Orbital and spin angular momentum in conical diffraction

Abstract

The angular momentum J inc of a light beam can be changed by passage through a slab of crystal. When the beam is incident along the optic axis of a biaxial crystal, which may also possess optical activity (chirality), the final angular momentum J can have both orbital (J orb) and spin (J sp) contributions, which we calculate paraxially exactly for arbitrary biaxiality and chirality and initially uniformly polarized beams with circular symmetry. For the familiar special case of a non-chiral crystal with fully developed conical-refraction rings, J is purely orbital and equal to J inc /2, reflecting an interesting singularity structure in the beam. Explicit formulas and numerical computations are presented for a Gaussian incident beam. The change in angular momentum results in a torque on the crystal, along the axis of the incident beam. An additional, much larger, torque, about an axis lying in the slab, arises from the offset of the cone of conical refraction relative to the incident beam.

Conical refraction: fundamentals and applications

“…As reported in Ref. [140], for ρ 0 = 1.50 the OAM of the CR beam is maximum compared with any other value of ρ 0 . Near the focal plane the twist is more appreciable at the central spot.…”

“…However, note that at variance with the results expected for a focused Gaussian beam, the S 1 and S 2 parameters of CR beams obtained from CP input beams not only rotate along the Z axis but also twist around it at the focal plane. CR beams possess non-integer OAM that is generated due to the spin-orbit coupling provided by the biaxial crystal, as it has been reported by Berry and co-workers [140]. In Ref.…”

“…In Ref. [140] it is shown that the total OAM J OAM and total spin angular momentum (SAM) J SAM carried by the CR beam as a function of ρ 0 and of the initial total angular momentum J 0 are:…”

“…It is also promising the generation of polarization-tunable potentials to inject, extract and ma-nipulate ultra-cold atoms [55,144]. Additionally, by taking into account that the CR beams posses orbital angular momentum [140] and that the biaxial crystals used are transparent to a wide frequency range, the presented technique could be an alternative for the production of high-frequency vortex beams for molecular-scale super-resolution microscopy [145]. Finally, by using quantum sources, CR vector beams can be a tool for testing new Bell-like inequalities with hybrid polarization-momentum states useful in quantum information technologies [146].…”

Conical intersections for light and matter waves

“…Alternatively in combination with a confining potential in the longitudinal (propagation) direction, one can create quasi-1D ring traps using either the two bright rings or the separating dark ring [68,69]. Additionally, the conversion between different pseudospin states during conical diffraction enables the controlled generation of orbital angular momentum, optical vortices, and other wave singularities [5,22,50,70].…”