Detecting small variation rate of refractive index based on OAM interferometry and time–frequency analysis

•A scheme for detecting a small variation rate of the refractive index based on orbital angular momentum interferometry is proposed and demonstrated in this paper.•A nonuniform RI variation rate is measurable by using the proposed scheme with a resolution of 3.46 × 10−7 s−1 in this work.•It is proved by experiments that the measurement error of variation rate of the refractive index of using the OAM beam is smaller than that using the Gaussian beam.•It is proved by numerical simulations and experiments that the measurement error of variation rate of the refractive index decreases with increasing topological charge of OAM beam. A scheme for detecting a small variation rate of the refractive index (RI) based on orbital angular momentum (OAM) interferometry and time–frequency analysis is proposed and demonstrated in this paper. Two vortex beams carrying OAM of opposite signs are used for interference to produce a petal-like intensity distribution. The RI variation of the sample leads to a time-varying phase delay between the reference and measurement paths and causes a rotation of the petal-like pattern. The rotation angular velocity of the petal-like pattern is proportional to the variation rate of RI, and the normalized cross correlation method is used to estimate it. Then, a time–frequency analysis method is employed to study the time evolution of the variation rate of RI. Four kinds of RI models with different variation rates are simulated, the results are consistent with expectations. Experiments for detecting the RI variation rate of water are also carried out, the results are generally in agreement with the theoretical values and confirm that a nonuniform RI variation rate is measurable. An RI variation rate resolution of 3.46 × 10−7 s−1 is obtained. It is proven that the measurement error of using the OAM beam is smaller than that using the Gaussian beam, and the measurement error decreases with increasing topological charge of OAM beam. The direction of RI changes can be distinguished. The proposed measurement method is simple in structure, and extends a new approach to detect the relation between the RI and other physical parameters.