analyzed. The simple relationship between the expectation values of position operators and the azimuthal and radial indexes of LG modes allows us to identify the mode indexes directly. A simple and robust scheme based on an optical window is demonstrated to monitor the LG mode indexes. These findings deepen the understanding of the weak measurement and provide an alternate and effective method for LG mode index monitoring.
Abstract 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.
As a special experimental technique, weak measurement extracts very little information about the measured system and will not cause the measured state collapse. When coupling the orbital angular momentum (OAM) state with a well-defined pre-selected and post-selected system of a weak measurement process, there is an indirect coupling between position and topological charge (TC) of OAM state. Based on these ideas, we propose an experimental scheme that experimentally measure the TC of OAM beams from -14 to 14 through weak measurement.
Through the von Neumann interaction followed by post-selection, we can extract not only the eigenvalue of an observable of the measured system but also the weak value. In this post-selected von Neumann measurement, the initial pointer state of the measuring device is assumed to be a fundamental Gaussian wave function. By considering the optical implementation of the post-selected von Neumann measurement, higher-order Gaussian modes can be used. In this paper, we consider the Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) modes as pointer states and calculate the average shift of the pointer states of the post-selected von Neumann measurement by assuming the system observable with and for an arbitrary interaction strength, where represents the identity operator. Our results show that the HG and LG pointer states for a given coupling direction have advantages and disadvantages over the fundamental Gaussian mode in improving the signal-to-noise ratio. We expect that our general treatment of the weak values will be helpful for understanding the connection between weak- and strong-measurement regimes and may be used to propose new experimental setups with higher-order Gaussian beams to investigate further the applications of weak measurement in optical systems such as the optical vortex.
We develop a novel technique to measure small angular and lateral displacements of structured light beams. The technique relies on using high-order Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) modes, which have well-defined symmetry under inversion. We show that the displacements of such fields lead to a crosstalk with modes with opposite parity under inversion, which we measure optimally with an interferometric parity sorter. Using this technique, we achieve improvement factors of up 41 in the signal-to-noise ratio using Hermite-Gaussian modes and 21 using Laguerre-Gaussian modes with order up to 20, as compared to the fundamental Gaussian mode. Our results present a viable way of using structured light for metrology that does not demand quantum light or homodyne detection.
The basics of weak measurement and its various applications are discussed here. The optical analogue of weak measurement. which was predicted by E C G Sudarshan was also demonstrated with the experimental results. The optical activity of chiral molecules is also calculated with the help of weak measurement. We also demonstrate simultaneous weak value amplification of both the angular GH and the IF shifts in partial reflection of a fundamental Gaussian beam at planar dielectric interfaces. We employ pre and post selection schemes with appropriate linear polarization basis states for simultaneous weak measurements and amplification of both of these shifts.We also studied these GH and IF shifts for higher order beams (for example Vortex beams)and how its get coupled. Geometric Hall effect of light is also studied with the help of weak measurement and we get the expected nature according to the theory.