Abstract
Optical states characterized by an electromagnetic field with a spiral azimuthal phase are known as orbital angular momentum (OAM) states. Examples of structured light carrying OAM states include Laguerre-Gauss (LG) beams, which can be transformed into Hermite-Gauss (HG) beams through astigmatic transformations using cylindrical or spherical lenses. In this study, we explore the dynamics of OAM conservation by combining two noncommutative operations: astigmatic transformation, achieved with a tilted spherical lens, and an up-conversion process facilitated by a χ(2) crystal. In this experiment, we observe that the intensity distribution in the second harmonic (SH) beam undergoes a separation process resembling the stages of mitosis, a biological process where a single cell divides into two genetically identical daughter cells. The transformations in the SH beam closely mirror key mitotic phases, including metaphase, anaphase, and telophase. To validate these similarities, we analyze the intensity, phase, and electric field profiles obtained from numerical simulations. These findings are further supported by experimental results and enhanced through phase retrieval techniques.