# The avalanche instability of the orbital angular momentum in combined vortex beams

## TL;DR

This paper introduces a real-time measurement method for the orbital angular momentum in vortex beams, revealing an avalanche instability where small perturbations cause significant changes in the orbital angular momentum.

## Contribution

The paper presents a novel real-time measurement technique for vortex beam amplitudes and phases, and demonstrates the avalanche instability of OAM in combined beams.

## Key findings

- Measurement error does not exceed 4% for 10-15 beams.
- OAM depends on fractional topological charge p, with maxima at integer charges.
- Weak perturbations cause sharp increases in partial beams with different topological charges.

## Abstract

We presented a new method for measuring the squares of the amplitudes and phases of partial vortex-beams in a complex beam array in real time. The method is based on measuring the high-order intensity moments and analyzing the solutions of a system of linear equations. Calibration measurements have shown that the measurement error at least for an array of 10-15 beams does not exceed 4%. It has theoretically and experimentally been shown that the orbital angular momentum (OAM) of combined singular beams depends essentially on the fractional topological charge p. For integer values of the topological charge, the OAM obtains the maximum value numerically equal to the topological charge of the singular beam. With weak deviations of the topological charge in the direction of fractional values, dips in the orbital moment appear. . It was experimentally shown that even a weak perturbation of the holographic grating leads to a sharp increase in the contribution of partial beams with other integer-order topological charges.

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Source: https://tomesphere.com/paper/1812.01257