&lt;title&gt;Analysis of optical vortex beams with integer and fractional topological charge&lt;/title&gt;

Pas’ko, V. A.; Basistiy, I. V.; Vasnetsov, M. V.; Soskin, M. S.

doi:10.1117/12.558807

Cited by 16 publications

(15 citation statements)

References 5 publications

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“…This discrepancy is not surprising in view of approximate character of Eqs. (36) and (38). As is predicted by Eqs.…”

Section: Angular Selectivitysupporting

confidence: 76%

“…A simple theory of a thick HE has been presented that is based on the linear single scattering model and the Born approximation in which the HE is considered as a consequence of thin layers parallel to the hologram surface. This approach enables to consider the volume HE as a generalization of a thin CGH model that was developed and substantiated in the previous works [35][36][37][38][39][40][41][42][43][44][45][46].…”

Section: Resultsmentioning

confidence: 90%

“…Properties of the OV beams produced with the help of such CGHs and transformations they perform to beams already possessing OVs were studied in detail in a series of experimental and theoretical works [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. In particular, it was shown that a diffracted beam of a certain selected diffraction order is mathematically described in the same way as the beam formed after passing a spiral phase plate (helicoidal phase step) (see, e.g., Refs.…”

mentioning

confidence: 99%

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Generation of optical vortex light beams by volume holograms with embedded phase singularity

Bekshaev

Sviridova

Popov

et al. 2012

Optics Communications

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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.

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“…This discrepancy is not surprising in view of approximate character of Eqs. (36) and (38). As is predicted by Eqs.…”

Section: Angular Selectivitysupporting

confidence: 76%

Section: Resultsmentioning

confidence: 90%

mentioning

confidence: 99%

See 1 more Smart Citation

Generation of optical vortex light beams by volume holograms with embedded phase singularity

Bekshaev

Sviridova

Popov

et al. 2012

Optics Communications

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“…where M symbolizes the confluent hypergeometric function (Kummer function). The beams with complex amplitude distribution in form (14) already occurred in the theory of fork-like CGH [32,[34][35][36]40] and were called "Kummer beams". Noteworthy, the Kummer functions of the form (14) with integer non-negative μ can be represented via sums of μ + 1 terms containing modified Bessel functions ( [45], pt.…”

Section: Mathematical Formulation and Analysismentioning

confidence: 99%

Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity

Bekshaev¹,

Sviridova²

2010

Optics Communications

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Spatial characteristics of diffracted beams produced by a "fork" hologram from an incident circular Laguerre-Gaussian beam whose axis differ from the hologram optical axis are studied theoretically.General analytical representations for the complex amplitude distribution of a diffracted beam are derived in terms of superposition of Kummer beams or hypergeometric-Gaussian beams. The diffracted beam structure is determined by combination of the "proper" topological charge m of the incident vortex beam and the topological charge l of the singularity "imparted" by the hologram.Evolution of the diffracted beam structure is studied in detail for several combinations of m and l and for various incident beam displacements with respect to the optical axis of the hologram.Variations of the intensity and phase distribution due to the incident beam misalignment are investigated and possible applications for the purposeful optical-vortex beam generation and optical measurements are discussed.

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“…Their properties have been studied in many experimental and theoretical works [17,24,[25][26][27][28][29][30][31][32][33][34][35][36], though practically all of the results are limited to the case of a thin (plane) HE (in this case the generated OV-beams can be united within a special class of 'Kummer beams' [30], or 'hypergeometric-Gaussian beams' [34]). However, operation of such thin HEs is not free from essential drawbacks: simultaneous diffraction to a number of orders leads to low intensities of any of the individual diffracted beams, each diffracted OV-beam is rather sensitive to uncontrollable conditions of HE-induced transformations, and the whole OV-generation procedure suffers from low angular and spectral selectivities.…”

Section: Introductionmentioning

confidence: 99%

Optical vortex generation by volume holographic elements with embedded phase singularity: Effects of misalignments

Bekshaev¹,

Sviridova²,

Popov³

et al. 2013

Ukr. J. Phys. Opt.

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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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<title>Analysis of optical vortex beams with integer and fractional topological charge</title>

Cited by 16 publications

References 5 publications

Generation of optical vortex light beams by volume holograms with embedded phase singularity

Generation of optical vortex light beams by volume holograms with embedded phase singularity

Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity

Optical vortex generation by volume holographic elements with embedded phase singularity: Effects of misalignments

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