Scaling of the Fractional Angular Momenta of a Light Polarization Möbius Strip in Extreme Non Linear Optics

The rotational symmetries of a light beam are linked with angular momenta. Thus, the spin and orbital angular momentum are respectively related to the rotational invariance of the polarization vector and of the spatial distribution of the light field. They may take values which are integer multiple of ℏ. In some cases, a generalized angular momentum, linear combination of the first two and taking fractional values, appears naturally. We have shown theoretically and experimentally that it is conserved during high harmonics generation, yielding beams with half integer units of ℏ angular momenta.