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Quasi-phase-matching of high-order-harmonic generation using polarization beating in optical waveguides

Lewis Z. Liu, Kevin O'Keeffe, and Simon M. Hooker
Phys. Rev. A 85, 053823 – Published 18 May 2012; Erratum Phys. Rev. A 87, 039902 (2013)
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  • INTRODUCTION
  • POLARIZATION BEATING QPM
  • ENVELOPE FUNCTION FOR PBQPM
  • PROPERTIES OF PBQPM
  • DISCUSSION
  • CONCLUSION
  • ACKNOWLEDGEMENTS
    • References

    Abstract

    A scheme for quasi-phase-matching high-harmonic generation is proposed in which polarization beating within a hollow core birefringent waveguide modulates the generation of harmonics. The evolution of the polarization of a laser pulse propagating in a birefringent waveguide is calculated and is shown to periodically modulate the harmonic generation process. The optimum conditions for achieving quasi-phase-matching using this scheme are explored and the growth of the harmonic intensity as a function of experimental parameters is investigated.

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    • Received 31 December 2011

    DOI:https://doi.org/10.1103/PhysRevA.85.053823

    ©2012 American Physical Society

    Erratum

    Erratum: Quasi-phase-matching of high-order-harmonic generation using polarization beating in optical waveguides [Phys. Rev. A 85, 053823 (2012)]

    Lewis Z. Liu, Kevin O’Keeffe, and Simon M. Hooker
    Phys. Rev. A 87, 039902 (2013)

    Authors & Affiliations

    Lewis Z. Liu*, Kevin O'Keeffe, and Simon M. Hooker

    • Clarendon Laboratory, Physics Department, University of Oxford Parks Road, Oxford OX1 3PU, United Kingdom

    • *l.liu1@physics.ox.ac.uk

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    Issue

    Vol. 85, Iss. 5 — May 2012

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    Images

    • Figure 1
      Figure 1
      Ellipticity beating for different incidence angles Θ. From top to bottom: Dotted light-gray line shows Θ=45∘, solid gray line shows Θ=30∘ and Θ=70∘; and dot-dashed gray line shows Θ=20∘ and Θ=80∘.Reuse & Permissions
    • Figure 2
      Figure 2
      Top graph: (a) Variation of the harmonic generation efficiency, f(z)=f[ɛ(z)], as a function z for q=27 and Θ=45∘. Bottom graph: (b) Real part of the of the x̂ component of the integrand (solid gray) and ŷ component (dashed black line). Assuming Lb=2Lc,y, Θ=45∘ and q=27.Reuse & Permissions
    • Figure 3
      Figure 3
      Relative HHG intensity for different phase-matching conditions assuming that Lb=2Lc,y, q=27, Θ=20∘ for PBQPM. The dashed magenta line shows perfect phase-matching, dashed black line for perfect quasi-phase-matching, dot-dashed cyan line for no phase-matching. The solid blue line shows the relative amplitude squared for the x̂ component while the solid red line shows the relative amplitude squared for the ŷ component. The thick gray line shows the total HHG intensity for PBQPM.Reuse & Permissions
    • Figure 4
      Figure 4
      PBQPM for Θ=34∘, q=27, and Lb=nLc,y with n=1,2,3,4. The top graph shows the relative harmonic intensity as a function of propagation distance z for perfect QPM (dashed black line), Lb=4Lc,y (dot-dashed red line), Lb=3Lc,y (solid green line), Lb=2Lc,y (dashed blue line), and Lb=Lc,y (dotted magenta line). The bottom four graphs show the p=y polarization source term Λy as a function of propagation distance z for (b) Lb=4Lc,y, (c) Lb=3Lc,y, (d) Lb=2Lc,y, and (e) Lb=Lc,y.Reuse & Permissions
    • Figure 5
      Figure 5
      PBQPM for q=27 and Lb=2Lc,y with Θ=30∘,80∘,45∘,20∘. The top graph shows the relative harmonic intensity as a function of z for perfect QPM (dashed black line) and coupling angles of Θ=30∘ (dot-dashed red line), Θ=80∘ (solid green line), Θ=45∘ (dashed blue line), Θ=20∘ (dotted magenta line). The bottom four groups show the p=y polarization source term Λy as a function of z for (b) Θ=30∘, (c) Θ=80∘, (d) Θ=45∘, and (e) Θ=20∘.Reuse & Permissions
    • Figure 6
      Figure 6
      Top graph: (a) Relative HHG intensity as a function of coupling angle Θ, normalized to perfect QPM after one beat length where Lb=2Lc,y for q=15 (solid red line), q=27 (dashed green line), q=39 (dotted blue line). Bottom graph: (b) Optimal angle Θ̂ as a function of harmonic order q for Lb=2Lc,y.Reuse & Permissions
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