Dynamical constants of structured photons with parabolic-cylindrical symmetry

Electromagnetic modes with parabolic-cylindrical symmetry and their dynamical variables are studied both in the classical and quantum realms. As a result, a dynamical constant for the electromagnetic field is identified and linked to the symmetry operator which supports it.

Figure 1

(Color online) Sample of (a) transverse intensity and (b) polarization structure of an odd EM TE Weber field. They correspond to the eigenvalue $a=-2$, $k_z=0.995\omega /c$, and the unit of length is taken as the wavelength.