• Chinese Optics Letters
  • Vol. 17, Issue 5, 050501 (2019)
Shasha Li1、2, Baifei Shen1、3、*, Wenpeng Wang1、**, Zhigang Bu1, Hao Zhang1、2, Hui Zhang1, and Shuhua Zhai1、2
Author Affiliations
  • 1State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
  • 2University of Chinese Academy of Sciences, Beijing 100049, China
  • 3Department of Physics, Shanghai Normal University, Shanghai 200234, China
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    DOI: 10.3788/COL201917.050501 Cite this Article Set citation alerts
    Shasha Li, Baifei Shen, Wenpeng Wang, Zhigang Bu, Hao Zhang, Hui Zhang, Shuhua Zhai. Diffraction of relativistic vortex harmonics with fractional average orbital angular momentum[J]. Chinese Optics Letters, 2019, 17(5): 050501 Copy Citation Text show less

    Abstract

    Vortex harmonics with fractional average orbital angular momentum are generated when a relativistic fractional vortex beam is incident on and reflected from an over-dense plane plasma target. A two-step model is presented to explain the far-field patterns of the harmonics. In the first step, a fundamental spot-shaped hole is produced during the hole-boring stage, and harmonics are generated simultaneously. In the second step, different order harmonics are diffracted by the hole and propagate to the far field. This process can be accurately described by the Fraunhofer diffraction theory. This work facilitates a basic recognition of fractional vortex beams.
    a(LGpl)=a0(2rr0)|l|exp(r2r02)exp(ilϕ)(1)pLpl(2r2r02)sin2(πt10T).(1)

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    ne={25ncexp(x13λ2λ)11λx13λ25nc13λx15λ,(2)

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    OAM¯=αsin(2απ)/2π.(3)

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    αnsin(2αnπ)/2π=n[α0sin(2α0π)]/2π.(4)

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    exp(iαϕ)=exp(iπα)sin(πα)π×m=+[exp(imϕ)/αm].(5)

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    E(x,y,z)=exp[i(x+πα)]sin(πα)π1+ix/ωG2×m=+[exp(imϕ)Pm(ρ)/αm],(6)

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    Pm(ρ)=π/8(i)|m|/2ρ1+ix/ωG2×exp[iρ24(1+ix/ωG2)]×[J|m|12ρ24(1+ix/ωG2)iJ|m|+12ρ24(1+ix/ωG2)],(7)

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    E(x,y,z)=exp[i(x+πα)]sin(πα)π1+ix/ωG2×m=100+100[exp(imϕ)Pm(ρ)/αm].(8)

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    E(y,z)=iλxholeexp(ikxhole)exp[ik(y2+z2)/(2xhole)]×E(yhole,zhole)exp[i2π(fyyhole+fzzhole)]dyholedzhole,(9)

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    Shasha Li, Baifei Shen, Wenpeng Wang, Zhigang Bu, Hao Zhang, Hui Zhang, Shuhua Zhai. Diffraction of relativistic vortex harmonics with fractional average orbital angular momentum[J]. Chinese Optics Letters, 2019, 17(5): 050501
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