Abstract

Since the IR multiple-photon decomposition probability of polyatomic molecules is a function of radiative fluence, the measured fraction of the dissociated molecules could be affected by the spatial distribution of radiation. In this paper the influence of the radiative distribution of a Gaussian beam on measured probability is investigated in detail. The main conclusions are that, for two special cases, namely, cylindrical beam and double-cone beam, one will be able to get information of the fluence dependence of real decomposition probability from measured energy dependence of average probability by means of a log–log plot. This article will be helpful for consideration of experimental conditions, summarizing of data, and comparison of the results of different experiments to avoid possible confusion.

© 1983 Optical Society of America

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References

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  1. S. Speiser, S. Kimel, Chem. Phys. Lett. 7, 19 (1970).
    [CrossRef]
  2. M. R. Cervenan, N. R. Isenor, Opt. Commun. 13, 175 (1975).
    [CrossRef]
  3. D. R. Keefer, J. E. Allen, W. B. Person, Chem. Phys. Lett. 43, 394 (1976).
    [CrossRef]
  4. W. Fuss, T. P. Cotter, Appl. Phys. 12, 265 (1977).
    [CrossRef]
  5. Ma Xing-Xiao, Hu Zhao-Lin, Acta Phys. Sin. 27, 645 (1978); (in Chinese).
  6. I. P. Herman, Opt. Lett. 4, 403 (1979); J. B. Marling, I. P. Herman, S. J. Thomas, J. Chem. Phys. 72, 5603 (1980).
    [CrossRef] [PubMed]
  7. A. C. Baldwin, J. R. Barkar, J. Chem. Phys. 74, 3823 (1981).
    [CrossRef]
  8. A. Norwak, D. O. Hame, Opt. Lett. 6, 185 (1981); P. Bernard, P. Galarneau, S. L. Chin, Opt. Lett. 6, 139 (1981).
    [CrossRef] [PubMed]
  9. See, for example, M. C. Gower, K. W. Billman, Appl. Phys. Lett. 30, 514 (1977); R. V. Ambartzumian, V. S. Letokhov, Acc. Chem. Res. 10, 61 (1977).
    [CrossRef]
  10. A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971).
  11. P. Fettweis, M. Néve de Méverguies, Appl. Phys. 12, 219 (1977).
    [CrossRef]

1981

1979

1978

Ma Xing-Xiao, Hu Zhao-Lin, Acta Phys. Sin. 27, 645 (1978); (in Chinese).

1977

See, for example, M. C. Gower, K. W. Billman, Appl. Phys. Lett. 30, 514 (1977); R. V. Ambartzumian, V. S. Letokhov, Acc. Chem. Res. 10, 61 (1977).
[CrossRef]

P. Fettweis, M. Néve de Méverguies, Appl. Phys. 12, 219 (1977).
[CrossRef]

W. Fuss, T. P. Cotter, Appl. Phys. 12, 265 (1977).
[CrossRef]

1976

D. R. Keefer, J. E. Allen, W. B. Person, Chem. Phys. Lett. 43, 394 (1976).
[CrossRef]

1975

M. R. Cervenan, N. R. Isenor, Opt. Commun. 13, 175 (1975).
[CrossRef]

1970

S. Speiser, S. Kimel, Chem. Phys. Lett. 7, 19 (1970).
[CrossRef]

Allen, J. E.

D. R. Keefer, J. E. Allen, W. B. Person, Chem. Phys. Lett. 43, 394 (1976).
[CrossRef]

Baldwin, A. C.

A. C. Baldwin, J. R. Barkar, J. Chem. Phys. 74, 3823 (1981).
[CrossRef]

Barkar, J. R.

A. C. Baldwin, J. R. Barkar, J. Chem. Phys. 74, 3823 (1981).
[CrossRef]

Billman, K. W.

See, for example, M. C. Gower, K. W. Billman, Appl. Phys. Lett. 30, 514 (1977); R. V. Ambartzumian, V. S. Letokhov, Acc. Chem. Res. 10, 61 (1977).
[CrossRef]

Cervenan, M. R.

M. R. Cervenan, N. R. Isenor, Opt. Commun. 13, 175 (1975).
[CrossRef]

Cotter, T. P.

W. Fuss, T. P. Cotter, Appl. Phys. 12, 265 (1977).
[CrossRef]

Fettweis, P.

P. Fettweis, M. Néve de Méverguies, Appl. Phys. 12, 219 (1977).
[CrossRef]

Fuss, W.

W. Fuss, T. P. Cotter, Appl. Phys. 12, 265 (1977).
[CrossRef]

Gower, M. C.

See, for example, M. C. Gower, K. W. Billman, Appl. Phys. Lett. 30, 514 (1977); R. V. Ambartzumian, V. S. Letokhov, Acc. Chem. Res. 10, 61 (1977).
[CrossRef]

Hame, D. O.

Herman, I. P.

Isenor, N. R.

M. R. Cervenan, N. R. Isenor, Opt. Commun. 13, 175 (1975).
[CrossRef]

Keefer, D. R.

D. R. Keefer, J. E. Allen, W. B. Person, Chem. Phys. Lett. 43, 394 (1976).
[CrossRef]

Kimel, S.

S. Speiser, S. Kimel, Chem. Phys. Lett. 7, 19 (1970).
[CrossRef]

Néve de Méverguies, M.

P. Fettweis, M. Néve de Méverguies, Appl. Phys. 12, 219 (1977).
[CrossRef]

Norwak, A.

Person, W. B.

D. R. Keefer, J. E. Allen, W. B. Person, Chem. Phys. Lett. 43, 394 (1976).
[CrossRef]

Siegman, A. E.

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971).

Speiser, S.

S. Speiser, S. Kimel, Chem. Phys. Lett. 7, 19 (1970).
[CrossRef]

Xing-Xiao, Ma

Ma Xing-Xiao, Hu Zhao-Lin, Acta Phys. Sin. 27, 645 (1978); (in Chinese).

Zhao-Lin, Hu

Ma Xing-Xiao, Hu Zhao-Lin, Acta Phys. Sin. 27, 645 (1978); (in Chinese).

Acta Phys. Sin.

Ma Xing-Xiao, Hu Zhao-Lin, Acta Phys. Sin. 27, 645 (1978); (in Chinese).

Appl. Phys.

W. Fuss, T. P. Cotter, Appl. Phys. 12, 265 (1977).
[CrossRef]

P. Fettweis, M. Néve de Méverguies, Appl. Phys. 12, 219 (1977).
[CrossRef]

Appl. Phys. Lett.

See, for example, M. C. Gower, K. W. Billman, Appl. Phys. Lett. 30, 514 (1977); R. V. Ambartzumian, V. S. Letokhov, Acc. Chem. Res. 10, 61 (1977).
[CrossRef]

Chem. Phys. Lett.

D. R. Keefer, J. E. Allen, W. B. Person, Chem. Phys. Lett. 43, 394 (1976).
[CrossRef]

S. Speiser, S. Kimel, Chem. Phys. Lett. 7, 19 (1970).
[CrossRef]

J. Chem. Phys.

A. C. Baldwin, J. R. Barkar, J. Chem. Phys. 74, 3823 (1981).
[CrossRef]

Opt. Commun.

M. R. Cervenan, N. R. Isenor, Opt. Commun. 13, 175 (1975).
[CrossRef]

Opt. Lett.

Other

A. E. Siegman, An Introduction to Lasers and Masers (McGraw-Hill, New York, 1971).

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Figures (6)

Fig. 1
Fig. 1

Typical schematic experimental setup.

Fig. 2
Fig. 2

Equifluence line plot with effective region of MPD. The shaded region corresponds to the effective region of MPD, where FFT.

Fig. 3
Fig. 3

Effective region of MPD and the boundaries of the observed region bounded by zW.

Fig. 4
Fig. 4

Variation of W ¯ with F0 in case of cylindric beam. W ¯ α = 2 π b 0 z W A α F 0 α / α k V represents the asymptotic expression of W ¯ α as FT/F0 → 0 in Eq. (21).

Fig. 5
Fig. 5

Variation of W ¯ with F0 in case of double-cone beam. W ¯ α = 2 π b 0 2 A α F T α G α / 3 k V, where G α is described by Eqs. (28)(30).

Fig. 6
Fig. 6

General form of W ¯: (a) the case of a cylindrical beam; (b) the case of a double-cone beam. Gα desired the variation of W ¯ α with fluence F0 [see Eq. (22)].

Equations (27)

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W ¯ = ( V ) W d V / V ,
F = F ( r ) = F ( r , ϕ , z )
W ¯ = 1 V ( V ) W r d r d ϕ d z = 1 v ( V ) W T d F d ϕ d z .
I ( r , ϕ , z , t ) = I ( r , z , t ) = I 0 ( t ) ( b 0 b ) exp ( - k r 2 / b ) ,
b = b 0 [ 1 + ( z / b 0 ) 2 ] = k w 2 / 2 ,
k = 2 π / λ ,
F ( r , ϕ , z ) = F ( r , z ) = F 0 ( b 0 b ) exp ( - k r 2 / b ) ,
F = I d t , F 0 = I 0 d t .
W ¯ = 2 π b 0 k V · F T F 0 W ( F ) d F / F 0 z m [ 1 + ( z / b 0 ) 2 ] d z , ( F 0 > F T ) ,
z m = either of [ b 0 ( F 0 / F ) - 1 , z W ] ,
W ( F ) { > 0 , F F T = 0 , F < F T according to assumption ( 2 ) ,
z T = b 0 ( F 0 / F T ) - 1 ,
z W = { b 0 ( F 0 / F ) - 1 , if z W z T , z W , if z W < z T and F T < F < F 0 / [ 1 + ( z W b 0 ) 2 ] , b 0 ( F 0 / F ) - 1 , if z W < z T and F 0 F F 0 / [ 1 + ( z W b 0 ) 2 ] ,
W ¯ = 2 π b 0 z W k V · [ 1 + 1 3 ( z W / b 0 ) 2 ] F T F 0 / [ 1 + ( z W / b 0 ) 2 ] W ( F ) d F / F + 2 π b 0 2 F 0 3 / 2 3 k V F 0 / [ 1 + ( z W / b 0 ) 2 ] F 0 ( 1 - F F 0 ) 1 / 2 ( 1 + 2 F F 0 ) W ( F ) d F / F 5 / 2             for z W < z T ,
W ¯ = 2 π b 0 2 F 0 3 / 2 3 k V · F T F 0 ( 1 - F F 0 ) 1 / 2 ( 1 + 2 F F 0 ) W ( F ) d F / F 5 / 2             for z W z T ,
W ¯ = 2 π b 0 z W k V · [ F T F 0 W ( F ) d F / F + 0 ( z W b 0 ) ] 2 π b 0 z W k V · F T F 0 W ( F ) d F / F             ( for z W b 0 ) .
V * volume within F F T and between boundaries r d r d ϕ d z
V * = { π [ w 0 2 ln ( F 0 F T ) ] z W for cylindrical beam 4 π b 0 2 9 k · ( F 0 F T ) 3 / 2 for double - cone beam .
E = 2 π 0 F 0 exp ( - k r 2 / b 0 ) r d r = π b 0 F 0 / k F 0 .
W = A α F α ,             0 α = const ,
W ¯ α = { 2 π b 0 z W α k V · A α F 0 α · [ 1 - ( F T F 0 ) α ] for cylindrical beam ( z W b 0 ) 2 π b 0 2 3 k V · A α F T α G α ( F 0 F T ) for double - cone beam ( z W z T ) ,
G α ( F 0 F T ) ( F 0 F T ) α ( F T / F 0 ) 1 ( 1 - x ) 1 / 2 ( 1 + 2 x ) x α - 5 / 2 d x ,
W ¯ α ~ F 0 α E α .
G α ( F 0 F T ) = { 2 3 - 2 α · ( F 0 F T ) 3 / 2 for α < 3 / 2 , ( F 0 F T ) 3 / 2 ln ( 4 F 0 F T ) for α = 3 / 2 , 6 ( α - 1 ) 2 α - 3 · [ 0 1 ( 1 - x ) 1 / 2 x α - 3 / 2 d x ] · ( F 0 F T ) α for α > 3 / 2.
W α { 2 π b 0 z W α k V A α F 0 α for α > 0 , 2 π b 0 z w k V A α ln ( F 0 F T ) for α = 0.
W ¯ α { 4 π b 0 2 3 ( 3 - 2 α ) k V · ( A α F T α ) ( F 0 F T ) 3 / 2 for α < 3 / 2 , 2 π b 0 2 3 k V · ( A 3 / 2 F T 3 / 2 ) ln ( 4 F 0 F T ) · ( F 0 F T ) 3 / 2 α = 3 / 2 , 4 π b 0 2 ( 2 α - 3 ) k V · [ 0 1 ( 1 - x ) 1 / 2 x α - 3 / 2 d x ] ( A α F T α ) ( F 0 F T ) α α > 3 / 2.
W ¯ α ~ { { ln E , α = 0 E α , α > 0 } for cylindrical beam , { E 3 / 2 , α < 3.2 ln E · E 3 / 2 , α = 3 / 2 E α , α > 3 / 2 } for double - cone beam .

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