Direct measurement of Stokes orbital parameters

The method of direct measurement of the Stokes orbital parameters is based on the analogy with the standard approach to measuring the Stokes polarization parameters of structured beams. A cylindrical lens serves as a quarter-wave plate, and the action of the polarizer is associated with the action of the matrix operator of the moments of intensity P of the second order on the intensity pattern of the structured beam, taken in front of the cylindrical lens and in the double focus plane. Physically measurable elements of the symplectic 4D matrix P are used, namely, the elements of the 2D submatrix W. The measurement process involves only two snapshots of the intensity distribution, the computer processing of which allows calculating six key components of the sought parameters. Calculation of the first two Stokes orbital parameters S1 and S2 involves computer processing of the first snapshot of the intensity pattern in front of the cylindrical lens. The third Stokes orbital parameter S3 is calculated during computer processing of the second snapshot of the intensity pattern in the double focus plane as the difference between the off-diagonal elements of the submatrix W in the ϕ1=π/4 and ϕ1=π/4 directions. The basis for such a choice of an approach to measuring the parameter S3 is the principle of reciprocity, discovered by us, between the orbital angular momentum of the beam under study and the off-diagonal elements Wxy in the plane of the double focus of the cylindrical lens. The experimental results obtained are in good agreement with computer modeling, as well as with the results of other authors.