The handedness of Lissajous singularities in polychromatic vector optical fields

Propagation property of the non-paraxial vector Lissajous singularity beams in free space

“…Since Kessler and Freund studied polarization singularities in polychromatic vector wave fields, much interest has been exhibited in the singular phenomena of polychromatic vector beams [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The Lissajous singularities can be created by second-hormonic generation with commensurate frequencies or can emerge from the incoherent addition of two incommensurate vector beams [1,4,[10][11][12].…”

“…The Lissajous singularities can be created by second-hormonic generation with commensurate frequencies or can emerge from the incoherent addition of two incommensurate vector beams [1,4,[10][11][12]. It is well known that there exist Lissajous figures with definite shapes after an enough large number of optical cycles whether the frequencies of polychromatic vector beams are coherent or incoherent [1,4,14,15].…”