Mode conversion of controllable anomalous elliptical hollow beams in strongly nonlocal nonlinear media induced by cross-phase

This paper proposes a controllable anomalous elliptical hollow cross-phase (CAEHCP) beam. Based on the Huygens-Fresnel integral principle and the transformation matrix of strong nonlocal nonlinear medium (SNNM), the analytical expression of beam propagation in SNNM is derived. The propagation characteristics of the CAEHCP beam-including intensity, phase, axial intensity, curvature radius, and beam width-are computed and analyzed numerically. Additionally, we examine the impact of the cross-phase on critical power variations. The results indicate that, under certain conditions, the intensity distribution demonstrates symmetry relative to parameter <i>a</i>, enabling the CAEHCP beam to transition into a hollow structure. The cross-phase effect induces periodic changes and rotation in the transverse intensity distribution of the CAEHCP beam. When the beam modulation parameter is a complex number, the intensity distribution exhibits rotational characteristics, with the rotation amplitude gradually increasing as the cross-phase increases. These findings establish a theoretical foundation for potential applications of cross-phase beams in optical communication, light-field control, and related fields.