Abstract

Picosecond laser pulses were used to study the highly forbidden resonant second-harmonic generation (SHG) in potassium vapor. The input intensity dependence, vapor density dependence, buffer-gas pressure dependence, and spatial profile of the SHG were measured. A pump–probe experiment was conducted to probe the time dependence of the SHG signal. The experimental results can be understood from an ionization-initiated dc-field-induced SHG model. A theory of a dc-field-induced SHG model is developed that takes into account the time development of the dc electric field in detail. This temporal buildup of the dc field along with transient coherent excitation between two-photon-allowed transitions can explain the experimental results quantitatively, including the previous vapor SHG results with nanosecond laser pulses.

© 1997 Optical Society of America

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  1. D. C. Hanna, M. A. Yuratich, and D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, Berlin, 1979), and references therein.
  2. R. T. Hodgson, P. P. Sorokin, and J. J. Wynne, “Tunable coherent vacuum-ultraviolet generation in atomic vapors,” Phys. Rev. Lett. 32, 343–346 (1974); P. P. Sorokin, J. J. Wynne, and J. R. Lankard, “Tunable coherent ir source based upon four-wave parametric conversionin alkali metal vapors,” Appl. Phys. Lett. 22, 342–344 (1973).
    [CrossRef]
  3. J. L. Carlsten and T. J. McIlrath, “Observations of stimulated anti-Stokes radiation in barium vapor,” J. Phys. B 6, L80–L85 (1973).
    [CrossRef]
  4. See, for example, Y. R. Shen, The Principlesof Nonlinear Optics (Wiley, New York, 1984).
  5. D. L. Andrews, “Forbidden nature of multipolar contributions to second-harmonic generationin isotropic fluids,” Phys. Rev. A 38, 3113–3115 (1988); T. F. Heinz and D. P. DiVincenzo “Comment on `Forbidden nature of multipolar contributions to second-harmonicgeneration in isotropic fluids, ' ” Phys. Rev. A 42, 6249–6251 (1990).
    [CrossRef] [PubMed]
  6. P. S. Pershan, “Nonlinear optical properties of solids: energy considerations,” Phys. Rev. 130, 919–929 (1963).
    [CrossRef]
  7. D. S. Bethune, R. W. Smith, and Y. R. Shen, “Optical quadrupole sum-frequency generation in sodium vapor,” Phys. Rev. Lett. 37, 431–434 (1976); “Sum-frequency generation via a resonant quadrupole transition in sodium,” Phys. Rev. A 17, 277–292 (1978).
    [CrossRef]
  8. T. Mossberg, A. Flusberg, and S. R. Hartmann, “Optical second-harmonic generation in atomic thallium vapor,” Opt. Commun. 25, 121–124 (1978).
    [CrossRef]
  9. J. Okada, Y. Fukuda, and M. Matsuoka, “Optical second harmonic generation in the forbidden 22S1/2–32S1/2 transitionof atomic lithium vapor,” J. Phys. Soc. Jpn. 50, 1301–1309 (1981).
    [CrossRef]
  10. J. Bokor, R. R. Freeman, R. L. Panock, and J. C. White, “Generation of high-brightness coherent radiation in the vacuum ultravioletby four-wave parametric oscillation in mercury vapor,” Opt. Lett. 6, 182–184 (1981).
    [CrossRef] [PubMed]
  11. R. R. Freeman, J. E. Bjorkholm, R. Panock, and W. E. Cooke, “Opticalsecond harmonic generation by a single laser beam in an isotropic medium,”in Laser Spectroscopy V, by A. R. W. McKellar, T. Oka, and B. P. Stoicheff, eds. (Springer-Verlag, Berlin, 1981), pp. 453–457.
  12. W. Jamroz, P. E. LaRocque, and B. P. Stoicheff, “Resonantly enhanced second-harmonic generation in zinc vapor,” Opt. Lett. 7, 148–150 (1982).
    [CrossRef] [PubMed]
  13. S. Dinev, “Two-photon resonant optical second harmonic generation from s, p, and d states of K atoms,” J. Phys. B 21, 1681–1697 (1988); “Second harmonic generation and parametric emission by two-photon excitationof the 5s2S1/2 state of sodium,” J. Phys. B 21, 1111–1119 (1988).
    [CrossRef]
  14. M. Lu and J. Tsai, “Optical second harmonic generation from low-lying excited states inpotassium vapor,” J. Phys. B 23, 921–935 (1990).
    [CrossRef]
  15. J. Y. Zhang, H. T. Zhou, and P. Jin, “Mechanism studyof the generation of frequency-doubled stimulated emission in metal vaporby using RIS,” in Resonance Ionization Spectroscopy 1988, T. B. Lucatorto and J. E. Parks, eds. (Institute of Physics, Bristol, UK, 1989), pp. 29–32.
  16. A. Elçi and D. Depatie, “Second-harmonic generation from collision complexes,” Phys. Rev. Lett. 60, 688–691 (1988).
    [CrossRef]
  17. S. Vianna and C. de Araujo, “Collision-assisted second-harmonic generation from Rydberg atoms,” Phys. Rev. A 44, 733–736 (1991).
    [CrossRef] [PubMed]
  18. D. S. Bethune, “Optical second-harmonic generation in atomic vapors with focused beams,” Phys. Rev. A 23, 3139–3151 (1981).
    [CrossRef]
  19. C. S. Mullin, D. Kim, M. B. Feller, and Y. R. Shen, “Picosecond studies of optical second harmonic generation in atomicvapor,” Phys. Rev. Lett. 74, 2678–2681 (1995); D. Kim, C. S. Mullin, and Y. R. Shen, “Theory of resonant second harmonic generation in atomic vapor,” Appl. Phys. B 60, S215–S220 (1995); “Resonant second harmonic generation in potassiumvapor,” in Laser Spectroscopy, M. Inguscio, M.Allegrini, and A. Sasso, eds. (World Scientific, Singapore, 1996), pp. 337–340.
    [CrossRef] [PubMed]
  20. K. Miyazaki, T. Sato, and H. Kashiwagi, “Spontaneous-field-induced optical second-harmonic generation in atomicvapors,” Phys. Rev. Lett. 43, 1154–1157 (1979).
    [CrossRef]
  21. M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rza¸żewski, “Anomalies in optical harmonic generation using high-intensity laserradiation,” Phys. Rev. A 41, 3822–3825 (1990).
    [CrossRef] [PubMed]
  22. K. Hakuta, L. Marmet, and B. P. Stoicheff, “Electric-field-induced second-harmonic generation with reduced absorptionin atomic hydrogen,” Phys. Rev. Lett. 66, 596–599 (1991); L. Marmet, K. Hakuta, and B. P. Stoicheff, “Second-harmonic generation at Lyman-α in atomic hydrogen,” Opt. Lett. 16, 261–263 (1991).
    [CrossRef] [PubMed]
  23. L. Marmet, K. Hakuta, and B. P. Stoicheff, “Second-harmonic generation in atomic hydrogen induced by a charge-separationfield,” J. Opt. Soc. Am. B 9, 1038–1046 (1992).
    [CrossRef]
  24. J. C. MacGillivray and M. S. Feld, “Theory of superradiance in an extended, optically thick medium,” Phys. Rev. A 14, 1169–1189 (1976).
    [CrossRef]
  25. R. B. Miles and S. E. Harris, “Optical third-harmonic generation in alkali metal vapors,” IEEE J. Quantum Electron. QE-9, 470–484 (1973); H. Eichner, “Third-order susceptibility of alkali metal vapors,” IEEE J. Quantum Electron. QE-11, 121–130 (1975); W. L. Wiese, M. W. Smith, and B. M. Miles, Atomic Transition Probabilities, Sodium through Calcium (NationalBureau of Standards, Washington, D.C., 1969), p. 225.
    [CrossRef]
  26. B. Warner, “Atomic oscillator strengths. III. Alkali-like spectra,” Mon. Not. R. Astron. Soc. 139, 115–128 (1968).
  27. T. F. Gallagher, S. A. Edelstein, and R. M. Hill, “Collisional angular-momentum mixing of Rydberg states of Na by He, Ne, and Ar,” Phys. Rev. A 15, 1945–1951 (1977); A. Flusberg, R. Kachru, T. Mossberg, and S. R. Hartmann, “Foreign-gas-induced relaxation of Rydberg S and D states in atomic sodium,” Phys. Rev. A 19, 1607–1621 (1979).
    [CrossRef]
  28. S. Augst, D. D. Meyerhofer, C. I. Moore, and J. Peatross, “Tunneling ionization and harmonic generation in krypton gas using ahigh-intensity, 1-μm, 1-ps laser,” in Femtosecondto Nanosecond High-Intensity Lasers and Applications, E. M. Campell, ed., Proc. SPIE 1229, 152–158 (1990).
    [CrossRef]
  29. M. Matsuoka, H. Nakatsuka, and J. Okada, “Free-precession decay of two-photon-induced coherence in Ca vapor,” Phys. Rev. A 12, 1062–1065 (1975).
    [CrossRef]
  30. C. R. Vidal and J. Cooper, “Heat-pipe oven: a new well-defined metal vapor device for spectroscopicmeasurements,” J. Appl. Phys. 40, 3370–3374 (1969).
    [CrossRef]
  31. J. Y. Zhang, J. Y. Huang, Y. R. Shen, and C. Chen, “Optical parametric generation and amplification in barium borate andlithium triborate crystals,” J. Opt. Soc. Am. B 10, 1758–1764 (1993).
    [CrossRef]
  32. D. E. Golden and H. W. Bandel, “Low energy e-Ar total scattering cross sections:the Ramsauer–Townsend effect,” Phys. Rev. 149, 58–59 (1966).
    [CrossRef]
  33. A. Kasden, T. M. Miller, and B. Bederson, “Absolute measurements of total cross sections for electron scatteringby sodium atoms (0.5–50 eV),” Phys. Rev. A 8, 1562–1569 (1973).
    [CrossRef]
  34. D. Grischkowsky, M. M. T. Loy, and P. F. Liao, “Adiabatic following model for two-photon transitions: nonlinear mixingand pulse propagation,” Phys. Rev. A 12, 2514–2533 (1975).
    [CrossRef]
  35. J. H. Brownell, X. Lu, and S. R. Hartmann, “Time-delayed second harmonic generation,” Phys. Rev. Lett. 75, 3657–3660 (1995).
    [CrossRef] [PubMed]

1995

J. H. Brownell, X. Lu, and S. R. Hartmann, “Time-delayed second harmonic generation,” Phys. Rev. Lett. 75, 3657–3660 (1995).
[CrossRef] [PubMed]

1993

1992

1991

S. Vianna and C. de Araujo, “Collision-assisted second-harmonic generation from Rydberg atoms,” Phys. Rev. A 44, 733–736 (1991).
[CrossRef] [PubMed]

1990

S. Augst, D. D. Meyerhofer, C. I. Moore, and J. Peatross, “Tunneling ionization and harmonic generation in krypton gas using ahigh-intensity, 1-μm, 1-ps laser,” in Femtosecondto Nanosecond High-Intensity Lasers and Applications, E. M. Campell, ed., Proc. SPIE 1229, 152–158 (1990).
[CrossRef]

M. Lu and J. Tsai, “Optical second harmonic generation from low-lying excited states inpotassium vapor,” J. Phys. B 23, 921–935 (1990).
[CrossRef]

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rza¸żewski, “Anomalies in optical harmonic generation using high-intensity laserradiation,” Phys. Rev. A 41, 3822–3825 (1990).
[CrossRef] [PubMed]

1988

A. Elçi and D. Depatie, “Second-harmonic generation from collision complexes,” Phys. Rev. Lett. 60, 688–691 (1988).
[CrossRef]

1982

1981

J. Okada, Y. Fukuda, and M. Matsuoka, “Optical second harmonic generation in the forbidden 22S1/2–32S1/2 transitionof atomic lithium vapor,” J. Phys. Soc. Jpn. 50, 1301–1309 (1981).
[CrossRef]

J. Bokor, R. R. Freeman, R. L. Panock, and J. C. White, “Generation of high-brightness coherent radiation in the vacuum ultravioletby four-wave parametric oscillation in mercury vapor,” Opt. Lett. 6, 182–184 (1981).
[CrossRef] [PubMed]

D. S. Bethune, “Optical second-harmonic generation in atomic vapors with focused beams,” Phys. Rev. A 23, 3139–3151 (1981).
[CrossRef]

1979

K. Miyazaki, T. Sato, and H. Kashiwagi, “Spontaneous-field-induced optical second-harmonic generation in atomicvapors,” Phys. Rev. Lett. 43, 1154–1157 (1979).
[CrossRef]

1978

T. Mossberg, A. Flusberg, and S. R. Hartmann, “Optical second-harmonic generation in atomic thallium vapor,” Opt. Commun. 25, 121–124 (1978).
[CrossRef]

1976

J. C. MacGillivray and M. S. Feld, “Theory of superradiance in an extended, optically thick medium,” Phys. Rev. A 14, 1169–1189 (1976).
[CrossRef]

1975

M. Matsuoka, H. Nakatsuka, and J. Okada, “Free-precession decay of two-photon-induced coherence in Ca vapor,” Phys. Rev. A 12, 1062–1065 (1975).
[CrossRef]

D. Grischkowsky, M. M. T. Loy, and P. F. Liao, “Adiabatic following model for two-photon transitions: nonlinear mixingand pulse propagation,” Phys. Rev. A 12, 2514–2533 (1975).
[CrossRef]

1973

A. Kasden, T. M. Miller, and B. Bederson, “Absolute measurements of total cross sections for electron scatteringby sodium atoms (0.5–50 eV),” Phys. Rev. A 8, 1562–1569 (1973).
[CrossRef]

J. L. Carlsten and T. J. McIlrath, “Observations of stimulated anti-Stokes radiation in barium vapor,” J. Phys. B 6, L80–L85 (1973).
[CrossRef]

1969

C. R. Vidal and J. Cooper, “Heat-pipe oven: a new well-defined metal vapor device for spectroscopicmeasurements,” J. Appl. Phys. 40, 3370–3374 (1969).
[CrossRef]

1968

B. Warner, “Atomic oscillator strengths. III. Alkali-like spectra,” Mon. Not. R. Astron. Soc. 139, 115–128 (1968).

1966

D. E. Golden and H. W. Bandel, “Low energy e-Ar total scattering cross sections:the Ramsauer–Townsend effect,” Phys. Rev. 149, 58–59 (1966).
[CrossRef]

1963

P. S. Pershan, “Nonlinear optical properties of solids: energy considerations,” Phys. Rev. 130, 919–929 (1963).
[CrossRef]

Augst, S.

S. Augst, D. D. Meyerhofer, C. I. Moore, and J. Peatross, “Tunneling ionization and harmonic generation in krypton gas using ahigh-intensity, 1-μm, 1-ps laser,” in Femtosecondto Nanosecond High-Intensity Lasers and Applications, E. M. Campell, ed., Proc. SPIE 1229, 152–158 (1990).
[CrossRef]

Bandel, H. W.

D. E. Golden and H. W. Bandel, “Low energy e-Ar total scattering cross sections:the Ramsauer–Townsend effect,” Phys. Rev. 149, 58–59 (1966).
[CrossRef]

Bederson, B.

A. Kasden, T. M. Miller, and B. Bederson, “Absolute measurements of total cross sections for electron scatteringby sodium atoms (0.5–50 eV),” Phys. Rev. A 8, 1562–1569 (1973).
[CrossRef]

Bethune, D. S.

D. S. Bethune, “Optical second-harmonic generation in atomic vapors with focused beams,” Phys. Rev. A 23, 3139–3151 (1981).
[CrossRef]

Bokor, J.

Boyd, R. W.

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rza¸żewski, “Anomalies in optical harmonic generation using high-intensity laserradiation,” Phys. Rev. A 41, 3822–3825 (1990).
[CrossRef] [PubMed]

Brownell, J. H.

J. H. Brownell, X. Lu, and S. R. Hartmann, “Time-delayed second harmonic generation,” Phys. Rev. Lett. 75, 3657–3660 (1995).
[CrossRef] [PubMed]

Carlsten, J. L.

J. L. Carlsten and T. J. McIlrath, “Observations of stimulated anti-Stokes radiation in barium vapor,” J. Phys. B 6, L80–L85 (1973).
[CrossRef]

Chen, C.

Cooper, J.

C. R. Vidal and J. Cooper, “Heat-pipe oven: a new well-defined metal vapor device for spectroscopicmeasurements,” J. Appl. Phys. 40, 3370–3374 (1969).
[CrossRef]

Davis, W. V.

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rza¸żewski, “Anomalies in optical harmonic generation using high-intensity laserradiation,” Phys. Rev. A 41, 3822–3825 (1990).
[CrossRef] [PubMed]

de Araujo, C.

S. Vianna and C. de Araujo, “Collision-assisted second-harmonic generation from Rydberg atoms,” Phys. Rev. A 44, 733–736 (1991).
[CrossRef] [PubMed]

Depatie, D.

A. Elçi and D. Depatie, “Second-harmonic generation from collision complexes,” Phys. Rev. Lett. 60, 688–691 (1988).
[CrossRef]

Elçi, A.

A. Elçi and D. Depatie, “Second-harmonic generation from collision complexes,” Phys. Rev. Lett. 60, 688–691 (1988).
[CrossRef]

Feld, M. S.

J. C. MacGillivray and M. S. Feld, “Theory of superradiance in an extended, optically thick medium,” Phys. Rev. A 14, 1169–1189 (1976).
[CrossRef]

Flusberg, A.

T. Mossberg, A. Flusberg, and S. R. Hartmann, “Optical second-harmonic generation in atomic thallium vapor,” Opt. Commun. 25, 121–124 (1978).
[CrossRef]

Freeman, R. R.

Fukuda, Y.

J. Okada, Y. Fukuda, and M. Matsuoka, “Optical second harmonic generation in the forbidden 22S1/2–32S1/2 transitionof atomic lithium vapor,” J. Phys. Soc. Jpn. 50, 1301–1309 (1981).
[CrossRef]

Golden, D. E.

D. E. Golden and H. W. Bandel, “Low energy e-Ar total scattering cross sections:the Ramsauer–Townsend effect,” Phys. Rev. 149, 58–59 (1966).
[CrossRef]

Grischkowsky, D.

D. Grischkowsky, M. M. T. Loy, and P. F. Liao, “Adiabatic following model for two-photon transitions: nonlinear mixingand pulse propagation,” Phys. Rev. A 12, 2514–2533 (1975).
[CrossRef]

Hakuta, K.

Hartmann, S. R.

J. H. Brownell, X. Lu, and S. R. Hartmann, “Time-delayed second harmonic generation,” Phys. Rev. Lett. 75, 3657–3660 (1995).
[CrossRef] [PubMed]

T. Mossberg, A. Flusberg, and S. R. Hartmann, “Optical second-harmonic generation in atomic thallium vapor,” Opt. Commun. 25, 121–124 (1978).
[CrossRef]

Huang, J. Y.

Jamroz, W.

Kasden, A.

A. Kasden, T. M. Miller, and B. Bederson, “Absolute measurements of total cross sections for electron scatteringby sodium atoms (0.5–50 eV),” Phys. Rev. A 8, 1562–1569 (1973).
[CrossRef]

Kashiwagi, H.

K. Miyazaki, T. Sato, and H. Kashiwagi, “Spontaneous-field-induced optical second-harmonic generation in atomicvapors,” Phys. Rev. Lett. 43, 1154–1157 (1979).
[CrossRef]

LaRocque, P. E.

Liao, P. F.

D. Grischkowsky, M. M. T. Loy, and P. F. Liao, “Adiabatic following model for two-photon transitions: nonlinear mixingand pulse propagation,” Phys. Rev. A 12, 2514–2533 (1975).
[CrossRef]

Loy, M. M. T.

D. Grischkowsky, M. M. T. Loy, and P. F. Liao, “Adiabatic following model for two-photon transitions: nonlinear mixingand pulse propagation,” Phys. Rev. A 12, 2514–2533 (1975).
[CrossRef]

Lu, M.

M. Lu and J. Tsai, “Optical second harmonic generation from low-lying excited states inpotassium vapor,” J. Phys. B 23, 921–935 (1990).
[CrossRef]

Lu, X.

J. H. Brownell, X. Lu, and S. R. Hartmann, “Time-delayed second harmonic generation,” Phys. Rev. Lett. 75, 3657–3660 (1995).
[CrossRef] [PubMed]

MacGillivray, J. C.

J. C. MacGillivray and M. S. Feld, “Theory of superradiance in an extended, optically thick medium,” Phys. Rev. A 14, 1169–1189 (1976).
[CrossRef]

Malcuit, M. S.

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rza¸żewski, “Anomalies in optical harmonic generation using high-intensity laserradiation,” Phys. Rev. A 41, 3822–3825 (1990).
[CrossRef] [PubMed]

Marmet, L.

Matsuoka, M.

J. Okada, Y. Fukuda, and M. Matsuoka, “Optical second harmonic generation in the forbidden 22S1/2–32S1/2 transitionof atomic lithium vapor,” J. Phys. Soc. Jpn. 50, 1301–1309 (1981).
[CrossRef]

M. Matsuoka, H. Nakatsuka, and J. Okada, “Free-precession decay of two-photon-induced coherence in Ca vapor,” Phys. Rev. A 12, 1062–1065 (1975).
[CrossRef]

McIlrath, T. J.

J. L. Carlsten and T. J. McIlrath, “Observations of stimulated anti-Stokes radiation in barium vapor,” J. Phys. B 6, L80–L85 (1973).
[CrossRef]

Meyerhofer, D. D.

S. Augst, D. D. Meyerhofer, C. I. Moore, and J. Peatross, “Tunneling ionization and harmonic generation in krypton gas using ahigh-intensity, 1-μm, 1-ps laser,” in Femtosecondto Nanosecond High-Intensity Lasers and Applications, E. M. Campell, ed., Proc. SPIE 1229, 152–158 (1990).
[CrossRef]

Miller, T. M.

A. Kasden, T. M. Miller, and B. Bederson, “Absolute measurements of total cross sections for electron scatteringby sodium atoms (0.5–50 eV),” Phys. Rev. A 8, 1562–1569 (1973).
[CrossRef]

Miyazaki, K.

K. Miyazaki, T. Sato, and H. Kashiwagi, “Spontaneous-field-induced optical second-harmonic generation in atomicvapors,” Phys. Rev. Lett. 43, 1154–1157 (1979).
[CrossRef]

Moore, C. I.

S. Augst, D. D. Meyerhofer, C. I. Moore, and J. Peatross, “Tunneling ionization and harmonic generation in krypton gas using ahigh-intensity, 1-μm, 1-ps laser,” in Femtosecondto Nanosecond High-Intensity Lasers and Applications, E. M. Campell, ed., Proc. SPIE 1229, 152–158 (1990).
[CrossRef]

Mossberg, T.

T. Mossberg, A. Flusberg, and S. R. Hartmann, “Optical second-harmonic generation in atomic thallium vapor,” Opt. Commun. 25, 121–124 (1978).
[CrossRef]

Nakatsuka, H.

M. Matsuoka, H. Nakatsuka, and J. Okada, “Free-precession decay of two-photon-induced coherence in Ca vapor,” Phys. Rev. A 12, 1062–1065 (1975).
[CrossRef]

Okada, J.

J. Okada, Y. Fukuda, and M. Matsuoka, “Optical second harmonic generation in the forbidden 22S1/2–32S1/2 transitionof atomic lithium vapor,” J. Phys. Soc. Jpn. 50, 1301–1309 (1981).
[CrossRef]

M. Matsuoka, H. Nakatsuka, and J. Okada, “Free-precession decay of two-photon-induced coherence in Ca vapor,” Phys. Rev. A 12, 1062–1065 (1975).
[CrossRef]

Panock, R. L.

Peatross, J.

S. Augst, D. D. Meyerhofer, C. I. Moore, and J. Peatross, “Tunneling ionization and harmonic generation in krypton gas using ahigh-intensity, 1-μm, 1-ps laser,” in Femtosecondto Nanosecond High-Intensity Lasers and Applications, E. M. Campell, ed., Proc. SPIE 1229, 152–158 (1990).
[CrossRef]

Pershan, P. S.

P. S. Pershan, “Nonlinear optical properties of solids: energy considerations,” Phys. Rev. 130, 919–929 (1963).
[CrossRef]

Rza¸zewski, K.

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rza¸żewski, “Anomalies in optical harmonic generation using high-intensity laserradiation,” Phys. Rev. A 41, 3822–3825 (1990).
[CrossRef] [PubMed]

Sato, T.

K. Miyazaki, T. Sato, and H. Kashiwagi, “Spontaneous-field-induced optical second-harmonic generation in atomicvapors,” Phys. Rev. Lett. 43, 1154–1157 (1979).
[CrossRef]

Shen, Y. R.

Stoicheff, B. P.

Tsai, J.

M. Lu and J. Tsai, “Optical second harmonic generation from low-lying excited states inpotassium vapor,” J. Phys. B 23, 921–935 (1990).
[CrossRef]

Vianna, S.

S. Vianna and C. de Araujo, “Collision-assisted second-harmonic generation from Rydberg atoms,” Phys. Rev. A 44, 733–736 (1991).
[CrossRef] [PubMed]

Vidal, C. R.

C. R. Vidal and J. Cooper, “Heat-pipe oven: a new well-defined metal vapor device for spectroscopicmeasurements,” J. Appl. Phys. 40, 3370–3374 (1969).
[CrossRef]

Warner, B.

B. Warner, “Atomic oscillator strengths. III. Alkali-like spectra,” Mon. Not. R. Astron. Soc. 139, 115–128 (1968).

White, J. C.

Zhang, J. Y.

J. Appl. Phys.

C. R. Vidal and J. Cooper, “Heat-pipe oven: a new well-defined metal vapor device for spectroscopicmeasurements,” J. Appl. Phys. 40, 3370–3374 (1969).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

J. L. Carlsten and T. J. McIlrath, “Observations of stimulated anti-Stokes radiation in barium vapor,” J. Phys. B 6, L80–L85 (1973).
[CrossRef]

M. Lu and J. Tsai, “Optical second harmonic generation from low-lying excited states inpotassium vapor,” J. Phys. B 23, 921–935 (1990).
[CrossRef]

J. Phys. Soc. Jpn.

J. Okada, Y. Fukuda, and M. Matsuoka, “Optical second harmonic generation in the forbidden 22S1/2–32S1/2 transitionof atomic lithium vapor,” J. Phys. Soc. Jpn. 50, 1301–1309 (1981).
[CrossRef]

Mon. Not. R. Astron. Soc.

B. Warner, “Atomic oscillator strengths. III. Alkali-like spectra,” Mon. Not. R. Astron. Soc. 139, 115–128 (1968).

Opt. Commun.

T. Mossberg, A. Flusberg, and S. R. Hartmann, “Optical second-harmonic generation in atomic thallium vapor,” Opt. Commun. 25, 121–124 (1978).
[CrossRef]

Opt. Lett.

Phys. Rev.

P. S. Pershan, “Nonlinear optical properties of solids: energy considerations,” Phys. Rev. 130, 919–929 (1963).
[CrossRef]

D. E. Golden and H. W. Bandel, “Low energy e-Ar total scattering cross sections:the Ramsauer–Townsend effect,” Phys. Rev. 149, 58–59 (1966).
[CrossRef]

Phys. Rev. A

A. Kasden, T. M. Miller, and B. Bederson, “Absolute measurements of total cross sections for electron scatteringby sodium atoms (0.5–50 eV),” Phys. Rev. A 8, 1562–1569 (1973).
[CrossRef]

D. Grischkowsky, M. M. T. Loy, and P. F. Liao, “Adiabatic following model for two-photon transitions: nonlinear mixingand pulse propagation,” Phys. Rev. A 12, 2514–2533 (1975).
[CrossRef]

M. Matsuoka, H. Nakatsuka, and J. Okada, “Free-precession decay of two-photon-induced coherence in Ca vapor,” Phys. Rev. A 12, 1062–1065 (1975).
[CrossRef]

J. C. MacGillivray and M. S. Feld, “Theory of superradiance in an extended, optically thick medium,” Phys. Rev. A 14, 1169–1189 (1976).
[CrossRef]

M. S. Malcuit, R. W. Boyd, W. V. Davis, and K. Rza¸żewski, “Anomalies in optical harmonic generation using high-intensity laserradiation,” Phys. Rev. A 41, 3822–3825 (1990).
[CrossRef] [PubMed]

S. Vianna and C. de Araujo, “Collision-assisted second-harmonic generation from Rydberg atoms,” Phys. Rev. A 44, 733–736 (1991).
[CrossRef] [PubMed]

D. S. Bethune, “Optical second-harmonic generation in atomic vapors with focused beams,” Phys. Rev. A 23, 3139–3151 (1981).
[CrossRef]

Phys. Rev. Lett.

A. Elçi and D. Depatie, “Second-harmonic generation from collision complexes,” Phys. Rev. Lett. 60, 688–691 (1988).
[CrossRef]

K. Miyazaki, T. Sato, and H. Kashiwagi, “Spontaneous-field-induced optical second-harmonic generation in atomicvapors,” Phys. Rev. Lett. 43, 1154–1157 (1979).
[CrossRef]

J. H. Brownell, X. Lu, and S. R. Hartmann, “Time-delayed second harmonic generation,” Phys. Rev. Lett. 75, 3657–3660 (1995).
[CrossRef] [PubMed]

Proc. SPIE

S. Augst, D. D. Meyerhofer, C. I. Moore, and J. Peatross, “Tunneling ionization and harmonic generation in krypton gas using ahigh-intensity, 1-μm, 1-ps laser,” in Femtosecondto Nanosecond High-Intensity Lasers and Applications, E. M. Campell, ed., Proc. SPIE 1229, 152–158 (1990).
[CrossRef]

Other

T. F. Gallagher, S. A. Edelstein, and R. M. Hill, “Collisional angular-momentum mixing of Rydberg states of Na by He, Ne, and Ar,” Phys. Rev. A 15, 1945–1951 (1977); A. Flusberg, R. Kachru, T. Mossberg, and S. R. Hartmann, “Foreign-gas-induced relaxation of Rydberg S and D states in atomic sodium,” Phys. Rev. A 19, 1607–1621 (1979).
[CrossRef]

K. Hakuta, L. Marmet, and B. P. Stoicheff, “Electric-field-induced second-harmonic generation with reduced absorptionin atomic hydrogen,” Phys. Rev. Lett. 66, 596–599 (1991); L. Marmet, K. Hakuta, and B. P. Stoicheff, “Second-harmonic generation at Lyman-α in atomic hydrogen,” Opt. Lett. 16, 261–263 (1991).
[CrossRef] [PubMed]

R. B. Miles and S. E. Harris, “Optical third-harmonic generation in alkali metal vapors,” IEEE J. Quantum Electron. QE-9, 470–484 (1973); H. Eichner, “Third-order susceptibility of alkali metal vapors,” IEEE J. Quantum Electron. QE-11, 121–130 (1975); W. L. Wiese, M. W. Smith, and B. M. Miles, Atomic Transition Probabilities, Sodium through Calcium (NationalBureau of Standards, Washington, D.C., 1969), p. 225.
[CrossRef]

C. S. Mullin, D. Kim, M. B. Feller, and Y. R. Shen, “Picosecond studies of optical second harmonic generation in atomicvapor,” Phys. Rev. Lett. 74, 2678–2681 (1995); D. Kim, C. S. Mullin, and Y. R. Shen, “Theory of resonant second harmonic generation in atomic vapor,” Appl. Phys. B 60, S215–S220 (1995); “Resonant second harmonic generation in potassiumvapor,” in Laser Spectroscopy, M. Inguscio, M.Allegrini, and A. Sasso, eds. (World Scientific, Singapore, 1996), pp. 337–340.
[CrossRef] [PubMed]

S. Dinev, “Two-photon resonant optical second harmonic generation from s, p, and d states of K atoms,” J. Phys. B 21, 1681–1697 (1988); “Second harmonic generation and parametric emission by two-photon excitationof the 5s2S1/2 state of sodium,” J. Phys. B 21, 1111–1119 (1988).
[CrossRef]

J. Y. Zhang, H. T. Zhou, and P. Jin, “Mechanism studyof the generation of frequency-doubled stimulated emission in metal vaporby using RIS,” in Resonance Ionization Spectroscopy 1988, T. B. Lucatorto and J. E. Parks, eds. (Institute of Physics, Bristol, UK, 1989), pp. 29–32.

D. S. Bethune, R. W. Smith, and Y. R. Shen, “Optical quadrupole sum-frequency generation in sodium vapor,” Phys. Rev. Lett. 37, 431–434 (1976); “Sum-frequency generation via a resonant quadrupole transition in sodium,” Phys. Rev. A 17, 277–292 (1978).
[CrossRef]

R. R. Freeman, J. E. Bjorkholm, R. Panock, and W. E. Cooke, “Opticalsecond harmonic generation by a single laser beam in an isotropic medium,”in Laser Spectroscopy V, by A. R. W. McKellar, T. Oka, and B. P. Stoicheff, eds. (Springer-Verlag, Berlin, 1981), pp. 453–457.

See, for example, Y. R. Shen, The Principlesof Nonlinear Optics (Wiley, New York, 1984).

D. L. Andrews, “Forbidden nature of multipolar contributions to second-harmonic generationin isotropic fluids,” Phys. Rev. A 38, 3113–3115 (1988); T. F. Heinz and D. P. DiVincenzo “Comment on `Forbidden nature of multipolar contributions to second-harmonicgeneration in isotropic fluids, ' ” Phys. Rev. A 42, 6249–6251 (1990).
[CrossRef] [PubMed]

D. C. Hanna, M. A. Yuratich, and D. Cotter, Nonlinear Optics of Free Atoms and Molecules (Springer-Verlag, Berlin, 1979), and references therein.

R. T. Hodgson, P. P. Sorokin, and J. J. Wynne, “Tunable coherent vacuum-ultraviolet generation in atomic vapors,” Phys. Rev. Lett. 32, 343–346 (1974); P. P. Sorokin, J. J. Wynne, and J. R. Lankard, “Tunable coherent ir source based upon four-wave parametric conversionin alkali metal vapors,” Appl. Phys. Lett. 22, 342–344 (1973).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Experimental setup: PD 1, reference photodiode; BS, beam splitter; PMT, photomultiplier tube; GI, gated integrator; L1–L3, lenses.

Fig. 2
Fig. 2

Output spectrum from the potassium–argon vapor obtained with the laser frequency tuned to the two-photon 4s9d resonance. The middle peak, at 297.87 nm (2978.7 Å) is the true resonant SHG signal. The peak at 297.63 nm comes from the residual 11s4s transition, and the peak at 299.3 nm comes from the 10p4s transition in a four-wave mixing process.

Fig. 3
Fig. 3

SH signal as a function of potassium-vapor density in the potassium–argon mixture. The dashed line describes an NK4 dependence.

Fig. 4
Fig. 4

SH signal as a function of pump intensity I (a) at the 4s9d resonance, (b) at the 4s11s resonance. The straight lines denote an I8 dependence.

Fig. 5
Fig. 5

Spatial profile of SHG measured by scanning a 100-µm slit (a) horizontally and (b) vertically over the output over the output beam. The theoretical curves (solid curves) are shown for comparison.

Fig. 6
Fig. 6

Dependence of SHG on argon pressure in a mixture with 0.6 Torr of potassium. The pump intensities used are 13 GW/cm2 (squares) and 7.5 GW/cm2 (circles). The curves are obtained from theoretical calculation.

Fig. 7
Fig. 7

SHG generated by the probe pulse as a function of time delay between the pump and the probe pulses. Squares, pump intensity at 12 GW/cm2; circles, pump intensity at 8 GW/cm2. The curves are theoretical fits. The buildup time of Edc is 30 ps for the upper curve and 150 ps for the lower curve.

Fig. 8
Fig. 8

SH signal as a function of probe intensity when the pump intensity is held fixed. The vapor mixture has 0.6 Torr of potassium and 20 Torr of argon, and the probe pulse is delayed by 100 ps from the pump pulse. The straight line denotes an I2 dependence.

Fig. 9
Fig. 9

(a) Cross-correlation traces of SHG between pump and probe pulses from the 4s9d (crosses) and 4s11s (circles) resonances. The dotted curve is a fit to the 4s9d data with a FWHM of 2.6 ps. (b) Autocorrelation trace of SHG from a lithium triborate crystal. The dotted curve is a theoretical fit to the data with a FWHM of 4.1 ps.

Fig. 10
Fig. 10

Input intensity dependence of SHG at the peak of the cross-correlation trace of the 4s9d case shown in Fig. 9. The solid line is proportional to I3.7.

Fig. 11
Fig. 11

Calculated dc electric field Edc(r, t) generated by three-photon ionization of potassium with a 2-ps laser pulse. The initial electron density is 3×1011 cm-3.

Fig. 12
Fig. 12

Calculated time development of Edc at r=200 µm for two initial electron densities, 3×1011 cm-3 (solid curve) and 1012 cm-3 (dotted curve).

Fig. 13
Fig. 13

Time development of Edc (solid curves) and ρfg (dashed curves) for (a) 10 Torr and (b) 50 Torr of argon pressure at I(ω) =10 GW/cm2 and r=200 µm.

Fig. 14
Fig. 14

Partial energy-level diagram of potassium. The energy levels are not to scale. Fine structures of atomic levels are not resolved in the experiment.

Fig. 15
Fig. 15

Calculated spatial profile of the SHG output. The radius of the input beam and the ratio of SHG horizontal to vertical polarization (S/S) are obtained from the experiment. The input beam shape is assumed to be Gaussian.

Equations (21)

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χQ(2)(2ω)Ne3302np 4s|r2|9d9d|r|npnp|r|4s(ω4s,9d-2ω)(ω4s,np-ω)2×10-18esu,
Px(2)(2ω)=χQ(2)(2ω) θ2ζ4x(E2),
χ(2)(2ω)0.1n(r)e32np×ab4s|r|npnp|r|9dnp|r|4s(ω4s,9d-2ω)(ω4s,np-ω)l,
P(2ω)=e34m2ω4(Ne·E)E,
Up=e2E22mω2.
Ne(r, 0)=σ(3)I3(r, t)dtNe(r, 0)
=N exp-r2Ri2,
Ne(r, t)t=·v0L3Ne(r, t)+eLv0meNe(r, t)Edc(r, t),
Edc(r, t)=4πer0r[Ni(r, 0)-Ne(r, t)]rdr
Edc(r)=-v02me3er[Ne(r, )]Ne(r, )-v02me3er[Ne(r, 0)]Ne(r, 0)=2v02mer3eRi2,r<Ri.
Heff=mg (eE)2x|mm|x(ω-ωmg),
ρfg(0)=if|Heff|gTL.
ρfg(t)=ρfg(0)expiωfgt-t2TD2-tT2,
T2=12vσNB,TD=2Mc2kBTωfg21/2,
P2ω(r, t)npNK e2g|x|npnp|x|f(ωnp,g-2ω)Edc(r, t)ρfg(r, t)=np,mpNK ie4g|x|npnp|x|ff|x|mpmp|x|g3(ωnp,g-2ω)(ω-ωmp,g)×E(r, 0)2Edc(r, t)expiωfgt-t2TD2-tT2TL.
S(2ω)|PQ(2ω)+Pdc(2ω)|2=|PQ(2ω)|2+2 Re[PQ(2ω)·Pdc(2ω)]+|Pdc(2ω)|2,
I(2ω)=8πω2cn(2ω)|P(2ω)|2sin(Δkz/2)Δkz/22z2,
P(2ω)=χ1k1(E1·E1)+χ2E1(k1·E1),
P(2ω)=χaE(ω)[E(ω)·Edc]+χbEdc[E(ω)·E(ω)],
P(2ω)=χbE02Edc exp(-2r2/R2)xrxˆ+(a+1) yryˆ,
|P(2ω)|2=χb2E04Edc2 exp(-4r2/R2)×x2r2+(a+1)2 y2r2,

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