The handedness of Lissajous singularities in polychromatic vector optical fields

•The expression for the handedness of Lissajous singularities is derived.•The handedness of Lissajous singularities in free space is studied.•The handedness of Lissajous singularities propagation through an astigmatic lens is studied.•The handedness relates to the Stokes parameters of individual optical components their frequencies and the amplitude factors.

Starting from the basic definition, the explicit expression for the handedness of Lissajous singularities in polychromatic vector optical fields is derived, which is illustrated and used to study the handedness of Lissajous singularities in free space and propagation through an astigmatic lens. It is found that the handedness is not only related to the Stokes parameters S3i (i = 1, 2, ……, n) of constituting components of the polychromatic vector electric field, but also to their frequencies and the amplitude factors.