Abstract

Presented are predicted conversion rates for four-wave mixing of the output of the Ne-like Y soft-x-ray laser (15.495 nm) with that of an optical laser in a Na-like Ca plasma to give radiation at ~ 7.8 nm (approximate frequency doubling). Also presented are frequency tripling rates of the Ne-like Y laser in a Na-like V plasma to give radiation at 5.165 nm. In each case the nonlinear susceptibilities and converted intensities are calculated, and phase-matching considerations are discussed.

© 1992 Optical Society of America

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  1. S. E. Harris, “Generation of vacuum-ultraviolet and soft-x-ray radiation using high-order nonlinear optical polarizabilities,” Phys. Rev. Lett. 31, 341–344 (1973).
    [CrossRef]
  2. M. H. Muendel, P. L. Hagelstein, “Analysis of a soft-x-ray frequency doubler,” in Proceedings of the International Conference on Lasers ’89, D. G. Harris, T. M. Shay, eds. (Society for Optical and Quantum Electronics, McLean, Va., 1990), p. 34.
  3. M. H. Muendel, P. L. Hagelstein, “Four-wave frequency conversion of coherent soft x-rays in a plasma,” Phys. Rev. A 44, 7573–7579 (1991).
    [CrossRef] [PubMed]
  4. L. B. Da Silva, M. H. Muendel, R. W. Falcone, D. J. Fields, J. B. Kortwright, B. J. MacGowan, D. L. Matthews, S. Mrowka, G. M. Shimkaveg, J. E. Trebes, “Nonlinear optics with focused x-ray lasers,” in X-Ray Lasers 1990, G. J. Tallents, ed. (Institute of Physics, Bristol, England, 1991), p. 177.
  5. P. L. Shkolnikov, A. E. Kaplan, “Feasibility of x-ray resonant nonlinear effects in plasmas,” Opt. Lett. 16, 1153–1155 (1991).
    [CrossRef] [PubMed]
  6. P. L. Shkolnikov, A. E. Kaplan, “Discharge-plasma-x-ray-laser resonant couples for x-ray nonlinear optics,” Phys. Rev. A 44, 6951–6953 (1991).
    [CrossRef] [PubMed]
  7. P. L. Shkolnikov, A. E. Kaplan, “X-ray third-harmonic generation in plasmas of alkalilike ions,” Opt. Lett. 16, 1973–1975 (1991).
    [CrossRef] [PubMed]
  8. B. J. MacGowan, J. L. Bourgade, P. Combis, C. J. Keane, R. A. London, M. Louis-Jacquet, D. L. Matthews, S. Maxon, D. Naccache, M. D. Rosen, G. Thiell, D. A. Whelan, “Progress towards a 44 Å x-ray laser,” in Short Wavelength Coherent Radiation: Generation and Applications, R. W. Falcone, J. Kirz, eds. (Optical Society of America, Washington, D.C., 1988), Vol. 2, p. 2.
  9. J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, Orlando, Fla., 1984), pp. 1–147.
  10. B. Edlén, E. Bodén, “The Na i-like spectra of potassium and calcium, K ix and Ca x,” Phys. Scr. 14, 31–38 (1976).
    [CrossRef]
  11. E. Biémont, “Theoretical f values for sodium-like ions (11 ≤ Z ≤ 26),” Astron. Astrophys. Suppl. 31, 285–290 (1978).
  12. M. Weissbluth, Atoms and Molecules, student ed. (Academic, New York, 1978), pp. 159, 505–517.
  13. L. Cohen, W. E. Behring, “Wavelengths and levels of the Na I isoelectronic sequence from K ix through Mn xv,” J. Opt. Soc. Am. 66, 899–904 (1976).
    [CrossRef]

1991

M. H. Muendel, P. L. Hagelstein, “Four-wave frequency conversion of coherent soft x-rays in a plasma,” Phys. Rev. A 44, 7573–7579 (1991).
[CrossRef] [PubMed]

P. L. Shkolnikov, A. E. Kaplan, “Discharge-plasma-x-ray-laser resonant couples for x-ray nonlinear optics,” Phys. Rev. A 44, 6951–6953 (1991).
[CrossRef] [PubMed]

P. L. Shkolnikov, A. E. Kaplan, “Feasibility of x-ray resonant nonlinear effects in plasmas,” Opt. Lett. 16, 1153–1155 (1991).
[CrossRef] [PubMed]

P. L. Shkolnikov, A. E. Kaplan, “X-ray third-harmonic generation in plasmas of alkalilike ions,” Opt. Lett. 16, 1973–1975 (1991).
[CrossRef] [PubMed]

1978

E. Biémont, “Theoretical f values for sodium-like ions (11 ≤ Z ≤ 26),” Astron. Astrophys. Suppl. 31, 285–290 (1978).

1976

B. Edlén, E. Bodén, “The Na i-like spectra of potassium and calcium, K ix and Ca x,” Phys. Scr. 14, 31–38 (1976).
[CrossRef]

L. Cohen, W. E. Behring, “Wavelengths and levels of the Na I isoelectronic sequence from K ix through Mn xv,” J. Opt. Soc. Am. 66, 899–904 (1976).
[CrossRef]

1973

S. E. Harris, “Generation of vacuum-ultraviolet and soft-x-ray radiation using high-order nonlinear optical polarizabilities,” Phys. Rev. Lett. 31, 341–344 (1973).
[CrossRef]

Behring, W. E.

Biémont, E.

E. Biémont, “Theoretical f values for sodium-like ions (11 ≤ Z ≤ 26),” Astron. Astrophys. Suppl. 31, 285–290 (1978).

Bodén, E.

B. Edlén, E. Bodén, “The Na i-like spectra of potassium and calcium, K ix and Ca x,” Phys. Scr. 14, 31–38 (1976).
[CrossRef]

Bourgade, J. L.

B. J. MacGowan, J. L. Bourgade, P. Combis, C. J. Keane, R. A. London, M. Louis-Jacquet, D. L. Matthews, S. Maxon, D. Naccache, M. D. Rosen, G. Thiell, D. A. Whelan, “Progress towards a 44 Å x-ray laser,” in Short Wavelength Coherent Radiation: Generation and Applications, R. W. Falcone, J. Kirz, eds. (Optical Society of America, Washington, D.C., 1988), Vol. 2, p. 2.

Cohen, L.

Combis, P.

B. J. MacGowan, J. L. Bourgade, P. Combis, C. J. Keane, R. A. London, M. Louis-Jacquet, D. L. Matthews, S. Maxon, D. Naccache, M. D. Rosen, G. Thiell, D. A. Whelan, “Progress towards a 44 Å x-ray laser,” in Short Wavelength Coherent Radiation: Generation and Applications, R. W. Falcone, J. Kirz, eds. (Optical Society of America, Washington, D.C., 1988), Vol. 2, p. 2.

Da Silva, L. B.

L. B. Da Silva, M. H. Muendel, R. W. Falcone, D. J. Fields, J. B. Kortwright, B. J. MacGowan, D. L. Matthews, S. Mrowka, G. M. Shimkaveg, J. E. Trebes, “Nonlinear optics with focused x-ray lasers,” in X-Ray Lasers 1990, G. J. Tallents, ed. (Institute of Physics, Bristol, England, 1991), p. 177.

Edlén, B.

B. Edlén, E. Bodén, “The Na i-like spectra of potassium and calcium, K ix and Ca x,” Phys. Scr. 14, 31–38 (1976).
[CrossRef]

Falcone, R. W.

L. B. Da Silva, M. H. Muendel, R. W. Falcone, D. J. Fields, J. B. Kortwright, B. J. MacGowan, D. L. Matthews, S. Mrowka, G. M. Shimkaveg, J. E. Trebes, “Nonlinear optics with focused x-ray lasers,” in X-Ray Lasers 1990, G. J. Tallents, ed. (Institute of Physics, Bristol, England, 1991), p. 177.

Fields, D. J.

L. B. Da Silva, M. H. Muendel, R. W. Falcone, D. J. Fields, J. B. Kortwright, B. J. MacGowan, D. L. Matthews, S. Mrowka, G. M. Shimkaveg, J. E. Trebes, “Nonlinear optics with focused x-ray lasers,” in X-Ray Lasers 1990, G. J. Tallents, ed. (Institute of Physics, Bristol, England, 1991), p. 177.

Hagelstein, P. L.

M. H. Muendel, P. L. Hagelstein, “Four-wave frequency conversion of coherent soft x-rays in a plasma,” Phys. Rev. A 44, 7573–7579 (1991).
[CrossRef] [PubMed]

M. H. Muendel, P. L. Hagelstein, “Analysis of a soft-x-ray frequency doubler,” in Proceedings of the International Conference on Lasers ’89, D. G. Harris, T. M. Shay, eds. (Society for Optical and Quantum Electronics, McLean, Va., 1990), p. 34.

Harris, S. E.

S. E. Harris, “Generation of vacuum-ultraviolet and soft-x-ray radiation using high-order nonlinear optical polarizabilities,” Phys. Rev. Lett. 31, 341–344 (1973).
[CrossRef]

Kaplan, A. E.

Keane, C. J.

B. J. MacGowan, J. L. Bourgade, P. Combis, C. J. Keane, R. A. London, M. Louis-Jacquet, D. L. Matthews, S. Maxon, D. Naccache, M. D. Rosen, G. Thiell, D. A. Whelan, “Progress towards a 44 Å x-ray laser,” in Short Wavelength Coherent Radiation: Generation and Applications, R. W. Falcone, J. Kirz, eds. (Optical Society of America, Washington, D.C., 1988), Vol. 2, p. 2.

Kortwright, J. B.

L. B. Da Silva, M. H. Muendel, R. W. Falcone, D. J. Fields, J. B. Kortwright, B. J. MacGowan, D. L. Matthews, S. Mrowka, G. M. Shimkaveg, J. E. Trebes, “Nonlinear optics with focused x-ray lasers,” in X-Ray Lasers 1990, G. J. Tallents, ed. (Institute of Physics, Bristol, England, 1991), p. 177.

London, R. A.

B. J. MacGowan, J. L. Bourgade, P. Combis, C. J. Keane, R. A. London, M. Louis-Jacquet, D. L. Matthews, S. Maxon, D. Naccache, M. D. Rosen, G. Thiell, D. A. Whelan, “Progress towards a 44 Å x-ray laser,” in Short Wavelength Coherent Radiation: Generation and Applications, R. W. Falcone, J. Kirz, eds. (Optical Society of America, Washington, D.C., 1988), Vol. 2, p. 2.

Louis-Jacquet, M.

B. J. MacGowan, J. L. Bourgade, P. Combis, C. J. Keane, R. A. London, M. Louis-Jacquet, D. L. Matthews, S. Maxon, D. Naccache, M. D. Rosen, G. Thiell, D. A. Whelan, “Progress towards a 44 Å x-ray laser,” in Short Wavelength Coherent Radiation: Generation and Applications, R. W. Falcone, J. Kirz, eds. (Optical Society of America, Washington, D.C., 1988), Vol. 2, p. 2.

MacGowan, B. J.

B. J. MacGowan, J. L. Bourgade, P. Combis, C. J. Keane, R. A. London, M. Louis-Jacquet, D. L. Matthews, S. Maxon, D. Naccache, M. D. Rosen, G. Thiell, D. A. Whelan, “Progress towards a 44 Å x-ray laser,” in Short Wavelength Coherent Radiation: Generation and Applications, R. W. Falcone, J. Kirz, eds. (Optical Society of America, Washington, D.C., 1988), Vol. 2, p. 2.

L. B. Da Silva, M. H. Muendel, R. W. Falcone, D. J. Fields, J. B. Kortwright, B. J. MacGowan, D. L. Matthews, S. Mrowka, G. M. Shimkaveg, J. E. Trebes, “Nonlinear optics with focused x-ray lasers,” in X-Ray Lasers 1990, G. J. Tallents, ed. (Institute of Physics, Bristol, England, 1991), p. 177.

Matthews, D. L.

L. B. Da Silva, M. H. Muendel, R. W. Falcone, D. J. Fields, J. B. Kortwright, B. J. MacGowan, D. L. Matthews, S. Mrowka, G. M. Shimkaveg, J. E. Trebes, “Nonlinear optics with focused x-ray lasers,” in X-Ray Lasers 1990, G. J. Tallents, ed. (Institute of Physics, Bristol, England, 1991), p. 177.

B. J. MacGowan, J. L. Bourgade, P. Combis, C. J. Keane, R. A. London, M. Louis-Jacquet, D. L. Matthews, S. Maxon, D. Naccache, M. D. Rosen, G. Thiell, D. A. Whelan, “Progress towards a 44 Å x-ray laser,” in Short Wavelength Coherent Radiation: Generation and Applications, R. W. Falcone, J. Kirz, eds. (Optical Society of America, Washington, D.C., 1988), Vol. 2, p. 2.

Maxon, S.

B. J. MacGowan, J. L. Bourgade, P. Combis, C. J. Keane, R. A. London, M. Louis-Jacquet, D. L. Matthews, S. Maxon, D. Naccache, M. D. Rosen, G. Thiell, D. A. Whelan, “Progress towards a 44 Å x-ray laser,” in Short Wavelength Coherent Radiation: Generation and Applications, R. W. Falcone, J. Kirz, eds. (Optical Society of America, Washington, D.C., 1988), Vol. 2, p. 2.

Mrowka, S.

L. B. Da Silva, M. H. Muendel, R. W. Falcone, D. J. Fields, J. B. Kortwright, B. J. MacGowan, D. L. Matthews, S. Mrowka, G. M. Shimkaveg, J. E. Trebes, “Nonlinear optics with focused x-ray lasers,” in X-Ray Lasers 1990, G. J. Tallents, ed. (Institute of Physics, Bristol, England, 1991), p. 177.

Muendel, M. H.

M. H. Muendel, P. L. Hagelstein, “Four-wave frequency conversion of coherent soft x-rays in a plasma,” Phys. Rev. A 44, 7573–7579 (1991).
[CrossRef] [PubMed]

M. H. Muendel, P. L. Hagelstein, “Analysis of a soft-x-ray frequency doubler,” in Proceedings of the International Conference on Lasers ’89, D. G. Harris, T. M. Shay, eds. (Society for Optical and Quantum Electronics, McLean, Va., 1990), p. 34.

L. B. Da Silva, M. H. Muendel, R. W. Falcone, D. J. Fields, J. B. Kortwright, B. J. MacGowan, D. L. Matthews, S. Mrowka, G. M. Shimkaveg, J. E. Trebes, “Nonlinear optics with focused x-ray lasers,” in X-Ray Lasers 1990, G. J. Tallents, ed. (Institute of Physics, Bristol, England, 1991), p. 177.

Naccache, D.

B. J. MacGowan, J. L. Bourgade, P. Combis, C. J. Keane, R. A. London, M. Louis-Jacquet, D. L. Matthews, S. Maxon, D. Naccache, M. D. Rosen, G. Thiell, D. A. Whelan, “Progress towards a 44 Å x-ray laser,” in Short Wavelength Coherent Radiation: Generation and Applications, R. W. Falcone, J. Kirz, eds. (Optical Society of America, Washington, D.C., 1988), Vol. 2, p. 2.

Reintjes, J. F.

J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, Orlando, Fla., 1984), pp. 1–147.

Rosen, M. D.

B. J. MacGowan, J. L. Bourgade, P. Combis, C. J. Keane, R. A. London, M. Louis-Jacquet, D. L. Matthews, S. Maxon, D. Naccache, M. D. Rosen, G. Thiell, D. A. Whelan, “Progress towards a 44 Å x-ray laser,” in Short Wavelength Coherent Radiation: Generation and Applications, R. W. Falcone, J. Kirz, eds. (Optical Society of America, Washington, D.C., 1988), Vol. 2, p. 2.

Shimkaveg, G. M.

L. B. Da Silva, M. H. Muendel, R. W. Falcone, D. J. Fields, J. B. Kortwright, B. J. MacGowan, D. L. Matthews, S. Mrowka, G. M. Shimkaveg, J. E. Trebes, “Nonlinear optics with focused x-ray lasers,” in X-Ray Lasers 1990, G. J. Tallents, ed. (Institute of Physics, Bristol, England, 1991), p. 177.

Shkolnikov, P. L.

Thiell, G.

B. J. MacGowan, J. L. Bourgade, P. Combis, C. J. Keane, R. A. London, M. Louis-Jacquet, D. L. Matthews, S. Maxon, D. Naccache, M. D. Rosen, G. Thiell, D. A. Whelan, “Progress towards a 44 Å x-ray laser,” in Short Wavelength Coherent Radiation: Generation and Applications, R. W. Falcone, J. Kirz, eds. (Optical Society of America, Washington, D.C., 1988), Vol. 2, p. 2.

Trebes, J. E.

L. B. Da Silva, M. H. Muendel, R. W. Falcone, D. J. Fields, J. B. Kortwright, B. J. MacGowan, D. L. Matthews, S. Mrowka, G. M. Shimkaveg, J. E. Trebes, “Nonlinear optics with focused x-ray lasers,” in X-Ray Lasers 1990, G. J. Tallents, ed. (Institute of Physics, Bristol, England, 1991), p. 177.

Weissbluth, M.

M. Weissbluth, Atoms and Molecules, student ed. (Academic, New York, 1978), pp. 159, 505–517.

Whelan, D. A.

B. J. MacGowan, J. L. Bourgade, P. Combis, C. J. Keane, R. A. London, M. Louis-Jacquet, D. L. Matthews, S. Maxon, D. Naccache, M. D. Rosen, G. Thiell, D. A. Whelan, “Progress towards a 44 Å x-ray laser,” in Short Wavelength Coherent Radiation: Generation and Applications, R. W. Falcone, J. Kirz, eds. (Optical Society of America, Washington, D.C., 1988), Vol. 2, p. 2.

Astron. Astrophys. Suppl.

E. Biémont, “Theoretical f values for sodium-like ions (11 ≤ Z ≤ 26),” Astron. Astrophys. Suppl. 31, 285–290 (1978).

J. Opt. Soc. Am.

Opt. Lett.

Phys. Rev. A

P. L. Shkolnikov, A. E. Kaplan, “Discharge-plasma-x-ray-laser resonant couples for x-ray nonlinear optics,” Phys. Rev. A 44, 6951–6953 (1991).
[CrossRef] [PubMed]

M. H. Muendel, P. L. Hagelstein, “Four-wave frequency conversion of coherent soft x-rays in a plasma,” Phys. Rev. A 44, 7573–7579 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett.

S. E. Harris, “Generation of vacuum-ultraviolet and soft-x-ray radiation using high-order nonlinear optical polarizabilities,” Phys. Rev. Lett. 31, 341–344 (1973).
[CrossRef]

Phys. Scr.

B. Edlén, E. Bodén, “The Na i-like spectra of potassium and calcium, K ix and Ca x,” Phys. Scr. 14, 31–38 (1976).
[CrossRef]

Other

M. H. Muendel, P. L. Hagelstein, “Analysis of a soft-x-ray frequency doubler,” in Proceedings of the International Conference on Lasers ’89, D. G. Harris, T. M. Shay, eds. (Society for Optical and Quantum Electronics, McLean, Va., 1990), p. 34.

M. Weissbluth, Atoms and Molecules, student ed. (Academic, New York, 1978), pp. 159, 505–517.

L. B. Da Silva, M. H. Muendel, R. W. Falcone, D. J. Fields, J. B. Kortwright, B. J. MacGowan, D. L. Matthews, S. Mrowka, G. M. Shimkaveg, J. E. Trebes, “Nonlinear optics with focused x-ray lasers,” in X-Ray Lasers 1990, G. J. Tallents, ed. (Institute of Physics, Bristol, England, 1991), p. 177.

B. J. MacGowan, J. L. Bourgade, P. Combis, C. J. Keane, R. A. London, M. Louis-Jacquet, D. L. Matthews, S. Maxon, D. Naccache, M. D. Rosen, G. Thiell, D. A. Whelan, “Progress towards a 44 Å x-ray laser,” in Short Wavelength Coherent Radiation: Generation and Applications, R. W. Falcone, J. Kirz, eds. (Optical Society of America, Washington, D.C., 1988), Vol. 2, p. 2.

J. F. Reintjes, Nonlinear Optical Parametric Processes in Liquids and Gases (Academic, Orlando, Fla., 1984), pp. 1–147.

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Figures (4)

Fig. 1
Fig. 1

Nonlinear susceptibility for four-wave mixing as a function of optical laser wavelength. The x-ray laser wavelength is fixed at 15.495 nm and the ion and electron temperatures at 2.5 × 105 K in this and the following figures.

Fig. 2
Fig. 2

Non-phase-matched conversion as a function of optical laser wavelength, assuming that the interaction length–ion density product has been set to give the maximum conversion (as plotted in Fig. 3). The soft-x-ray and optical laser intensities are taken to be 1014 W/cm2 .

Fig. 3
Fig. 3

Values of the length–density product for maximal non-phase-matched conversion and for 10% conversion assuming laser intensities of 1014 W/cm2 and attainment of phase matching.

Fig. 4
Fig. 4

Nonlinear susceptibility for frequency tripling as a function of x-ray laser wavelength.

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