Self-healing and self-matching effects in astigmatic structured beams as a basis for measuring orbital Stokes parameters

We have developed and experimentally implemented a technique for measuring the orbital Stokes parameters in both uniform, astigmatic-free and non-uniform, astigmatic structured beams in a first-order optical system, which generalizes a similar method [Photonics 11, 1095 (2024)10.3390/photonics11111095] developed only for astigmatic-free structured beams. The technique is based on the direct measurement of the <i>W</i>_xx, <i>W</i>_yy, and <i>W</i>_xy intensity moments as the observable average squared deviations in the beam intensity pattern. The relationship between the intensity moments and the orbital Stokes parameters is carried out due to the direct and reverse self-matching effect and self-healing effect, which, as we have revealed, manifest themselves in two critical planes of the astigmatic beam. The locations of these critical planes are specified by the equality of the radii of the astigmatic beam in the <i>x</i>- and <i>y</i>-directions. Besides, in the first and second critical planes, the phase Gouy difference <i>Γ</i>_xy in the <i>x</i> and <i>y</i> directions has a sharp burst to <i>π</i>/2 or vanish, respectively, that also was experimentally confirmed by us. To experimentally find locations of the critical planes, singularities in the ellipticity and the inclination angle of the major axis of the intensity ellipse of the beam intensity moments was employed. The considered technique of measuring the orbital Stokes parameters in astigmatic and astigmatism-free structured beams, followed by mapping onto the orbital Poincaré sphere, is easy to implement into a miniature measuring device with the appropriate choice of the lenses and improved computer software.