A New Twist on Astigmatic Transformation: Beyond Laguerre-Gaussian Beams

Abstract

Astigmatic transformation is widely used to convert the azimuthal phase structure of Laguerre-Gaussian vortex beams into intensity patterns from which the topological charge can be read out. Here, we show that this phase-to-intensity conversion is not just restricted to the Laguerre-Gaussian radial profile. We derive analytical expressions for the astigmatically transformed high-order Bessel--Gauss and perfect optical vortex fields, and find that, despite their substantially different radial structures, the number of intensity minima is directly set by the accumulated azimuthal phase winding. Numerical simulations and experimental measurements on both beam families confirm this result, establishing astigmatic transformation as a direct probe of the topological charge of scalar structured optical fields. We further extend the approach to non-separable vector Bessel-Gauss beams, in which the spatial and polarization degrees of freedom are coupled, and show that polarization-resolved detection allows the topological charge of the constituent spatial modes to be determined independently.