Special features of the optical-vortex (OV) beams generated by thick holographic elements (HE) with embedded phase singularity are considered theoretically. The volume HE structure is based on the 3D pattern of interference between an OV beam and a standard reference wave with regular wavefront. The incident beam diffraction is described within the framework of a linear single-scattering model in which the volume HE is represented by a set of parallel thin layers with the "fork" holographic structure. An explicit integral expression is derived for the complex amplitude distribution of the diffracted paraxial beam with OV. The numerical analysis demonstrates that the HE thickness may essentially influence not only selectivity and efficiency of the OV beam generation but also the amplitude and phase profile of the diffracted beam as well as regularities of its propagation. We have studied the generated OV morphology and laws of its evolution; in particular, the possibility of obtaining a circularly symmetric OV beam regardless of the diffraction angle is revealed.
The frequency shift of a helical light beam experiencing the rotation near the axis differing from its own axis (conical evolution) is studied theoretically. Both the energy and the kinematic approaches lead to a paradoxical conclusion that after a whole cycle of the system rotation the beam does not return to its initial state. Another paradox is manifested in the peculiar behavior of the beam transverse pattern rotation at different geometric parameters of the evolving system. A fundamental role of the detecting system motion is substantiated. The special 'natural" observer's motion is found for which both paradoxes are eliminated. Relations ofthe described facts with the Hannay's geometric phase concept are discussed.
Abstract. Based on the linear theory for optical vortex (OV) formation in volume holographic elements (HE) with embedded phase singularity (A. Bekshaev et al., Opt. Commun. 285 (2012) 4005), we analyze theoretically the OV-beams obtained when the incident Gaussian beam axis deviates from the optical axis of the HE. For different displacements of the incident beam with respect to the HE centre, the spatial characteristics of the diffracted beams and their evolution during the post-HE propagation are investigated numerically with allowance for the radiation extinction in the HE depth. A special attention is paid to behaviour of the beam centroid (centre of gravity) trajectory. The sensitivity of the generated OV-beam profile to the incident beam misalignments can be used for the output beam shaping and control, in particular, for compensation of the OV-beam distortions associated with the light extinction.
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