Sensing with Twisted Light: Precision Measurement of Fractional Azimuthal Index to Determine Refractive Index

Light beams possessing orbital angular momentum (OAM) have gained significant interest in areas such as optical manipulation, quantum entanglement, and super-resolved imaging. In itself, the OAM for a Laguerre-Gaussian beam is proportional to the azimuthal index of the light field, $l$. It is in fact continuous in nature and a non-trivial parameter to measure. The ability to determine $l$ precisely would broaden the use of such beams for new applications. In this study, we generate Laguerre-Gaussian beams of differing $l$ through mode conversion using microscopic spiral phase plates (SPPs). The exact value of $l$ imparted for a given incident wavelength is dependant upon the refractive index of the media within which the SPP is immersed. Here, we show an ultra-precise approach based on laser speckle to measure the azimuthal index of these generated beams to a precision of $2\,{\times}\,10^{-5}$. This is an improvement of three orders of magnitude over previous studies. In turn, this leverages an ultra-precise measurement of the refractive index of the medium surrounding the SPP, with a best measured precision of $6.4\,{\times}\,10^{-7}$\,refractive index units. This is confirmed to be at the shot-noise limit of the system. Our study interrogates samples of sucrose and haemoglobin, only 300\,pL in volume, within a microfluidic channel. This demonstration of an original form of microfluidic refractive index sensor, based on mode conversion to light fields with OAM, may be multiplexed to measure spatio-temporal variations and gradients within biological samples.