• Photonics Research
  • Vol. 12, Issue 1, 172 (2024)
Shengyang Wu1、2, Benli Yu1、2, and Lei Zhang1、2、*
Author Affiliations
  • 1Key Laboratory of Opto-electronic Information Acquisition and Manipulation, Ministry of Education, Anhui University, Hefei 230601, China
  • 2Information Materials and Intelligent Sensing Laboratory of Anhui Province, Anhui University, Hefei 230601, China
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    DOI: 10.1364/PRJ.498502 Cite this Article Set citation alerts
    Shengyang Wu, Benli Yu, Lei Zhang. Mutual aid instead of mutual restraint: interactive probing for topological charge and phase of a vortex beam of large aberrations[J]. Photonics Research, 2024, 12(1): 172 Copy Citation Text show less

    Abstract

    An imperfect propagation environment or optical system would introduce wavefront aberrations to vortex beams. The phase aberrations and orbital angular momentum in a vortex beam are proved to be mutually restrictive in parameter measurement. Aberrations make traditional topological charge (TC) probing methods ineffective while the phase singularity makes phase retrieval difficult due to the aliasing between the wrapped phase jump and the vortex phase jump. An interactive probing method is proposed to make measurements of the aberrated phase and orbital angular momentum in a vortex beam assist rather than hinder each other. The phase unwrapping is liberated from the phase singularity by an annular shearing interference technique while the TC value is determined by a Moiré technique immune to aberrations. Simulation and experimental results proving the method effective are presented. It is of great significance to judge the characteristics of vortex beams passing through non-ideal environments and optical systems.
    U=Rexp[i(lθ+φ)],

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    Ii=R2+R02+2RR0cos[lθ+φ+(i1)(π/2)],

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    Ip=cos(lθ+φ)=(I1I3)/(I1I3)2+(I2I4)2.

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    {E(sr,θ)=R(rs,θ)exp{i[lθ+φ(sr,θ)]}E(r/s,θ)=R(r/s,θ)exp{i[lθ+φ(r/s,θ)]},

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    Is=|E(rs,θ)+E(r/s,θ)|2=A+Bcos[φ(rs,θ)φ(r/s,θ)],

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    φ=φ(r,θ)=RSPR[φ(rs,θ)φ(r/s,θ)].

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    Iv=cos[φ(r,θ)].

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    IM=2·Iv·Ip=2  cos(lθ+φ)cos(φ)=cos(lθ)+cos(lθ+2φ).

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    IM=cos(lθ)+cos[lθ+2(φ+φc)].

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    ProbeM=cos(lθ)=IFT{TL[FT(IM)]},

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    cos(lθ+φi)=cosl(θ+Δθ)Δθ=φil,

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    l=p1+Δαα¯,

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    Shengyang Wu, Benli Yu, Lei Zhang. Mutual aid instead of mutual restraint: interactive probing for topological charge and phase of a vortex beam of large aberrations[J]. Photonics Research, 2024, 12(1): 172
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