Abstract

The results of a theoretical and experimental investigation of parametric conversion of coherent and incoherent conical beams are presented. Special attention is paid to the problems of cumulative action of the incoherent conical pump and formation of output patterns in optical parametric oscillators and optical parametric generators. The theoretical model is based on transverse and longitudinal phase matching of three and four conical beams. The experimental results for optical parametric oscillators and optical parametric generators are based on KTP crystal pumped by coherent and incoherent conical beams at 532 nm as well as on a sodium-vapor optical parametric generator that is pumped simultaneously by Bessel and Gaussian beams.

© 1999 Optical Society of America

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  1. G. L. Schuster and J. R. Andrews, “Coherent summation of saturated AlGaAs amplifiers,” Opt. Lett. 18, 619–621 (1993).
    [CrossRef] [PubMed]
  2. G. L. Schuster and J. R. Andrews, “Coherent beam combining: optical loss effects on power scaling,” Appl. Opt. 34, 6801–6805 (1995).
    [CrossRef] [PubMed]
  3. M. J. Shaw, J. P. Partanen, Y. Owadano, I. N. Ross, E. Hodgson, C. B. Edwards, and F. O’Neill, “High-power forward Raman amplifiers employing low-pressure gases in light guides,” J. Opt. Soc. Am. B 3, 1466–1475 (1986).
    [CrossRef]
  4. I. N. Ross, M. J. Shaw, C. J. Hooker, M. H. Key, E. C. Harvey, J. M. D. Lister, J. E. Andrew, G. J. Hirst, and P. A. Rodgers, “A high performance excimer pump Raman laser,” Opt. Commun. 78, 263–270 (1990).
    [CrossRef]
  5. S. E. Harris, “Threshold of multimode parametric oscillators,” IEEE J. Quantum Electron. QE-2, 701–702 (1966).
    [CrossRef]
  6. R. L. Byer, M. K. Oshman, J. F. Young, and S. E. Harris, “Visible cw parametric oscillator,” Appl. Phys. Lett. 13, 109–111 (1968).
    [CrossRef]
  7. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [CrossRef]
  8. R. M. Herman and T. A. Wiggins, “Production and use of diffractionless beams,” J. Opt. Soc. Am. A 8, 932–942 (1991).
    [CrossRef]
  9. Y. Lin, W. Seka, J. H. Eberly, H. Huang, and D. L. Brown, “Experimental investigation of Bessel beam characteristics,” Appl. Opt. 31, 2708–2713 (1992).
    [CrossRef] [PubMed]
  10. M. R. Lapointe, “Review of non-diffracting Bessel beam experiments,” Opt. Laser Technol. 24, 315–321 (1992).
    [CrossRef]
  11. N. Davidson, A. A. Friesem, and E. Hasman, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
    [CrossRef]
  12. A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Optical parametric oscillation excited by an incoherent conical beam,” Opt. Commun. 143, 72–74 (1997).
    [CrossRef]
  13. R. Gadonas, A. Marcinkevičius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Travelling-wave optical parametric generator pumped by a conical beam,” Opt. Commun. 146, 253–256 (1998).
    [CrossRef]
  14. A. Piskarskas, V. Smilgevičius, A. Stabinis, and V. Jarutis, “Output patterns of optical parametric amplifiers and generators pumped by conical beams,” J. Opt. B 1, 52–57 (1999).
    [CrossRef]
  15. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  16. S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of self-phase-matching,” Phys. Rev. A 51, R2707–R2710 (1995).
    [CrossRef] [PubMed]
  17. V. Smilgevičius and A. Stabinis, “Two-beam pumped travelling-wave optical parametric generator,” Opt. Commun. 106, 69–74 (1994).
    [CrossRef]
  18. A. Baltuška, A. Beržanskis, R. Gadonas, A. Pugžlys, V. Smilgevičius, and A. Stabinis, “Angular structure formation in single-pass optical parametric generators pumped by intersecting beams,” Opt. Lett. 20, 2174–2176 (1995).
    [CrossRef] [PubMed]
  19. A. Dubietis, R. Danielius, G. Tamošauskas, and A. Piskarskas, “Combining effect in a multiple-beam pumped optical parametric amplifier,” J. Opt. Soc. Am. B 15, 1135–1139 (1998).
    [CrossRef]
  20. A. Marcinkevicius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Parametric superfluorescence excited in a nonlinear crystal by two uncorrelated pump beams,” Opt. Commun. 158, 101–104 (1998).
    [CrossRef]
  21. A. Piskarskas, A. Stabinis, V. Vaičaitis, and V. Jarutis, “Parametric superfluorescence excited in sodium vapour by Bessel beams,” Opt. Commun. 158, 298–304 (1998).
    [CrossRef]
  22. A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Optical parametric oscillator pumped by a Bessel beam,” Appl. Opt. 36, 7779–7782 (1997).
    [CrossRef]
  23. V. Vaičaitis, M. Ignatavichyus, V. A. Kudryashov, Yu. N. Pimenov, and N. D. Ustinov, “Four-photon parametric luminescence during noncollinear two-frequency excitation,” JETP Lett. 41, 78–82 (1985).

1999 (1)

A. Piskarskas, V. Smilgevičius, A. Stabinis, and V. Jarutis, “Output patterns of optical parametric amplifiers and generators pumped by conical beams,” J. Opt. B 1, 52–57 (1999).
[CrossRef]

1998 (4)

R. Gadonas, A. Marcinkevičius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Travelling-wave optical parametric generator pumped by a conical beam,” Opt. Commun. 146, 253–256 (1998).
[CrossRef]

A. Dubietis, R. Danielius, G. Tamošauskas, and A. Piskarskas, “Combining effect in a multiple-beam pumped optical parametric amplifier,” J. Opt. Soc. Am. B 15, 1135–1139 (1998).
[CrossRef]

A. Marcinkevicius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Parametric superfluorescence excited in a nonlinear crystal by two uncorrelated pump beams,” Opt. Commun. 158, 101–104 (1998).
[CrossRef]

A. Piskarskas, A. Stabinis, V. Vaičaitis, and V. Jarutis, “Parametric superfluorescence excited in sodium vapour by Bessel beams,” Opt. Commun. 158, 298–304 (1998).
[CrossRef]

1997 (2)

A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Optical parametric oscillator pumped by a Bessel beam,” Appl. Opt. 36, 7779–7782 (1997).
[CrossRef]

A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Optical parametric oscillation excited by an incoherent conical beam,” Opt. Commun. 143, 72–74 (1997).
[CrossRef]

1995 (3)

1994 (1)

V. Smilgevičius and A. Stabinis, “Two-beam pumped travelling-wave optical parametric generator,” Opt. Commun. 106, 69–74 (1994).
[CrossRef]

1993 (1)

1992 (3)

Y. Lin, W. Seka, J. H. Eberly, H. Huang, and D. L. Brown, “Experimental investigation of Bessel beam characteristics,” Appl. Opt. 31, 2708–2713 (1992).
[CrossRef] [PubMed]

M. R. Lapointe, “Review of non-diffracting Bessel beam experiments,” Opt. Laser Technol. 24, 315–321 (1992).
[CrossRef]

N. Davidson, A. A. Friesem, and E. Hasman, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

1991 (1)

1990 (1)

I. N. Ross, M. J. Shaw, C. J. Hooker, M. H. Key, E. C. Harvey, J. M. D. Lister, J. E. Andrew, G. J. Hirst, and P. A. Rodgers, “A high performance excimer pump Raman laser,” Opt. Commun. 78, 263–270 (1990).
[CrossRef]

1987 (1)

1986 (1)

1985 (1)

V. Vaičaitis, M. Ignatavichyus, V. A. Kudryashov, Yu. N. Pimenov, and N. D. Ustinov, “Four-photon parametric luminescence during noncollinear two-frequency excitation,” JETP Lett. 41, 78–82 (1985).

1968 (1)

R. L. Byer, M. K. Oshman, J. F. Young, and S. E. Harris, “Visible cw parametric oscillator,” Appl. Phys. Lett. 13, 109–111 (1968).
[CrossRef]

1966 (1)

S. E. Harris, “Threshold of multimode parametric oscillators,” IEEE J. Quantum Electron. QE-2, 701–702 (1966).
[CrossRef]

Andrew, J. E.

I. N. Ross, M. J. Shaw, C. J. Hooker, M. H. Key, E. C. Harvey, J. M. D. Lister, J. E. Andrew, G. J. Hirst, and P. A. Rodgers, “A high performance excimer pump Raman laser,” Opt. Commun. 78, 263–270 (1990).
[CrossRef]

Andrews, J. R.

Baltuška, A.

Beržanskis, A.

Boyd, R. W.

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of self-phase-matching,” Phys. Rev. A 51, R2707–R2710 (1995).
[CrossRef] [PubMed]

Brown, D. L.

Byer, R. L.

R. L. Byer, M. K. Oshman, J. F. Young, and S. E. Harris, “Visible cw parametric oscillator,” Appl. Phys. Lett. 13, 109–111 (1968).
[CrossRef]

Danielius, R.

Davidson, N.

N. Davidson, A. A. Friesem, and E. Hasman, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

Dubietis, A.

Durnin, J.

Eberly, J. H.

Edwards, C. B.

Friesem, A. A.

N. Davidson, A. A. Friesem, and E. Hasman, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

Gadonas, R.

R. Gadonas, A. Marcinkevičius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Travelling-wave optical parametric generator pumped by a conical beam,” Opt. Commun. 146, 253–256 (1998).
[CrossRef]

A. Baltuška, A. Beržanskis, R. Gadonas, A. Pugžlys, V. Smilgevičius, and A. Stabinis, “Angular structure formation in single-pass optical parametric generators pumped by intersecting beams,” Opt. Lett. 20, 2174–2176 (1995).
[CrossRef] [PubMed]

Harris, S. E.

R. L. Byer, M. K. Oshman, J. F. Young, and S. E. Harris, “Visible cw parametric oscillator,” Appl. Phys. Lett. 13, 109–111 (1968).
[CrossRef]

S. E. Harris, “Threshold of multimode parametric oscillators,” IEEE J. Quantum Electron. QE-2, 701–702 (1966).
[CrossRef]

Harvey, E. C.

I. N. Ross, M. J. Shaw, C. J. Hooker, M. H. Key, E. C. Harvey, J. M. D. Lister, J. E. Andrew, G. J. Hirst, and P. A. Rodgers, “A high performance excimer pump Raman laser,” Opt. Commun. 78, 263–270 (1990).
[CrossRef]

Hasman, E.

N. Davidson, A. A. Friesem, and E. Hasman, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

Herman, R. M.

Hirst, G. J.

I. N. Ross, M. J. Shaw, C. J. Hooker, M. H. Key, E. C. Harvey, J. M. D. Lister, J. E. Andrew, G. J. Hirst, and P. A. Rodgers, “A high performance excimer pump Raman laser,” Opt. Commun. 78, 263–270 (1990).
[CrossRef]

Hodgson, E.

Hooker, C. J.

I. N. Ross, M. J. Shaw, C. J. Hooker, M. H. Key, E. C. Harvey, J. M. D. Lister, J. E. Andrew, G. J. Hirst, and P. A. Rodgers, “A high performance excimer pump Raman laser,” Opt. Commun. 78, 263–270 (1990).
[CrossRef]

Huang, H.

Ignatavichyus, M.

V. Vaičaitis, M. Ignatavichyus, V. A. Kudryashov, Yu. N. Pimenov, and N. D. Ustinov, “Four-photon parametric luminescence during noncollinear two-frequency excitation,” JETP Lett. 41, 78–82 (1985).

Jarutis, V.

A. Piskarskas, V. Smilgevičius, A. Stabinis, and V. Jarutis, “Output patterns of optical parametric amplifiers and generators pumped by conical beams,” J. Opt. B 1, 52–57 (1999).
[CrossRef]

A. Piskarskas, A. Stabinis, V. Vaičaitis, and V. Jarutis, “Parametric superfluorescence excited in sodium vapour by Bessel beams,” Opt. Commun. 158, 298–304 (1998).
[CrossRef]

Key, M. H.

I. N. Ross, M. J. Shaw, C. J. Hooker, M. H. Key, E. C. Harvey, J. M. D. Lister, J. E. Andrew, G. J. Hirst, and P. A. Rodgers, “A high performance excimer pump Raman laser,” Opt. Commun. 78, 263–270 (1990).
[CrossRef]

Kudryashov, V. A.

V. Vaičaitis, M. Ignatavichyus, V. A. Kudryashov, Yu. N. Pimenov, and N. D. Ustinov, “Four-photon parametric luminescence during noncollinear two-frequency excitation,” JETP Lett. 41, 78–82 (1985).

Lapointe, M. R.

M. R. Lapointe, “Review of non-diffracting Bessel beam experiments,” Opt. Laser Technol. 24, 315–321 (1992).
[CrossRef]

Lin, Y.

Lister, J. M. D.

I. N. Ross, M. J. Shaw, C. J. Hooker, M. H. Key, E. C. Harvey, J. M. D. Lister, J. E. Andrew, G. J. Hirst, and P. A. Rodgers, “A high performance excimer pump Raman laser,” Opt. Commun. 78, 263–270 (1990).
[CrossRef]

Marcinkevicius, A.

R. Gadonas, A. Marcinkevičius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Travelling-wave optical parametric generator pumped by a conical beam,” Opt. Commun. 146, 253–256 (1998).
[CrossRef]

A. Marcinkevicius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Parametric superfluorescence excited in a nonlinear crystal by two uncorrelated pump beams,” Opt. Commun. 158, 101–104 (1998).
[CrossRef]

O’Neill, F.

Oshman, M. K.

R. L. Byer, M. K. Oshman, J. F. Young, and S. E. Harris, “Visible cw parametric oscillator,” Appl. Phys. Lett. 13, 109–111 (1968).
[CrossRef]

Owadano, Y.

Partanen, J. P.

Pimenov, Yu. N.

V. Vaičaitis, M. Ignatavichyus, V. A. Kudryashov, Yu. N. Pimenov, and N. D. Ustinov, “Four-photon parametric luminescence during noncollinear two-frequency excitation,” JETP Lett. 41, 78–82 (1985).

Piskarskas, A.

A. Piskarskas, V. Smilgevičius, A. Stabinis, and V. Jarutis, “Output patterns of optical parametric amplifiers and generators pumped by conical beams,” J. Opt. B 1, 52–57 (1999).
[CrossRef]

R. Gadonas, A. Marcinkevičius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Travelling-wave optical parametric generator pumped by a conical beam,” Opt. Commun. 146, 253–256 (1998).
[CrossRef]

A. Marcinkevicius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Parametric superfluorescence excited in a nonlinear crystal by two uncorrelated pump beams,” Opt. Commun. 158, 101–104 (1998).
[CrossRef]

A. Piskarskas, A. Stabinis, V. Vaičaitis, and V. Jarutis, “Parametric superfluorescence excited in sodium vapour by Bessel beams,” Opt. Commun. 158, 298–304 (1998).
[CrossRef]

A. Dubietis, R. Danielius, G. Tamošauskas, and A. Piskarskas, “Combining effect in a multiple-beam pumped optical parametric amplifier,” J. Opt. Soc. Am. B 15, 1135–1139 (1998).
[CrossRef]

A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Optical parametric oscillator pumped by a Bessel beam,” Appl. Opt. 36, 7779–7782 (1997).
[CrossRef]

A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Optical parametric oscillation excited by an incoherent conical beam,” Opt. Commun. 143, 72–74 (1997).
[CrossRef]

Pugžlys, A.

Rodgers, P. A.

I. N. Ross, M. J. Shaw, C. J. Hooker, M. H. Key, E. C. Harvey, J. M. D. Lister, J. E. Andrew, G. J. Hirst, and P. A. Rodgers, “A high performance excimer pump Raman laser,” Opt. Commun. 78, 263–270 (1990).
[CrossRef]

Ross, I. N.

I. N. Ross, M. J. Shaw, C. J. Hooker, M. H. Key, E. C. Harvey, J. M. D. Lister, J. E. Andrew, G. J. Hirst, and P. A. Rodgers, “A high performance excimer pump Raman laser,” Opt. Commun. 78, 263–270 (1990).
[CrossRef]

M. J. Shaw, J. P. Partanen, Y. Owadano, I. N. Ross, E. Hodgson, C. B. Edwards, and F. O’Neill, “High-power forward Raman amplifiers employing low-pressure gases in light guides,” J. Opt. Soc. Am. B 3, 1466–1475 (1986).
[CrossRef]

Schuster, G. L.

Seka, W.

Shaw, M. J.

I. N. Ross, M. J. Shaw, C. J. Hooker, M. H. Key, E. C. Harvey, J. M. D. Lister, J. E. Andrew, G. J. Hirst, and P. A. Rodgers, “A high performance excimer pump Raman laser,” Opt. Commun. 78, 263–270 (1990).
[CrossRef]

M. J. Shaw, J. P. Partanen, Y. Owadano, I. N. Ross, E. Hodgson, C. B. Edwards, and F. O’Neill, “High-power forward Raman amplifiers employing low-pressure gases in light guides,” J. Opt. Soc. Am. B 3, 1466–1475 (1986).
[CrossRef]

Smilgevicius, V.

A. Piskarskas, V. Smilgevičius, A. Stabinis, and V. Jarutis, “Output patterns of optical parametric amplifiers and generators pumped by conical beams,” J. Opt. B 1, 52–57 (1999).
[CrossRef]

R. Gadonas, A. Marcinkevičius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Travelling-wave optical parametric generator pumped by a conical beam,” Opt. Commun. 146, 253–256 (1998).
[CrossRef]

A. Marcinkevicius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Parametric superfluorescence excited in a nonlinear crystal by two uncorrelated pump beams,” Opt. Commun. 158, 101–104 (1998).
[CrossRef]

A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Optical parametric oscillation excited by an incoherent conical beam,” Opt. Commun. 143, 72–74 (1997).
[CrossRef]

A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Optical parametric oscillator pumped by a Bessel beam,” Appl. Opt. 36, 7779–7782 (1997).
[CrossRef]

A. Baltuška, A. Beržanskis, R. Gadonas, A. Pugžlys, V. Smilgevičius, and A. Stabinis, “Angular structure formation in single-pass optical parametric generators pumped by intersecting beams,” Opt. Lett. 20, 2174–2176 (1995).
[CrossRef] [PubMed]

V. Smilgevičius and A. Stabinis, “Two-beam pumped travelling-wave optical parametric generator,” Opt. Commun. 106, 69–74 (1994).
[CrossRef]

Stabinis, A.

A. Piskarskas, V. Smilgevičius, A. Stabinis, and V. Jarutis, “Output patterns of optical parametric amplifiers and generators pumped by conical beams,” J. Opt. B 1, 52–57 (1999).
[CrossRef]

R. Gadonas, A. Marcinkevičius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Travelling-wave optical parametric generator pumped by a conical beam,” Opt. Commun. 146, 253–256 (1998).
[CrossRef]

A. Marcinkevicius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Parametric superfluorescence excited in a nonlinear crystal by two uncorrelated pump beams,” Opt. Commun. 158, 101–104 (1998).
[CrossRef]

A. Piskarskas, A. Stabinis, V. Vaičaitis, and V. Jarutis, “Parametric superfluorescence excited in sodium vapour by Bessel beams,” Opt. Commun. 158, 298–304 (1998).
[CrossRef]

A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Optical parametric oscillator pumped by a Bessel beam,” Appl. Opt. 36, 7779–7782 (1997).
[CrossRef]

A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Optical parametric oscillation excited by an incoherent conical beam,” Opt. Commun. 143, 72–74 (1997).
[CrossRef]

A. Baltuška, A. Beržanskis, R. Gadonas, A. Pugžlys, V. Smilgevičius, and A. Stabinis, “Angular structure formation in single-pass optical parametric generators pumped by intersecting beams,” Opt. Lett. 20, 2174–2176 (1995).
[CrossRef] [PubMed]

V. Smilgevičius and A. Stabinis, “Two-beam pumped travelling-wave optical parametric generator,” Opt. Commun. 106, 69–74 (1994).
[CrossRef]

Tamošauskas, G.

Tewari, S. P.

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of self-phase-matching,” Phys. Rev. A 51, R2707–R2710 (1995).
[CrossRef] [PubMed]

Ustinov, N. D.

V. Vaičaitis, M. Ignatavichyus, V. A. Kudryashov, Yu. N. Pimenov, and N. D. Ustinov, “Four-photon parametric luminescence during noncollinear two-frequency excitation,” JETP Lett. 41, 78–82 (1985).

Vaicaitis, V.

A. Piskarskas, A. Stabinis, V. Vaičaitis, and V. Jarutis, “Parametric superfluorescence excited in sodium vapour by Bessel beams,” Opt. Commun. 158, 298–304 (1998).
[CrossRef]

V. Vaičaitis, M. Ignatavichyus, V. A. Kudryashov, Yu. N. Pimenov, and N. D. Ustinov, “Four-photon parametric luminescence during noncollinear two-frequency excitation,” JETP Lett. 41, 78–82 (1985).

Wiggins, T. A.

Young, J. F.

R. L. Byer, M. K. Oshman, J. F. Young, and S. E. Harris, “Visible cw parametric oscillator,” Appl. Phys. Lett. 13, 109–111 (1968).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

R. L. Byer, M. K. Oshman, J. F. Young, and S. E. Harris, “Visible cw parametric oscillator,” Appl. Phys. Lett. 13, 109–111 (1968).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. E. Harris, “Threshold of multimode parametric oscillators,” IEEE J. Quantum Electron. QE-2, 701–702 (1966).
[CrossRef]

J. Opt. B (1)

A. Piskarskas, V. Smilgevičius, A. Stabinis, and V. Jarutis, “Output patterns of optical parametric amplifiers and generators pumped by conical beams,” J. Opt. B 1, 52–57 (1999).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (2)

JETP Lett. (1)

V. Vaičaitis, M. Ignatavichyus, V. A. Kudryashov, Yu. N. Pimenov, and N. D. Ustinov, “Four-photon parametric luminescence during noncollinear two-frequency excitation,” JETP Lett. 41, 78–82 (1985).

Opt. Commun. (7)

A. Marcinkevicius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Parametric superfluorescence excited in a nonlinear crystal by two uncorrelated pump beams,” Opt. Commun. 158, 101–104 (1998).
[CrossRef]

A. Piskarskas, A. Stabinis, V. Vaičaitis, and V. Jarutis, “Parametric superfluorescence excited in sodium vapour by Bessel beams,” Opt. Commun. 158, 298–304 (1998).
[CrossRef]

V. Smilgevičius and A. Stabinis, “Two-beam pumped travelling-wave optical parametric generator,” Opt. Commun. 106, 69–74 (1994).
[CrossRef]

N. Davidson, A. A. Friesem, and E. Hasman, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Optical parametric oscillation excited by an incoherent conical beam,” Opt. Commun. 143, 72–74 (1997).
[CrossRef]

R. Gadonas, A. Marcinkevičius, A. Piskarskas, V. Smilgevičius, and A. Stabinis, “Travelling-wave optical parametric generator pumped by a conical beam,” Opt. Commun. 146, 253–256 (1998).
[CrossRef]

I. N. Ross, M. J. Shaw, C. J. Hooker, M. H. Key, E. C. Harvey, J. M. D. Lister, J. E. Andrew, G. J. Hirst, and P. A. Rodgers, “A high performance excimer pump Raman laser,” Opt. Commun. 78, 263–270 (1990).
[CrossRef]

Opt. Laser Technol. (1)

M. R. Lapointe, “Review of non-diffracting Bessel beam experiments,” Opt. Laser Technol. 24, 315–321 (1992).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

S. P. Tewari, H. Huang, and R. W. Boyd, “Theory of self-phase-matching,” Phys. Rev. A 51, R2707–R2710 (1995).
[CrossRef] [PubMed]

Other (1)

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

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Figures (14)

Fig. 1
Fig. 1

Spatial spectra of interacting conical beams in (a) Cartesian coordinates and in (b) the transverse θ, φ plane.

Fig. 2
Fig. 2

Dependence of transverse phase-matching integral T1(p, q) on p and q. g=150.

Fig. 3
Fig. 3

Dispositions of the wave vectors of the most effectively interacting three plane waves: 1, signal; 2, idler; and 3, pump. (a) k1α1+k2α2=k3α3, ψ1=ψ2=ψ3; (b) k1α1-k2α2=k3α3, ψ1=ψ3, ψ2=ψ3±π; (c) k2α2-k1α1=k3α3, ψ1=ψ3±π, ψ2=ψ3; (d) α1=0, k2α2=k3α3, ψ2=ψ3; (e) α2=0, k1α1=k3α3, ψ1=ψ3; (f ) α1=α2=α3, ψ1=ψ2=ψ3; (g) k1α1=k2α2, α3=0, ψ2=ψ1±π.

Fig. 4
Fig. 4

Dependence of transverse phase-matching integral T2(p, q) on p and q. g=150, γ=0.553.

Fig. 5
Fig. 5

Dispositions of the wave vectors of the most effectively interacting four plane waves for β4=0: 1, signal; 2, idler; and 3, 4, pump. (a) k1α1+k2α2=k3α3, (b) k1α1-k2α2=k3α3, (c) k2α2-k1α1=k3α3, (d) α1=0 and k2α2=k3α3, (e) α2=0 and k1α1=k3α3.

Fig. 6
Fig. 6

Disposition of pump rings of different frequencies in the θ, φ plane for coherent amplification of an axial signal wave by a multicolor conical pump.

Fig. 7
Fig. 7

Experimental setup for a KTP OPO pumped by (a) coherent and (b) incoherent conical beams: L’s, lenses; M’s, mirrors; F, filter.

Fig. 8
Fig. 8

Far-field patterns of (a) the coherent conical beam formed by a ring diaphragm and (b) the incoherent conical beam formed by the nonaxially excited multimode fiber.

Fig. 9
Fig. 9

Far-field patterns of the OPO o-polarized output radiation pumped by (a) a coherent conical beam and (b) an incoherent conical beam. (c) Area marked out by the solid circle in (b). Spatial profiles of the central spot: (d) TEM00, (e) TEM01, (f) TEM11, (g) TEM07.

Fig. 10
Fig. 10

Experimental setup of a KTP OPG pumped by coherent and incoherent conical beams: F, filter; OMA, optical multichannel analyzer; TOPG, traveling-wave optical parametric generator.

Fig. 11
Fig. 11

Spatial profiles of (a) the coherent conical pump beam, (b) its angular spectrum, and (c) the corresponding OPG o-polarized output radiation in the far field. Spatial profiles of (d) the incoherent conical pump beam, (e) its angular spectrum, and (f) the corresponding OPG o-polarized output in the far field.

Fig. 12
Fig. 12

Schematic energy-level diagram of sodium for two-photon excitation.

Fig. 13
Fig. 13

Experimental setup for investigation of parametric superfluorescence in sodium vapor excited by Bessel and Gaussian beams: SHG, second-harmonic generator.

Fig. 14
Fig. 14

Angular spectra of the Bessel pump beam (left) and parametric superfluorescence (right) excited in sodium vapor by Bessel and Gaussian beams. Only the radiation of signal frequency is presented.

Equations (40)

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fm(t, x, y, z)=exp[i(ωmt-kmzz)] 12π02πSm(ψm)
×exp[-iβm(x cos ψm+y sin ψm)]dψm,
m=1, 2, 3.
fm(t, x, y, z)=exp[i(ωmt-kmzz)]SmJ0(βmx2+y2).
k1x+k2x=k3x,k1y+k2y=k3y,
k1z+k2z=k3z,ω1+ω2=ω3,
β1 cos ψ1+β2 cos ψ2=β3 cos ψ3,
β1 sin ψ1+β2 sin ψ2=β3 sin ψ3.
β1 cos ϕ1+β2 cos ϕ2=β3,
β1 sin ϕ1+β2 sin ϕ2=0.
F1(β1, β2)0rA2*(β2r)A3(β3r)J0(β1r)dr,
T1(p, q)=0ν exp-ν2g2J0(pν)J0(qν)J0(ν)dν,
k1α1+k2α2=k3α3
k1α1-k2α2=k3α3
k2α2-k1α1=k3α3.
k1α12+k2α22=k3α32+2(k1+k2-k3).
α1=α10+α3,α2=|α20-α3|;
α1=|α10-α3|,α2=α20+α3,
α10=k2/k1R,α20=k1/k2R,
R2=2(k1+k2-k3)/(k1+k2),
k1x+k2x=k3x+k4x,
k1y+k2y=k3y+k4y,
k1z+k2z=k3z+k4z,
ω1+ω2=ω3+ω4,
β1 cos ψ1+β2 cos ψ2=β3 cos ψ3+β4 cos ψ4,
β1 sin ψ1+β2 sin ψ2=β3 sin ψ3+β4 sin ψ4,
F2(β1, β2)=0rA2*(β2r)A3(β3r)A4(β4r)J0(β1r)dr.
T2(p, q)=0ν exp-ν2g2J0(pν)J0(qν)J0(γν)J0(ν)dν,
k1α12+k2α22
=k3α32+k4α42+2(k1+k2-k3-k4)
S3(β, ψ)=a3G3(β)H3(ψ),
G3(β)=πd32 exp-β32+β24d32I0β3βd322,
A3(r, ϑ)=a34π20βG3(β)dβ02πH3(ψ)×exp[-iβr cos(ψ-ϑ)]dψ.
A3(r, ϑ)=a34π2n(-i)n exp(-inϑ)×02πH3(ψ)exp(inψ)dψ×0βG3(β)Jn(βr)dβ.
A3(r, ϑ)=a32πn(-i)n exp(-inϑ)bnBn(r);
A1z=iσ1A2*A3,A2z=iσ2A1*A3,
F1(β1)0r|A3|2J0(β1r)dr.
F1(β1)n|bn|20rBn2(r)J0(β1r)dr.
F1(0)n|bn|20βG32(β)dβ.
F1(0)02π|H3(ψ)|2dψ.

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