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Scientific Reports

Measuring the Topological Charge of Orbital Angular Momentum Beams by Utilizing Weak Measurement Principle

Zhu Jing, Pei Zhang, Qichang Li, Feiran Wang, Chenhui Wang, Yingnan Zhou, Jinwen Wang, Hong Gao, L. C. Kwek, Fuli Li

Published May 29, 2019• 17 citations
Publisher

Abstract

According to the principle of weak measurement, when coupling the orbital angular momentum (OAM) state with a well-defined pre-selected and post-selected system of a weak measurement process, there will be an indirect coupling between position and topological charge (TC) of OAM state. Based on this we propose an experiment scheme and experimentally measure the TC of OAM beams from -14 to 14 according to the weak measurement principle. After the experiment the intrinsic OAM of the beams changed very little. Weak measurement, Topological Charge, OAM beams.

DOI
10.1038/s41598-019-44465-z

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According to the principle of weak measurement, when coupling the orbital angular momentum (OAM) state with a well-defined pre-selected and post-selected system of a weak measurement process, there will be an indirect coupling between position and topological charge (TC) of OAM state. Based on this we propose an experiment scheme and experimentally measure the TC of OAM beams from -14 to 14 according to the weak measurement principle. After the experiment the intrinsic OAM of the beams changed very little. Weak measurement, Topological Charge, OAM beams.
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.
We proposed and analyzed a scheme of precisely measuring orbital angular momentum (OAM) of the vortex beams with the help of weak measurement process. The orbital angular momentum information lll of the unknown OAM state can be obtained by its spatial displacements. The valid condition of precisely measuring orbital angular momentum was completely discussed. Interestingly, it is shown that the measurement by using the two-dimensional spatial displacements jointly is very useful for precisely measuring the OAM state with a large orbital angular momentum lll. The signal-to-noise ratio of the measurement can be enhanced by increasing the weak-coupling $\ensuremath{\gamma}$ linearly as the valid condition is still satisfied. For fixed $\ensuremath{\gamma}$, the maximal signal-to-noise ratio for each weak value increases with the decrease of the weak value.
We develop a weak measurement scheme for measuring orbital angular momentum (OAM) of light based on the global topology in wave function. We introduce the spin-orbit coupling to transform the measurement of OAM to the pre- and postselected measurement of polarization. The OAM number can be precisely and promptly recognized using single-shot detection without the need for spatial resolution. More significantly, the measurement results exhibit topological robustness under random phase perturbations. This scheme has the potential to be applied as a paradigm in the OAM-based optical computing, metrology and communication.
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.
In the paper, we present a method for the measurement of the orbital angular momentum (OAM) superposition state by making use of the characteristics of the beam's helical phase structure and Gouy phase. With the rotation angle and the petal-like number of the OAM superposition state, one can efficiently extract the component OAM mode of the OAM super-position state by the method. We derive the simple relationship between the OAM superposition state's rotation angle and the propagation distance, which is verified by numerical simulations and experiments. The results show that the proposed method can detect the sign and the topological charge of the component OAM modes. Additionally, the proposed method has a higher fault tolerance and has significance for optical communication based on OAM superposition state.