Abstract

The generation of UV third-harmonic radiation by a focused laser beam in a positively dispersive gaseous medium is investigated. The nonlinear gas is confined to a focal half-space by using a differentially pumped gas cell. The resulting density gradient along the beam axis is shown to provide an efficient frequency conversion in spectral regions of positive dispersion. Experimental results obtained in argon at λ ∼ 197 nm, which compare favorably with theory, are presented.

© 1994 Optical Society of America

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References

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  1. C. R. Vidal, Tunable Lasers, Vol. 59 of Springer Topics in Applied Physics (Springer-Verlag, Berlin, 1987), Chap. 3, p. 57, and references therein.
    [CrossRef]
  2. G. C. Bjorklund, “Effects of focusing on third-order nonlinear processes in isotropic media,” IEEE J. Quantum Electron. QE-11, 287–296 (1975).
    [CrossRef]
  3. V. G. Arkhipkin, Yu. I. Heller, A. K. Popov, A. S. Provorov, “Frequency mixing in a gas-filled waveguide for VUV light generation,” Appl. Phys. B 37, 93–97 (1985).
    [CrossRef]
  4. M. Castillejo, J. Y. Zhou, M. H. R. Hutchinson, “Coherent vacuum ultraviolet generation by frequency mixing in glass hollow waveguides,” Appl. Phys. B 45, 293–299 (1988).
    [CrossRef]
  5. J. Reintjes, “Generation of coherent tunable VUV radiation near the Ly-β transition of atomic hydrogen,” Opt. Lett. 5, 342–344 (1980).
    [CrossRef] [PubMed]
  6. J. Bokor, P. H. Bucksbaum, R. R. Freeman, “Generation of 35.5-nm coherent radiation,” Opt. Lett. 8, 217–219 (1983).
    [CrossRef] [PubMed]
  7. D. S. Bethune, C. T. Rettner, “Optical harmonic generation in nonuniform gaseous media with application to frequency tripling in free-jet expansions,” IEEE J. Quantum Electron. QE-23, 1348–1360 (1987).
    [CrossRef]
  8. R. Hilbig, R. Wallenstein, “Narrowband tunable VUV radiation generated by nonresonant sum- and difference-frequency mixing in xenon and krypton,” Appl. Opt. 21, 913–917 (1982).
    [CrossRef] [PubMed]
  9. G. F. Ward, G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
    [CrossRef]
  10. A. Lago, G. Hilber, R. Wallenstein, “Optical-frequency conversion in gaseous media,” Phys. Rev. A 36, 3827–3836 (1987).
    [CrossRef] [PubMed]
  11. P. N. Butcher, D. Cotter, The Elements of Nonlinear Optics, Vol. 9 of Cambridge Studies in Nonlinear Optics (Cambridge U. Press, Cambridge, 1990), Chap. 2, p. 12.
    [CrossRef]
  12. P. J. Leonard, “Refractive indices, Verdet constants, and polarizabilities of the inert gases,” At. Data Nucl. Data Tables 14, 21–29 (1976).
    [CrossRef]

1988 (1)

M. Castillejo, J. Y. Zhou, M. H. R. Hutchinson, “Coherent vacuum ultraviolet generation by frequency mixing in glass hollow waveguides,” Appl. Phys. B 45, 293–299 (1988).
[CrossRef]

1987 (2)

D. S. Bethune, C. T. Rettner, “Optical harmonic generation in nonuniform gaseous media with application to frequency tripling in free-jet expansions,” IEEE J. Quantum Electron. QE-23, 1348–1360 (1987).
[CrossRef]

A. Lago, G. Hilber, R. Wallenstein, “Optical-frequency conversion in gaseous media,” Phys. Rev. A 36, 3827–3836 (1987).
[CrossRef] [PubMed]

1985 (1)

V. G. Arkhipkin, Yu. I. Heller, A. K. Popov, A. S. Provorov, “Frequency mixing in a gas-filled waveguide for VUV light generation,” Appl. Phys. B 37, 93–97 (1985).
[CrossRef]

1983 (1)

1982 (1)

1980 (1)

1976 (1)

P. J. Leonard, “Refractive indices, Verdet constants, and polarizabilities of the inert gases,” At. Data Nucl. Data Tables 14, 21–29 (1976).
[CrossRef]

1975 (1)

G. C. Bjorklund, “Effects of focusing on third-order nonlinear processes in isotropic media,” IEEE J. Quantum Electron. QE-11, 287–296 (1975).
[CrossRef]

1969 (1)

G. F. Ward, G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
[CrossRef]

Arkhipkin, V. G.

V. G. Arkhipkin, Yu. I. Heller, A. K. Popov, A. S. Provorov, “Frequency mixing in a gas-filled waveguide for VUV light generation,” Appl. Phys. B 37, 93–97 (1985).
[CrossRef]

Bethune, D. S.

D. S. Bethune, C. T. Rettner, “Optical harmonic generation in nonuniform gaseous media with application to frequency tripling in free-jet expansions,” IEEE J. Quantum Electron. QE-23, 1348–1360 (1987).
[CrossRef]

Bjorklund, G. C.

G. C. Bjorklund, “Effects of focusing on third-order nonlinear processes in isotropic media,” IEEE J. Quantum Electron. QE-11, 287–296 (1975).
[CrossRef]

Bokor, J.

Bucksbaum, P. H.

Butcher, P. N.

P. N. Butcher, D. Cotter, The Elements of Nonlinear Optics, Vol. 9 of Cambridge Studies in Nonlinear Optics (Cambridge U. Press, Cambridge, 1990), Chap. 2, p. 12.
[CrossRef]

Castillejo, M.

M. Castillejo, J. Y. Zhou, M. H. R. Hutchinson, “Coherent vacuum ultraviolet generation by frequency mixing in glass hollow waveguides,” Appl. Phys. B 45, 293–299 (1988).
[CrossRef]

Cotter, D.

P. N. Butcher, D. Cotter, The Elements of Nonlinear Optics, Vol. 9 of Cambridge Studies in Nonlinear Optics (Cambridge U. Press, Cambridge, 1990), Chap. 2, p. 12.
[CrossRef]

Freeman, R. R.

Heller, Yu. I.

V. G. Arkhipkin, Yu. I. Heller, A. K. Popov, A. S. Provorov, “Frequency mixing in a gas-filled waveguide for VUV light generation,” Appl. Phys. B 37, 93–97 (1985).
[CrossRef]

Hilber, G.

A. Lago, G. Hilber, R. Wallenstein, “Optical-frequency conversion in gaseous media,” Phys. Rev. A 36, 3827–3836 (1987).
[CrossRef] [PubMed]

Hilbig, R.

Hutchinson, M. H. R.

M. Castillejo, J. Y. Zhou, M. H. R. Hutchinson, “Coherent vacuum ultraviolet generation by frequency mixing in glass hollow waveguides,” Appl. Phys. B 45, 293–299 (1988).
[CrossRef]

Lago, A.

A. Lago, G. Hilber, R. Wallenstein, “Optical-frequency conversion in gaseous media,” Phys. Rev. A 36, 3827–3836 (1987).
[CrossRef] [PubMed]

Leonard, P. J.

P. J. Leonard, “Refractive indices, Verdet constants, and polarizabilities of the inert gases,” At. Data Nucl. Data Tables 14, 21–29 (1976).
[CrossRef]

New, G. H. C.

G. F. Ward, G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
[CrossRef]

Popov, A. K.

V. G. Arkhipkin, Yu. I. Heller, A. K. Popov, A. S. Provorov, “Frequency mixing in a gas-filled waveguide for VUV light generation,” Appl. Phys. B 37, 93–97 (1985).
[CrossRef]

Provorov, A. S.

V. G. Arkhipkin, Yu. I. Heller, A. K. Popov, A. S. Provorov, “Frequency mixing in a gas-filled waveguide for VUV light generation,” Appl. Phys. B 37, 93–97 (1985).
[CrossRef]

Reintjes, J.

Rettner, C. T.

D. S. Bethune, C. T. Rettner, “Optical harmonic generation in nonuniform gaseous media with application to frequency tripling in free-jet expansions,” IEEE J. Quantum Electron. QE-23, 1348–1360 (1987).
[CrossRef]

Vidal, C. R.

C. R. Vidal, Tunable Lasers, Vol. 59 of Springer Topics in Applied Physics (Springer-Verlag, Berlin, 1987), Chap. 3, p. 57, and references therein.
[CrossRef]

Wallenstein, R.

Ward, G. F.

G. F. Ward, G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
[CrossRef]

Zhou, J. Y.

M. Castillejo, J. Y. Zhou, M. H. R. Hutchinson, “Coherent vacuum ultraviolet generation by frequency mixing in glass hollow waveguides,” Appl. Phys. B 45, 293–299 (1988).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (2)

V. G. Arkhipkin, Yu. I. Heller, A. K. Popov, A. S. Provorov, “Frequency mixing in a gas-filled waveguide for VUV light generation,” Appl. Phys. B 37, 93–97 (1985).
[CrossRef]

M. Castillejo, J. Y. Zhou, M. H. R. Hutchinson, “Coherent vacuum ultraviolet generation by frequency mixing in glass hollow waveguides,” Appl. Phys. B 45, 293–299 (1988).
[CrossRef]

At. Data Nucl. Data Tables (1)

P. J. Leonard, “Refractive indices, Verdet constants, and polarizabilities of the inert gases,” At. Data Nucl. Data Tables 14, 21–29 (1976).
[CrossRef]

IEEE J. Quantum Electron. (2)

D. S. Bethune, C. T. Rettner, “Optical harmonic generation in nonuniform gaseous media with application to frequency tripling in free-jet expansions,” IEEE J. Quantum Electron. QE-23, 1348–1360 (1987).
[CrossRef]

G. C. Bjorklund, “Effects of focusing on third-order nonlinear processes in isotropic media,” IEEE J. Quantum Electron. QE-11, 287–296 (1975).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

G. F. Ward, G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57–72 (1969).
[CrossRef]

Phys. Rev. A (1)

A. Lago, G. Hilber, R. Wallenstein, “Optical-frequency conversion in gaseous media,” Phys. Rev. A 36, 3827–3836 (1987).
[CrossRef] [PubMed]

Other (2)

P. N. Butcher, D. Cotter, The Elements of Nonlinear Optics, Vol. 9 of Cambridge Studies in Nonlinear Optics (Cambridge U. Press, Cambridge, 1990), Chap. 2, p. 12.
[CrossRef]

C. R. Vidal, Tunable Lasers, Vol. 59 of Springer Topics in Applied Physics (Springer-Verlag, Berlin, 1987), Chap. 3, p. 57, and references therein.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

G factor versus bΔk under tight-focusing conditions (b/L = 0.1) for f/L = 0.5 (focus in the middle of the cell) and f/L = 0 (focus at the beginning of the cell).

Fig. 2
Fig. 2

G factor versus bΔk for different density gradient parameters Δζ = 10−6, 10−1, 1: (a) S1 = 0 (zero input density), (b) S1 = 0.1 S2 (residual input density).

Fig. 3
Fig. 3

Schematic diagram of the experimental apparatus: DL, dye laser; PD, beam monitor photodiode; BS, beam splitter; S, mirror; F, focusing lens; C, cell; P1, input vacuum gauge; P2, output vacuum gauge; L, monochromator lens; P, prism; M, diffraction grating monochromator; PM, photomultiplier.

Fig. 4
Fig. 4

Dependence of the third-harmonic power, Wg, on the fundamental power, W. The maximum peak power of the input pulses is ∼ 6MW.

Fig. 5
Fig. 5

Dependence of the third-harmonic power on the ratio of the Ar pressures in the input and output half-cells.

Fig. 6
Fig. 6

Dependence of the third-harmonic power on the Ar pressure.

Equations (18)

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E ( r , t ) = E 0 exp { i [ L ( z ) ω t ] } exp [ k ( x 2 + y 2 ) b ( 1 + i ζ ) ] ( 1 + i ζ ) ,
ζ = z f b / 2 .
L ( z ) = z d z k ( z ) .
W g = ( 4 π c ) 2 N 0 2 χ 2 k g k 3 W 3 F ,
F = | d ζ S ( ζ ) exp [ i b Δ k ζ d ζ S ( ζ ) / 2 ] ( 1 + i ζ ) 2 | 2 ,
G = ( b Δ k ) 2 F .
S = { 0 for z < 0 or z > L 1 otherwise ,
F = | 2 f / b 2 ( L f ) / b d ζ exp ( i ζ b Δ k / 2 ) ( 1 + i ζ ) 2 | 2 .
S = S 1 + ( S 2 S 1 ) 1 2 ( 2 π arctan π ζ Δ ζ + 1 )
Δ ϕ ( ζ ) = b Δ k 2 ζ d ζ S ( ζ ) .
G = G ( S 1 , Δ ζ , b Δ k ) ,
b Δ k / ( b Δ k ) STP = P 2 / P STP .
Δ ζ = 0.4 , ( b Δ k ) STP = 36 .
( W g ) opt = ε ( b ) W 3 ,
ε ( b 1 ) ε ( b 2 ) 0.4 ,
b 2 b 1 = ( l 2 l 1 ) 2 = ( 5 3 ) 2 .
ε ( b 1 ) ε ( b 2 ) = G opt ( b 1 Δ k ; Δ ζ 1 ) G opt ( b 2 Δ k ; Δ ζ 2 ) ( b 2 b 1 ) 2 .
ε ( b 1 ) ε ( b 2 ) = 3.2 ( 3 5 ) 4 = 0.41 ,

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