Liquid crystal geometrical phase optical elements and a system for generating and rapidly switching helical modes of an electromagnetic wave, based on these optical elements

An optical system for generating helical modes of propagation of an input beam of optical radiation having a predetermined circular polarization state, including:

• a geometrical phase optical element (q-PBOE) orientated transversely to the direction of propagation of the beam, comprising a birefringent means with a spatially inhomogeneous optical axis in a plane orthogonal to the direction of propagation of the input radiation beam, for modulating the phase of the wavefront of the said radiation, the optical axis being orientated according to the geometrical relation
• α(x, y)=α(r, Φ)=qΦ+α0
• where α is the angle formed between the optical axis of the birefringent means and a reference axis of a predetermined Cartesian reference system in a plane orthogonal to the direction of propagation of the beam, in which r, Φ are coordinates of the corresponding polar reference system, centred on the axis of propagation of the wavefront, q and α0 being constants,
• the said element (q-PBOE) being adapted to transform a circular polarized input radiation beam into a helical mode with a wavefront having a helical surface, the handedness of which is a function of the handedness of the input polarization, and
• electro-optical modulation means (EO, QW) for switching the circular polarization of the input radiation between a pair of polarization states of opposite handedness,
• the system being arranged to switch between different orders of helicity of the radiation beam emerging from the said geometrical phase optical element (q-PBOE) by switching the circular polarization state of the input radiation.