Abstract

A new method is presented that yields absolute multiphoton cross-section value γn (n = 2,3) by comparative one-, two-, and three-photon luminescence measurements and by utilizing low-power single-mode cw lasers. The experiments were performed on different dye solutions. The γ2 and γ3 experimental values obtained are compared with previous experimental data obtained with high-power laser sources.

© 1982 Optical Society of America

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  1. I. M. Catalano, A. Cingolani, J. Appl. Phys. 50, 5638 (1979).
    [CrossRef]
  2. I. M. Catalano, A. Cihgolani, M. Ferrara, M. Lugara, Opt. Acta 27, 625 (1980).
    [CrossRef]
  3. Cz. Radzewicz, P. Glowczewski, J. Krasinski, Appl. Phys. 17, 423 (1978).
    [CrossRef]
  4. I. M. Catalano, A. Cingolani, Opt. Commun. 23, 159 (1980).
    [CrossRef]
  5. E. H. A. Grannaman, M. J. Van der Wiel, Rev. Sci. Instrum. 46, 332 (1975).
    [CrossRef]
  6. A. Saissy, A. Azema, J. Botineau, F. Gires, Appl. Phys. 15, 99 (1978).
    [CrossRef]
  7. J. P. Hermann, J. Ducuing, Phys. Rev. A 5, 2557 (1972).
    [CrossRef]
  8. G. S. Agarwal, Phys. Rev. A 1, 1445 (1970).
    [CrossRef]
  9. J. Krasinski, S. Chudzjnski, W. Majewski, M. Glodz, Opt. Commun. 12, 304 (1974).
    [CrossRef]
  10. J. Krasinski, B. Karczewski, W. Majewski, M. Glodz, Opt. Commun. 15, 409 (1975).
    [CrossRef]
  11. F. P. Schafer, W. Schmidt, IEEE J. Quantum Electron. QE-2, 357 (1966).
    [CrossRef]
  12. J. P. Hermann, J. Ducuing, Opt. Commun. 6, 101 (1972).
    [CrossRef]
  13. I. M. Catalano, A. Cingolani, A. Minafra, Sol. State Commun. 16, 417 (1975); I. M. Catalano, A. Cingolani, M. Ferrara, A. Minafra, Opt. Commun. 15, 281 (1975).
    [CrossRef]
  14. A. Penzhofer, W. Falkenstein, Opt. Commun. 16, 247 (1976).
    [CrossRef]
  15. F. P. Schäfer, W. Schmidt, Opt. Commun. 17, 11 (1976).
    [CrossRef]
  16. B. Foucault, J. P. Hermann, Opt. Commun. 15, 412 (1975).
    [CrossRef]
  17. H. Lotem, Cid B. de Araujo, Phys. Rev. B 16, 1711 (1976).
    [CrossRef]
  18. I. M. Catalano, A. Cingolani, Phys. Rev. B 19, 1049 (1979).
    [CrossRef]

1980 (2)

I. M. Catalano, A. Cihgolani, M. Ferrara, M. Lugara, Opt. Acta 27, 625 (1980).
[CrossRef]

I. M. Catalano, A. Cingolani, Opt. Commun. 23, 159 (1980).
[CrossRef]

1979 (2)

I. M. Catalano, A. Cingolani, J. Appl. Phys. 50, 5638 (1979).
[CrossRef]

I. M. Catalano, A. Cingolani, Phys. Rev. B 19, 1049 (1979).
[CrossRef]

1978 (2)

A. Saissy, A. Azema, J. Botineau, F. Gires, Appl. Phys. 15, 99 (1978).
[CrossRef]

Cz. Radzewicz, P. Glowczewski, J. Krasinski, Appl. Phys. 17, 423 (1978).
[CrossRef]

1976 (3)

H. Lotem, Cid B. de Araujo, Phys. Rev. B 16, 1711 (1976).
[CrossRef]

A. Penzhofer, W. Falkenstein, Opt. Commun. 16, 247 (1976).
[CrossRef]

F. P. Schäfer, W. Schmidt, Opt. Commun. 17, 11 (1976).
[CrossRef]

1975 (4)

B. Foucault, J. P. Hermann, Opt. Commun. 15, 412 (1975).
[CrossRef]

J. Krasinski, B. Karczewski, W. Majewski, M. Glodz, Opt. Commun. 15, 409 (1975).
[CrossRef]

I. M. Catalano, A. Cingolani, A. Minafra, Sol. State Commun. 16, 417 (1975); I. M. Catalano, A. Cingolani, M. Ferrara, A. Minafra, Opt. Commun. 15, 281 (1975).
[CrossRef]

E. H. A. Grannaman, M. J. Van der Wiel, Rev. Sci. Instrum. 46, 332 (1975).
[CrossRef]

1974 (1)

J. Krasinski, S. Chudzjnski, W. Majewski, M. Glodz, Opt. Commun. 12, 304 (1974).
[CrossRef]

1972 (2)

J. P. Hermann, J. Ducuing, Phys. Rev. A 5, 2557 (1972).
[CrossRef]

J. P. Hermann, J. Ducuing, Opt. Commun. 6, 101 (1972).
[CrossRef]

1970 (1)

G. S. Agarwal, Phys. Rev. A 1, 1445 (1970).
[CrossRef]

1966 (1)

F. P. Schafer, W. Schmidt, IEEE J. Quantum Electron. QE-2, 357 (1966).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, Phys. Rev. A 1, 1445 (1970).
[CrossRef]

Azema, A.

A. Saissy, A. Azema, J. Botineau, F. Gires, Appl. Phys. 15, 99 (1978).
[CrossRef]

Botineau, J.

A. Saissy, A. Azema, J. Botineau, F. Gires, Appl. Phys. 15, 99 (1978).
[CrossRef]

Catalano, I. M.

I. M. Catalano, A. Cingolani, Opt. Commun. 23, 159 (1980).
[CrossRef]

I. M. Catalano, A. Cihgolani, M. Ferrara, M. Lugara, Opt. Acta 27, 625 (1980).
[CrossRef]

I. M. Catalano, A. Cingolani, J. Appl. Phys. 50, 5638 (1979).
[CrossRef]

I. M. Catalano, A. Cingolani, Phys. Rev. B 19, 1049 (1979).
[CrossRef]

I. M. Catalano, A. Cingolani, A. Minafra, Sol. State Commun. 16, 417 (1975); I. M. Catalano, A. Cingolani, M. Ferrara, A. Minafra, Opt. Commun. 15, 281 (1975).
[CrossRef]

Chudzjnski, S.

J. Krasinski, S. Chudzjnski, W. Majewski, M. Glodz, Opt. Commun. 12, 304 (1974).
[CrossRef]

Cihgolani, A.

I. M. Catalano, A. Cihgolani, M. Ferrara, M. Lugara, Opt. Acta 27, 625 (1980).
[CrossRef]

Cingolani, A.

I. M. Catalano, A. Cingolani, Opt. Commun. 23, 159 (1980).
[CrossRef]

I. M. Catalano, A. Cingolani, J. Appl. Phys. 50, 5638 (1979).
[CrossRef]

I. M. Catalano, A. Cingolani, Phys. Rev. B 19, 1049 (1979).
[CrossRef]

I. M. Catalano, A. Cingolani, A. Minafra, Sol. State Commun. 16, 417 (1975); I. M. Catalano, A. Cingolani, M. Ferrara, A. Minafra, Opt. Commun. 15, 281 (1975).
[CrossRef]

de Araujo, Cid B.

H. Lotem, Cid B. de Araujo, Phys. Rev. B 16, 1711 (1976).
[CrossRef]

Ducuing, J.

J. P. Hermann, J. Ducuing, Opt. Commun. 6, 101 (1972).
[CrossRef]

J. P. Hermann, J. Ducuing, Phys. Rev. A 5, 2557 (1972).
[CrossRef]

Falkenstein, W.

A. Penzhofer, W. Falkenstein, Opt. Commun. 16, 247 (1976).
[CrossRef]

Ferrara, M.

I. M. Catalano, A. Cihgolani, M. Ferrara, M. Lugara, Opt. Acta 27, 625 (1980).
[CrossRef]

Foucault, B.

B. Foucault, J. P. Hermann, Opt. Commun. 15, 412 (1975).
[CrossRef]

Gires, F.

A. Saissy, A. Azema, J. Botineau, F. Gires, Appl. Phys. 15, 99 (1978).
[CrossRef]

Glodz, M.

J. Krasinski, B. Karczewski, W. Majewski, M. Glodz, Opt. Commun. 15, 409 (1975).
[CrossRef]

J. Krasinski, S. Chudzjnski, W. Majewski, M. Glodz, Opt. Commun. 12, 304 (1974).
[CrossRef]

Glowczewski, P.

Cz. Radzewicz, P. Glowczewski, J. Krasinski, Appl. Phys. 17, 423 (1978).
[CrossRef]

Grannaman, E. H. A.

E. H. A. Grannaman, M. J. Van der Wiel, Rev. Sci. Instrum. 46, 332 (1975).
[CrossRef]

Hermann, J. P.

B. Foucault, J. P. Hermann, Opt. Commun. 15, 412 (1975).
[CrossRef]

J. P. Hermann, J. Ducuing, Opt. Commun. 6, 101 (1972).
[CrossRef]

J. P. Hermann, J. Ducuing, Phys. Rev. A 5, 2557 (1972).
[CrossRef]

Karczewski, B.

J. Krasinski, B. Karczewski, W. Majewski, M. Glodz, Opt. Commun. 15, 409 (1975).
[CrossRef]

Krasinski, J.

Cz. Radzewicz, P. Glowczewski, J. Krasinski, Appl. Phys. 17, 423 (1978).
[CrossRef]

J. Krasinski, B. Karczewski, W. Majewski, M. Glodz, Opt. Commun. 15, 409 (1975).
[CrossRef]

J. Krasinski, S. Chudzjnski, W. Majewski, M. Glodz, Opt. Commun. 12, 304 (1974).
[CrossRef]

Lotem, H.

H. Lotem, Cid B. de Araujo, Phys. Rev. B 16, 1711 (1976).
[CrossRef]

Lugara, M.

I. M. Catalano, A. Cihgolani, M. Ferrara, M. Lugara, Opt. Acta 27, 625 (1980).
[CrossRef]

Majewski, W.

J. Krasinski, B. Karczewski, W. Majewski, M. Glodz, Opt. Commun. 15, 409 (1975).
[CrossRef]

J. Krasinski, S. Chudzjnski, W. Majewski, M. Glodz, Opt. Commun. 12, 304 (1974).
[CrossRef]

Minafra, A.

I. M. Catalano, A. Cingolani, A. Minafra, Sol. State Commun. 16, 417 (1975); I. M. Catalano, A. Cingolani, M. Ferrara, A. Minafra, Opt. Commun. 15, 281 (1975).
[CrossRef]

Penzhofer, A.

A. Penzhofer, W. Falkenstein, Opt. Commun. 16, 247 (1976).
[CrossRef]

Radzewicz, Cz.

Cz. Radzewicz, P. Glowczewski, J. Krasinski, Appl. Phys. 17, 423 (1978).
[CrossRef]

Saissy, A.

A. Saissy, A. Azema, J. Botineau, F. Gires, Appl. Phys. 15, 99 (1978).
[CrossRef]

Schafer, F. P.

F. P. Schafer, W. Schmidt, IEEE J. Quantum Electron. QE-2, 357 (1966).
[CrossRef]

Schäfer, F. P.

F. P. Schäfer, W. Schmidt, Opt. Commun. 17, 11 (1976).
[CrossRef]

Schmidt, W.

F. P. Schäfer, W. Schmidt, Opt. Commun. 17, 11 (1976).
[CrossRef]

F. P. Schafer, W. Schmidt, IEEE J. Quantum Electron. QE-2, 357 (1966).
[CrossRef]

Van der Wiel, M. J.

E. H. A. Grannaman, M. J. Van der Wiel, Rev. Sci. Instrum. 46, 332 (1975).
[CrossRef]

Appl. Phys. (2)

Cz. Radzewicz, P. Glowczewski, J. Krasinski, Appl. Phys. 17, 423 (1978).
[CrossRef]

A. Saissy, A. Azema, J. Botineau, F. Gires, Appl. Phys. 15, 99 (1978).
[CrossRef]

IEEE J. Quantum Electron. (1)

F. P. Schafer, W. Schmidt, IEEE J. Quantum Electron. QE-2, 357 (1966).
[CrossRef]

J. Appl. Phys. (1)

I. M. Catalano, A. Cingolani, J. Appl. Phys. 50, 5638 (1979).
[CrossRef]

Opt. Acta (1)

I. M. Catalano, A. Cihgolani, M. Ferrara, M. Lugara, Opt. Acta 27, 625 (1980).
[CrossRef]

Opt. Commun. (7)

I. M. Catalano, A. Cingolani, Opt. Commun. 23, 159 (1980).
[CrossRef]

J. Krasinski, S. Chudzjnski, W. Majewski, M. Glodz, Opt. Commun. 12, 304 (1974).
[CrossRef]

J. Krasinski, B. Karczewski, W. Majewski, M. Glodz, Opt. Commun. 15, 409 (1975).
[CrossRef]

J. P. Hermann, J. Ducuing, Opt. Commun. 6, 101 (1972).
[CrossRef]

A. Penzhofer, W. Falkenstein, Opt. Commun. 16, 247 (1976).
[CrossRef]

F. P. Schäfer, W. Schmidt, Opt. Commun. 17, 11 (1976).
[CrossRef]

B. Foucault, J. P. Hermann, Opt. Commun. 15, 412 (1975).
[CrossRef]

Phys. Rev. A (2)

J. P. Hermann, J. Ducuing, Phys. Rev. A 5, 2557 (1972).
[CrossRef]

G. S. Agarwal, Phys. Rev. A 1, 1445 (1970).
[CrossRef]

Phys. Rev. B (2)

H. Lotem, Cid B. de Araujo, Phys. Rev. B 16, 1711 (1976).
[CrossRef]

I. M. Catalano, A. Cingolani, Phys. Rev. B 19, 1049 (1979).
[CrossRef]

Rev. Sci. Instrum. (1)

E. H. A. Grannaman, M. J. Van der Wiel, Rev. Sci. Instrum. 46, 332 (1975).
[CrossRef]

Sol. State Commun. (1)

I. M. Catalano, A. Cingolani, A. Minafra, Sol. State Commun. 16, 417 (1975); I. M. Catalano, A. Cingolani, M. Ferrara, A. Minafra, Opt. Commun. 15, 281 (1975).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Experimental setup for two-photon cross-section measurements by means of cw laser PNd and PSHG are the Nd:YAG and its second-harmonic beam powers; Mi (i = 1,2) are the mirrors; OB1, OB2 are 100× microscope objectives; P is the flat optical quartz plate 0.5 mm thick. (b) Experimental setup for three-photon cross-section measurements by means of cw lasers. PNd and PHe–Ne are Nd:YAG and He–Ne beams.

Fig. 2
Fig. 2

Rhodamine 6G luminescence intensity at λl = 0.560 μm vs laser input power: (a) Nd:YAG excitation (PNd); (b) Nd:YAG second harmonic excitation (PSHG).

Fig. 3
Fig. 3

Dimethyl–POPOP and PPF luminescence intensity vs laser excitation power: (a) and (b) 2 under He–Ne laser excitation; (a1 and b1) 3 under Nd:YAG laser excitation.

Equations (9)

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L n = A n η n N n = A n η n n c γ n V I n ( r , z ) d V ,
I ( r , z ) = 2 P o n π w z 2 exp ( - 2 r 2 / w z 2 ) ,
w z 2 = w o n 2 ( 1 + λ n 2 z 2 π 2 w o n 4 ) ,
L n = A n η n c γ n 2 n - 1 π n - 1 P o n n w o n 2 ( n - 1 ) - + d z ( 1 + λ n 2 z 2 π 2 w o n 4 ) n - 1 .
L 1 = A 1 η 1 P 01 [ 1 - exp ( - α 1 L ) ] ,
L 2 = 2 π A 2 η 2 c γ 2 P 02 2 λ 2 ,
γ 2 = L 2 L 1 P 01 P 02 2 [ 1 - exp ( - α 1 L ) ] λ 2 2 π c .
L 3 = 2 A 3 η 3 c γ 3 P 03 3 λ 3 w 03 2 ,
γ 3 = L 3 L 2 P 02 2 P 03 3 λ 3 λ 2 w 03 2 γ 2 .

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