Birefringence detection of a gradient-index lens based on astigmatic transformation of a Bessel beam

A method is proposed for detecting birefringence of mechanically free parabolic gradient-index lenses based on the astigmatic transformation of the zero-order Bessel beam. Numerical simulation shows a clearly visible distortion of the intensity structure in the propagation of scalable astigmatic Bessel beams. The degree of astigmatism can be determined from the intensity distribution of the distorted beam. Similar patterns are also obtained in an experimental study of the passage of a Bessel beam through a quarter-pitch gradient-index lens, which indicates the presence of birefringence of the lens material. Comparison of experimental data and numerical simulation shows the possibility of measuring the optical path difference of no worse than 0.05λ0 between ordinary and extraordinary beams.