Abstract

Two-photon absorption from crossed Gaussian laser beams creates a volume grating containing both a primary and a second-order sinusoidal index modulation. Unlike with linear excitation, the two-photon-induced grating exhibits two Bragg diffraction peaks having different decay rates. Comparison of diffracted orders from volume gratings allows the order of the excitation process to be determined.

© 1985 Optical Society of America

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  1. M. E. Mack, Phys. Rev. Lett. 22, 13 (1969).
    [CrossRef]
  2. P. Y. Key, R. G. Harrison, V. I. Little, J. Katzenstein, IEEE J. Quantum Electron. QE-6, 641 (1970).
    [CrossRef]
  3. H. Eichler, G. Enterlein, J. Munschau, H. Stahl, Z. Angew. Phys. 31, 1 (1971).
  4. H. Eichler, G. Enterlein, P. Glozbach, J. Munschau, H. Stahl, Appl. Opt. 11, 372 (1972).
    [CrossRef] [PubMed]
  5. R. I. Scarlet, Phys. Rev. A 6, 2281 (1972).
    [CrossRef]
  6. D. P. Phillon, D. J. Kuizenga, A. E. Siegman, Appl. Phys. Lett. 27, 85 (1975).
    [CrossRef]
  7. K. Jarasiunas, H. J. Gerritsen, Appl. Phys. Lett. 33, 190 (1978).
    [CrossRef]
  8. H. J. Eichler, J. Eichler, J. Knof, C. H. Noack, Phys. Status Solidi A 52, 481 (1979).
    [CrossRef]
  9. J. R. Salcedo, A. E. Siegman, D. D. Dlott, M. D. Fayer, Phys. Rev. Lett. 41, 131 (1978).
    [CrossRef]
  10. K. A. Nelson, D. Miller, D. R. Lutz, M. D. Fayer, J. Appl. Phys. 53, 1144 (1982).
    [CrossRef]
  11. F. Rondelez, H. Hervet, W. Urbach, Chem. Phys. Lett. 53, 138 (1978).
    [CrossRef]
  12. D. M. Burland, C. Brauchle, J. Chem. Phys. 76, 4502 (1982).
    [CrossRef]
  13. D. R. Dean, R. J. Collins, J. Appl. Phys. 44, 5455 (1973).
    [CrossRef]
  14. T. K. Gaylord, M. G. Moharam, Appl. Opt. 20, 3271 (1981).
    [CrossRef] [PubMed]
  15. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  16. R. K. Raj, Q. F. Gao, D. Bloch, M. Ducloy, Opt. Commun. 51, 117 (1984).
    [CrossRef]
  17. A. E. Siegman, J. Opt. Soc. Am. 67, 545 (1977).
    [CrossRef]
  18. G. Eyring, M. D. Fayer, J. Appl. Phys. 55, 4072 (1984).
    [CrossRef]
  19. R. W. Burke, E. R. Deardorff, O. Menis, J. Res. Natl. Bur. Stand. Sect. A 76, 469 (1972).
  20. M. J. Pelletier, J. M. Harris, Anal. Chem. 55, 1537 (1983).
    [CrossRef]
  21. A. Tam, C. K. N. Patel, Rev. Mod. Phys. 53, 517 (1981).
    [CrossRef]

1984 (2)

R. K. Raj, Q. F. Gao, D. Bloch, M. Ducloy, Opt. Commun. 51, 117 (1984).
[CrossRef]

G. Eyring, M. D. Fayer, J. Appl. Phys. 55, 4072 (1984).
[CrossRef]

1983 (1)

M. J. Pelletier, J. M. Harris, Anal. Chem. 55, 1537 (1983).
[CrossRef]

1982 (2)

K. A. Nelson, D. Miller, D. R. Lutz, M. D. Fayer, J. Appl. Phys. 53, 1144 (1982).
[CrossRef]

D. M. Burland, C. Brauchle, J. Chem. Phys. 76, 4502 (1982).
[CrossRef]

1981 (2)

1979 (1)

H. J. Eichler, J. Eichler, J. Knof, C. H. Noack, Phys. Status Solidi A 52, 481 (1979).
[CrossRef]

1978 (3)

J. R. Salcedo, A. E. Siegman, D. D. Dlott, M. D. Fayer, Phys. Rev. Lett. 41, 131 (1978).
[CrossRef]

F. Rondelez, H. Hervet, W. Urbach, Chem. Phys. Lett. 53, 138 (1978).
[CrossRef]

K. Jarasiunas, H. J. Gerritsen, Appl. Phys. Lett. 33, 190 (1978).
[CrossRef]

1977 (1)

1975 (1)

D. P. Phillon, D. J. Kuizenga, A. E. Siegman, Appl. Phys. Lett. 27, 85 (1975).
[CrossRef]

1973 (1)

D. R. Dean, R. J. Collins, J. Appl. Phys. 44, 5455 (1973).
[CrossRef]

1972 (3)

H. Eichler, G. Enterlein, P. Glozbach, J. Munschau, H. Stahl, Appl. Opt. 11, 372 (1972).
[CrossRef] [PubMed]

R. I. Scarlet, Phys. Rev. A 6, 2281 (1972).
[CrossRef]

R. W. Burke, E. R. Deardorff, O. Menis, J. Res. Natl. Bur. Stand. Sect. A 76, 469 (1972).

1971 (1)

H. Eichler, G. Enterlein, J. Munschau, H. Stahl, Z. Angew. Phys. 31, 1 (1971).

1970 (1)

P. Y. Key, R. G. Harrison, V. I. Little, J. Katzenstein, IEEE J. Quantum Electron. QE-6, 641 (1970).
[CrossRef]

1969 (2)

M. E. Mack, Phys. Rev. Lett. 22, 13 (1969).
[CrossRef]

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Bloch, D.

R. K. Raj, Q. F. Gao, D. Bloch, M. Ducloy, Opt. Commun. 51, 117 (1984).
[CrossRef]

Brauchle, C.

D. M. Burland, C. Brauchle, J. Chem. Phys. 76, 4502 (1982).
[CrossRef]

Burke, R. W.

R. W. Burke, E. R. Deardorff, O. Menis, J. Res. Natl. Bur. Stand. Sect. A 76, 469 (1972).

Burland, D. M.

D. M. Burland, C. Brauchle, J. Chem. Phys. 76, 4502 (1982).
[CrossRef]

Collins, R. J.

D. R. Dean, R. J. Collins, J. Appl. Phys. 44, 5455 (1973).
[CrossRef]

Dean, D. R.

D. R. Dean, R. J. Collins, J. Appl. Phys. 44, 5455 (1973).
[CrossRef]

Deardorff, E. R.

R. W. Burke, E. R. Deardorff, O. Menis, J. Res. Natl. Bur. Stand. Sect. A 76, 469 (1972).

Dlott, D. D.

J. R. Salcedo, A. E. Siegman, D. D. Dlott, M. D. Fayer, Phys. Rev. Lett. 41, 131 (1978).
[CrossRef]

Ducloy, M.

R. K. Raj, Q. F. Gao, D. Bloch, M. Ducloy, Opt. Commun. 51, 117 (1984).
[CrossRef]

Eichler, H.

H. Eichler, G. Enterlein, P. Glozbach, J. Munschau, H. Stahl, Appl. Opt. 11, 372 (1972).
[CrossRef] [PubMed]

H. Eichler, G. Enterlein, J. Munschau, H. Stahl, Z. Angew. Phys. 31, 1 (1971).

Eichler, H. J.

H. J. Eichler, J. Eichler, J. Knof, C. H. Noack, Phys. Status Solidi A 52, 481 (1979).
[CrossRef]

Eichler, J.

H. J. Eichler, J. Eichler, J. Knof, C. H. Noack, Phys. Status Solidi A 52, 481 (1979).
[CrossRef]

Enterlein, G.

H. Eichler, G. Enterlein, P. Glozbach, J. Munschau, H. Stahl, Appl. Opt. 11, 372 (1972).
[CrossRef] [PubMed]

H. Eichler, G. Enterlein, J. Munschau, H. Stahl, Z. Angew. Phys. 31, 1 (1971).

Eyring, G.

G. Eyring, M. D. Fayer, J. Appl. Phys. 55, 4072 (1984).
[CrossRef]

Fayer, M. D.

G. Eyring, M. D. Fayer, J. Appl. Phys. 55, 4072 (1984).
[CrossRef]

K. A. Nelson, D. Miller, D. R. Lutz, M. D. Fayer, J. Appl. Phys. 53, 1144 (1982).
[CrossRef]

J. R. Salcedo, A. E. Siegman, D. D. Dlott, M. D. Fayer, Phys. Rev. Lett. 41, 131 (1978).
[CrossRef]

Gao, Q. F.

R. K. Raj, Q. F. Gao, D. Bloch, M. Ducloy, Opt. Commun. 51, 117 (1984).
[CrossRef]

Gaylord, T. K.

Gerritsen, H. J.

K. Jarasiunas, H. J. Gerritsen, Appl. Phys. Lett. 33, 190 (1978).
[CrossRef]

Glozbach, P.

Harris, J. M.

M. J. Pelletier, J. M. Harris, Anal. Chem. 55, 1537 (1983).
[CrossRef]

Harrison, R. G.

P. Y. Key, R. G. Harrison, V. I. Little, J. Katzenstein, IEEE J. Quantum Electron. QE-6, 641 (1970).
[CrossRef]

Hervet, H.

F. Rondelez, H. Hervet, W. Urbach, Chem. Phys. Lett. 53, 138 (1978).
[CrossRef]

Jarasiunas, K.

K. Jarasiunas, H. J. Gerritsen, Appl. Phys. Lett. 33, 190 (1978).
[CrossRef]

Katzenstein, J.

P. Y. Key, R. G. Harrison, V. I. Little, J. Katzenstein, IEEE J. Quantum Electron. QE-6, 641 (1970).
[CrossRef]

Key, P. Y.

P. Y. Key, R. G. Harrison, V. I. Little, J. Katzenstein, IEEE J. Quantum Electron. QE-6, 641 (1970).
[CrossRef]

Knof, J.

H. J. Eichler, J. Eichler, J. Knof, C. H. Noack, Phys. Status Solidi A 52, 481 (1979).
[CrossRef]

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Kuizenga, D. J.

D. P. Phillon, D. J. Kuizenga, A. E. Siegman, Appl. Phys. Lett. 27, 85 (1975).
[CrossRef]

Little, V. I.

P. Y. Key, R. G. Harrison, V. I. Little, J. Katzenstein, IEEE J. Quantum Electron. QE-6, 641 (1970).
[CrossRef]

Lutz, D. R.

K. A. Nelson, D. Miller, D. R. Lutz, M. D. Fayer, J. Appl. Phys. 53, 1144 (1982).
[CrossRef]

Mack, M. E.

M. E. Mack, Phys. Rev. Lett. 22, 13 (1969).
[CrossRef]

Menis, O.

R. W. Burke, E. R. Deardorff, O. Menis, J. Res. Natl. Bur. Stand. Sect. A 76, 469 (1972).

Miller, D.

K. A. Nelson, D. Miller, D. R. Lutz, M. D. Fayer, J. Appl. Phys. 53, 1144 (1982).
[CrossRef]

Moharam, M. G.

Munschau, J.

H. Eichler, G. Enterlein, P. Glozbach, J. Munschau, H. Stahl, Appl. Opt. 11, 372 (1972).
[CrossRef] [PubMed]

H. Eichler, G. Enterlein, J. Munschau, H. Stahl, Z. Angew. Phys. 31, 1 (1971).

Nelson, K. A.

K. A. Nelson, D. Miller, D. R. Lutz, M. D. Fayer, J. Appl. Phys. 53, 1144 (1982).
[CrossRef]

Noack, C. H.

H. J. Eichler, J. Eichler, J. Knof, C. H. Noack, Phys. Status Solidi A 52, 481 (1979).
[CrossRef]

Patel, C. K. N.

A. Tam, C. K. N. Patel, Rev. Mod. Phys. 53, 517 (1981).
[CrossRef]

Pelletier, M. J.

M. J. Pelletier, J. M. Harris, Anal. Chem. 55, 1537 (1983).
[CrossRef]

Phillon, D. P.

D. P. Phillon, D. J. Kuizenga, A. E. Siegman, Appl. Phys. Lett. 27, 85 (1975).
[CrossRef]

Raj, R. K.

R. K. Raj, Q. F. Gao, D. Bloch, M. Ducloy, Opt. Commun. 51, 117 (1984).
[CrossRef]

Rondelez, F.

F. Rondelez, H. Hervet, W. Urbach, Chem. Phys. Lett. 53, 138 (1978).
[CrossRef]

Salcedo, J. R.

J. R. Salcedo, A. E. Siegman, D. D. Dlott, M. D. Fayer, Phys. Rev. Lett. 41, 131 (1978).
[CrossRef]

Scarlet, R. I.

R. I. Scarlet, Phys. Rev. A 6, 2281 (1972).
[CrossRef]

Siegman, A. E.

J. R. Salcedo, A. E. Siegman, D. D. Dlott, M. D. Fayer, Phys. Rev. Lett. 41, 131 (1978).
[CrossRef]

A. E. Siegman, J. Opt. Soc. Am. 67, 545 (1977).
[CrossRef]

D. P. Phillon, D. J. Kuizenga, A. E. Siegman, Appl. Phys. Lett. 27, 85 (1975).
[CrossRef]

Stahl, H.

H. Eichler, G. Enterlein, P. Glozbach, J. Munschau, H. Stahl, Appl. Opt. 11, 372 (1972).
[CrossRef] [PubMed]

H. Eichler, G. Enterlein, J. Munschau, H. Stahl, Z. Angew. Phys. 31, 1 (1971).

Tam, A.

A. Tam, C. K. N. Patel, Rev. Mod. Phys. 53, 517 (1981).
[CrossRef]

Urbach, W.

F. Rondelez, H. Hervet, W. Urbach, Chem. Phys. Lett. 53, 138 (1978).
[CrossRef]

Anal. Chem. (1)

M. J. Pelletier, J. M. Harris, Anal. Chem. 55, 1537 (1983).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

D. P. Phillon, D. J. Kuizenga, A. E. Siegman, Appl. Phys. Lett. 27, 85 (1975).
[CrossRef]

K. Jarasiunas, H. J. Gerritsen, Appl. Phys. Lett. 33, 190 (1978).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Chem. Phys. Lett. (1)

F. Rondelez, H. Hervet, W. Urbach, Chem. Phys. Lett. 53, 138 (1978).
[CrossRef]

IEEE J. Quantum Electron. (1)

P. Y. Key, R. G. Harrison, V. I. Little, J. Katzenstein, IEEE J. Quantum Electron. QE-6, 641 (1970).
[CrossRef]

J. Appl. Phys. (3)

K. A. Nelson, D. Miller, D. R. Lutz, M. D. Fayer, J. Appl. Phys. 53, 1144 (1982).
[CrossRef]

D. R. Dean, R. J. Collins, J. Appl. Phys. 44, 5455 (1973).
[CrossRef]

G. Eyring, M. D. Fayer, J. Appl. Phys. 55, 4072 (1984).
[CrossRef]

J. Chem. Phys. (1)

D. M. Burland, C. Brauchle, J. Chem. Phys. 76, 4502 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Res. Natl. Bur. Stand. Sect. A (1)

R. W. Burke, E. R. Deardorff, O. Menis, J. Res. Natl. Bur. Stand. Sect. A 76, 469 (1972).

Opt. Commun. (1)

R. K. Raj, Q. F. Gao, D. Bloch, M. Ducloy, Opt. Commun. 51, 117 (1984).
[CrossRef]

Phys. Rev. A (1)

R. I. Scarlet, Phys. Rev. A 6, 2281 (1972).
[CrossRef]

Phys. Rev. Lett. (2)

M. E. Mack, Phys. Rev. Lett. 22, 13 (1969).
[CrossRef]

J. R. Salcedo, A. E. Siegman, D. D. Dlott, M. D. Fayer, Phys. Rev. Lett. 41, 131 (1978).
[CrossRef]

Phys. Status Solidi A (1)

H. J. Eichler, J. Eichler, J. Knof, C. H. Noack, Phys. Status Solidi A 52, 481 (1979).
[CrossRef]

Rev. Mod. Phys. (1)

A. Tam, C. K. N. Patel, Rev. Mod. Phys. 53, 517 (1981).
[CrossRef]

Z. Angew. Phys. (1)

H. Eichler, G. Enterlein, J. Munschau, H. Stahl, Z. Angew. Phys. 31, 1 (1971).

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Figures (4)

Fig. 1
Fig. 1

Schematic of two-photon thermal-grating experiment. PMT, photomultiplier tube.

Fig. 2
Fig. 2

Double-logarithmic plot of diffraction efficiency versus excitation-pulse energy. Data from a one-photon-absorbing sample, CoSO4 in aqueous H2SO4 (triangles), fall on the solid line, which has a slope of 2, and diffraction from benzene in CCI4 (circles) is characterized by a fourth-order power dependence, indicated by the dashed line, which has a slope of 4 Diffraction is measured at the primary Bragg incidence ϕ1.

Fig. 3
Fig. 3

Diffraction intensity versus probe-beam incident angle. Data from a 9.4 × 10−4 molar CoSO4 solution, triangles, illustrate a one-photon-excited grating. A two-photon-excited thermal grating in benzene with 30% CCI4 produced the data shown by circles. ϕ1 and ϕ2 are the Bragg angles for the primary and secondary gratings, respectively.

Fig. 4
Fig. 4

Diffraction intensity transients from two-photon-excited benzene. The primary grating transient is probed at ϕ1, and the secondary grating transient, scaled to comparable amplitude, is probed at ϕ2.

Equations (7)

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I ( x , y , z ) = ½ [ cosh ( 4 θ x z / w o 2 ) + cos ( 4 π θ x / λ e ) ] × exp [ 2 ( x 2 + θ 2 z 2 + y 2 ) / w o 2 ] ,
n ( x , y , z ) = n 0 δ n I 2 ( x , y , z ) = n 0 δ n 4 [ 1 + ½ cosh ( 8 θ x z / w o 2 ) + 2 cosh ( 4 θ x z / w o 2 ) cos ( 4 π θ x / λ e ) + ½ cos ( 8 π θ x / λ e ) ] exp [ 4 ( x 2 + θ 2 z 2 + y 2 ) / w o 2 ] ,
η = ( π Δ n l / λ p ) 2 ,
l eff = 1 δ n Δ n ( x , y , z ) d z ,
Δ n 1 ( x , y , z ) = δ n 2 exp [ 4 ( x 2 + y 2 + θ 2 z 2 ) / w o 2 ] × cosh ( 4 x z θ / w o 2 ) ,
Δ n 2 ( x , y , z ) = δ n 8 exp [ 4 ( x 2 + y 2 + θ 2 z 2 ) / w o 2 ] .
l ̅ 2 = 1 P I p ( x , y ) l eff 2 ( x , y ) d x d y ,

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