Interaction of the Lissajous singularity and singular Lissajous line passing through an astigmatic lens

The interaction of the Lissajous singularity and singular Lissajous line in the presence of an astigmatic lens is studied. It is found that the singular Lissajous line is usually unstable, and disappears after passage through the lens. The creation and annihilation of one or two Lissajous singularities may take place by varying the astigmatic coefficient, off-axis parameter, and propagation distance. A comparison with the interaction of the Lissajous singularity and singular Lissajous line in the free-space propagation and in the presence of an ideal lens, and with the vortex–edge dislocation interaction is made. The results are illustrated numerically and interpreted analytically.