  We continue the study, from a semiclassical viewpoint, of Calvo and Picon's
operators, as manipulating photon states in quantum communication. In a
previous paper, we defined a one-dimensional model operator and studied it
analytically before moving on to Calvo and Picon's full two-dimensional
operators. In the present paper, we show how the one-dimensional operator may
also be useful as an experimental model, since it allows manipulations of
two-dimensional Laguerre-Gaussian modes; the intensity distributions (in
physical space) of the Laguerre-Gaussian modes then approximately flow along
the elliptic curves studied earlier. Since the Wigner transform is fundamental
in the study of Laguerre-Gaussian modes, we give a slightly expanded and
improved treatment of the semiclassical Wigner transform, which was only
briefly mentioned in the previous paper.
