Quantitatively measuring the orbital angular momentum density of light

Abstract

Although many techniques are efficient at measuring optical orbital angular momentum (OAM), they do not allow one to obtain a quantitative measurement for the OAM density across an optical field and instead only measure its global OAM. Numerous publications have demonstrated the transfer of local OAM to trapped particles by illustrating that particles trapped at different radial positions in an optical field rotate at different rotation rates. Measuring these rotation rates to quantitatively extract the OAM density is not only an indirect measurement but also a complicated experiment to execute. In this work we theoretically calculate and experimentally measure the OAM density of light, for both symmetric and non-symmetric optical fields. We outline a simple approach using only a spatial light modulator and a Fourier transforming lens to measure the OAM spectrum of an optical field and we test the approach on superimposed non-diffracting higher-order Bessel beams. We obtain quantitative measurements for the OAM density as a function of the radial position in the optical field for both symmetric and non-symmetric superpositions, illustrating good agreement with the theoretical prediction. The ability to measure the OAM distribution of optical fields has relevance in optical tweezing, and quantum information and processing.