• Photonics Research
  • Vol. 12, Issue 11, 2726 (2024)
Tushar Sarkar1,3, Jiapeng Cai1, Xiang Peng1, and Wenqi He1,2,*
Author Affiliations
  • 1Key Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
  • 2Shenzhen Key Laboratory of Intelligent Optical Measurement and Detection, Shenzhen University, Shenzhen 518060, China
  • 3e-mail: tusharsarkar.sarkar@gmail.com
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    DOI: 10.1364/PRJ.538320 Cite this Article Set citation alerts
    Tushar Sarkar, Jiapeng Cai, Xiang Peng, Wenqi He, "Measuring the OAM spectrum of a fractional helical beam in a single shot," Photonics Res. 12, 2726 (2024) Copy Citation Text show less

    Abstract

    We propose and experimentally demonstrate a new technique, to our knowledge, to precisely measure the orbital angular momentum (OAM) spectrum of the fractional helical beam in a single shot. This is realized using a single-path interferometer scheme combined with space division multiplexing and polarization phase-shifting. Such a combination enables the single-shot recording of multiple phase-shifted interferograms, which leads to extracting the phase profile of the incident fractional helical beam. Furthermore, by adopting an orthogonal projection method, this measured phase is utilized to evaluate the corresponding OAM spectrum. To test the efficacy, a set of simulations and experiments for different fractional helical beams is demonstrated. The proposed method shows enormous potential to characterize the OAM spectrum in real time.
    U(r)=Alexp[i(lφφR)]x^+AR(r)y^,

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    exp(ilφ)=m=Cm(l)exp(imφ),

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    Up(ρ)=12(1ii1)Up(r),

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    Up(ρ)=(cos2βsinβcosβcosβsinβsin2β)Up(ρ),

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    Iβ(ρ)=Up*(ρ)Up(ρ)[|Ux(ρ)|2+|Uy(ρ)|2+Ux*(ρ)Uy(ρ)+Ux(ρ)Uy*(ρ)]{|Ux(ρ)|2+|Uy(ρ)|2+|Ux(ρ)||Uy(ρ)|cos[2β(φφR)]}[|Ux(ρ)|2+|Uy(ρ)|2+|Ux(ρ)||Uy(ρ)|cos(2βφd)],

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    Iβ(ρ)[Al2(ρ)+AR2(ρ)+2Al(ρ)AR(ρ)cos(2βφd)].

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    I0(ρ)[Al2(ρ)+AR2(ρ)+2Al(ρ)AR(ρ)cosφd],

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    Iπ/2(ρ)[Al2(ρ)+AR2(ρ)+2Al(ρ)AR(ρ)sinφd],

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    Iπ(ρ)[Al2(ρ)+AR2(ρ)2Al(ρ)AR(ρ)cosφd],

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    I3π/2(ρ)[Al2(ρ)+AR2(ρ)2Al(ρ)AR(ρ)sinφd].

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    φ(ρ)=arctan[I4(ρ)I2(ρ)I1(ρ)I3(ρ)],

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    Cm(ρ)=02πexp(imφ)U(ρ)dφ.

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    P(m)=1S0|Cm(ρ)|2rdr,

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