Abstract

It is shown that the output wavelength λm of a dye laser may be shifted with respect to λ0, the wavelength setting to which the dye laser is tuned by an intracavity wavelength-selective optical element such as a diffraction grating. The shift δλ = λ0 − λm is toward the wavelengths at which lasing would occur without the tuning element in the cavity. The magnitude of δλ is determined by the spectral width of the tuning element by the gain characteristics of the laser dye and by cavity design parameters. An analytic expression is presented for a dye laser oscillating at threshold gain and for a Gaussian wavelength distribution of the dispersive element. Some examples are discussed where wavelength shifts may be significant.

© 1976 Optical Society of America

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References

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  1. T. W. Hänsch, “Applications of Dye Lasers,” in Dye Lasers: Topics in Applied Physics, F. P. Schäfer, Ed. (Springer, Berlin, 1973), Vol. 1, pp. 194–259.
  2. F. P. Schäfer, “Principles of Dye Laser Operation,” in Ref. 1, pp. 1–85.
  3. B. B. Snavely, “Continuous-Wave Dye Lasers,” in Ref. 1, pp. 86–120.
  4. O. G. Peterson, J. P. Webb, W. C. McColgin, J. H. Eberly, J. Appl. Phys. 42, 1917 (1971).
    [CrossRef]
  5. S. Speiser, A. Bromberg, Chem. Phys. 9, 191 (1975).
    [CrossRef]
  6. R. F. Leheny, J. Shah, IEEE J. Quantum Electron. 11, 70 (1975).
    [CrossRef]
  7. T. W. Hänsch, Appl. Opt. 11, 895 (1972).
    [CrossRef] [PubMed]
  8. K. Kato, Jpn. J. Appl. Phys. 11, 912 (1972).
    [CrossRef]
  9. R. P. Drucker, W. M. McClain, J. Chem. Phys. 61, 2609, 2616 (1974).
    [CrossRef]
  10. A. Bergman, J. Jortner, Chem. Phys. Lett. 26, 323 (1974).
    [CrossRef]
  11. N. Mikami, M. Ito, Chem. Phys. Lett. 31, 472 (1975).
    [CrossRef]
  12. E. E. Marinero, A. M. Angus, M. J. Colles, Opt. Commun. 14, 226 (1975).
    [CrossRef]
  13. R. Wallenstein, T. W. Hänsch, Opt. Commun. 14, 353 (1975).
    [CrossRef]
  14. J. B. Marling, J. G. Hawley, E. M. Liston, W. B. Grant, Appl. Opt. 13, 2317 (1974).
    [CrossRef] [PubMed]
  15. M. Lamotte, H. J. Dewey, R. A. Keller, J. J. Ritter, Chem. Phys. Lett. 30, 165 (1975).
    [CrossRef]
  16. C. B. Moore, Acc. Chem. Res. 6, 323 (1973).
    [CrossRef]
  17. J. B. Marling, D. W. Gregg, L. Wood, Appl. Phys. Lett. 17, 527 (1970).
    [CrossRef]
  18. R. A. Keller, E. F. Zalewski, N. C. Peterson, J. Opt. Soc. Am. 62, 319 (1972).
    [CrossRef]
  19. D. C. Harrington, H. V. Malmstadt, Anal. Chem. 47, 271 (1975).
    [CrossRef]
  20. G. K. Klauminzer, Opt. Eng. 13, 528 (1974).
    [CrossRef]

1975

S. Speiser, A. Bromberg, Chem. Phys. 9, 191 (1975).
[CrossRef]

R. F. Leheny, J. Shah, IEEE J. Quantum Electron. 11, 70 (1975).
[CrossRef]

N. Mikami, M. Ito, Chem. Phys. Lett. 31, 472 (1975).
[CrossRef]

E. E. Marinero, A. M. Angus, M. J. Colles, Opt. Commun. 14, 226 (1975).
[CrossRef]

R. Wallenstein, T. W. Hänsch, Opt. Commun. 14, 353 (1975).
[CrossRef]

M. Lamotte, H. J. Dewey, R. A. Keller, J. J. Ritter, Chem. Phys. Lett. 30, 165 (1975).
[CrossRef]

D. C. Harrington, H. V. Malmstadt, Anal. Chem. 47, 271 (1975).
[CrossRef]

1974

G. K. Klauminzer, Opt. Eng. 13, 528 (1974).
[CrossRef]

R. P. Drucker, W. M. McClain, J. Chem. Phys. 61, 2609, 2616 (1974).
[CrossRef]

A. Bergman, J. Jortner, Chem. Phys. Lett. 26, 323 (1974).
[CrossRef]

J. B. Marling, J. G. Hawley, E. M. Liston, W. B. Grant, Appl. Opt. 13, 2317 (1974).
[CrossRef] [PubMed]

1973

C. B. Moore, Acc. Chem. Res. 6, 323 (1973).
[CrossRef]

1972

1971

O. G. Peterson, J. P. Webb, W. C. McColgin, J. H. Eberly, J. Appl. Phys. 42, 1917 (1971).
[CrossRef]

1970

J. B. Marling, D. W. Gregg, L. Wood, Appl. Phys. Lett. 17, 527 (1970).
[CrossRef]

Angus, A. M.

E. E. Marinero, A. M. Angus, M. J. Colles, Opt. Commun. 14, 226 (1975).
[CrossRef]

Bergman, A.

A. Bergman, J. Jortner, Chem. Phys. Lett. 26, 323 (1974).
[CrossRef]

Bromberg, A.

S. Speiser, A. Bromberg, Chem. Phys. 9, 191 (1975).
[CrossRef]

Colles, M. J.

E. E. Marinero, A. M. Angus, M. J. Colles, Opt. Commun. 14, 226 (1975).
[CrossRef]

Dewey, H. J.

M. Lamotte, H. J. Dewey, R. A. Keller, J. J. Ritter, Chem. Phys. Lett. 30, 165 (1975).
[CrossRef]

Drucker, R. P.

R. P. Drucker, W. M. McClain, J. Chem. Phys. 61, 2609, 2616 (1974).
[CrossRef]

Eberly, J. H.

O. G. Peterson, J. P. Webb, W. C. McColgin, J. H. Eberly, J. Appl. Phys. 42, 1917 (1971).
[CrossRef]

Grant, W. B.

Gregg, D. W.

J. B. Marling, D. W. Gregg, L. Wood, Appl. Phys. Lett. 17, 527 (1970).
[CrossRef]

Hänsch, T. W.

R. Wallenstein, T. W. Hänsch, Opt. Commun. 14, 353 (1975).
[CrossRef]

T. W. Hänsch, Appl. Opt. 11, 895 (1972).
[CrossRef] [PubMed]

T. W. Hänsch, “Applications of Dye Lasers,” in Dye Lasers: Topics in Applied Physics, F. P. Schäfer, Ed. (Springer, Berlin, 1973), Vol. 1, pp. 194–259.

Harrington, D. C.

D. C. Harrington, H. V. Malmstadt, Anal. Chem. 47, 271 (1975).
[CrossRef]

Hawley, J. G.

Ito, M.

N. Mikami, M. Ito, Chem. Phys. Lett. 31, 472 (1975).
[CrossRef]

Jortner, J.

A. Bergman, J. Jortner, Chem. Phys. Lett. 26, 323 (1974).
[CrossRef]

Kato, K.

K. Kato, Jpn. J. Appl. Phys. 11, 912 (1972).
[CrossRef]

Keller, R. A.

M. Lamotte, H. J. Dewey, R. A. Keller, J. J. Ritter, Chem. Phys. Lett. 30, 165 (1975).
[CrossRef]

R. A. Keller, E. F. Zalewski, N. C. Peterson, J. Opt. Soc. Am. 62, 319 (1972).
[CrossRef]

Klauminzer, G. K.

G. K. Klauminzer, Opt. Eng. 13, 528 (1974).
[CrossRef]

Lamotte, M.

M. Lamotte, H. J. Dewey, R. A. Keller, J. J. Ritter, Chem. Phys. Lett. 30, 165 (1975).
[CrossRef]

Leheny, R. F.

R. F. Leheny, J. Shah, IEEE J. Quantum Electron. 11, 70 (1975).
[CrossRef]

Liston, E. M.

Malmstadt, H. V.

D. C. Harrington, H. V. Malmstadt, Anal. Chem. 47, 271 (1975).
[CrossRef]

Marinero, E. E.

E. E. Marinero, A. M. Angus, M. J. Colles, Opt. Commun. 14, 226 (1975).
[CrossRef]

Marling, J. B.

McClain, W. M.

R. P. Drucker, W. M. McClain, J. Chem. Phys. 61, 2609, 2616 (1974).
[CrossRef]

McColgin, W. C.

O. G. Peterson, J. P. Webb, W. C. McColgin, J. H. Eberly, J. Appl. Phys. 42, 1917 (1971).
[CrossRef]

Mikami, N.

N. Mikami, M. Ito, Chem. Phys. Lett. 31, 472 (1975).
[CrossRef]

Moore, C. B.

C. B. Moore, Acc. Chem. Res. 6, 323 (1973).
[CrossRef]

Peterson, N. C.

Peterson, O. G.

O. G. Peterson, J. P. Webb, W. C. McColgin, J. H. Eberly, J. Appl. Phys. 42, 1917 (1971).
[CrossRef]

Ritter, J. J.

M. Lamotte, H. J. Dewey, R. A. Keller, J. J. Ritter, Chem. Phys. Lett. 30, 165 (1975).
[CrossRef]

Schäfer, F. P.

F. P. Schäfer, “Principles of Dye Laser Operation,” in Ref. 1, pp. 1–85.

Shah, J.

R. F. Leheny, J. Shah, IEEE J. Quantum Electron. 11, 70 (1975).
[CrossRef]

Snavely, B. B.

B. B. Snavely, “Continuous-Wave Dye Lasers,” in Ref. 1, pp. 86–120.

Speiser, S.

S. Speiser, A. Bromberg, Chem. Phys. 9, 191 (1975).
[CrossRef]

Wallenstein, R.

R. Wallenstein, T. W. Hänsch, Opt. Commun. 14, 353 (1975).
[CrossRef]

Webb, J. P.

O. G. Peterson, J. P. Webb, W. C. McColgin, J. H. Eberly, J. Appl. Phys. 42, 1917 (1971).
[CrossRef]

Wood, L.

J. B. Marling, D. W. Gregg, L. Wood, Appl. Phys. Lett. 17, 527 (1970).
[CrossRef]

Zalewski, E. F.

Acc. Chem. Res.

C. B. Moore, Acc. Chem. Res. 6, 323 (1973).
[CrossRef]

Anal. Chem.

D. C. Harrington, H. V. Malmstadt, Anal. Chem. 47, 271 (1975).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. B. Marling, D. W. Gregg, L. Wood, Appl. Phys. Lett. 17, 527 (1970).
[CrossRef]

Chem. Phys.

S. Speiser, A. Bromberg, Chem. Phys. 9, 191 (1975).
[CrossRef]

Chem. Phys. Lett.

M. Lamotte, H. J. Dewey, R. A. Keller, J. J. Ritter, Chem. Phys. Lett. 30, 165 (1975).
[CrossRef]

A. Bergman, J. Jortner, Chem. Phys. Lett. 26, 323 (1974).
[CrossRef]

N. Mikami, M. Ito, Chem. Phys. Lett. 31, 472 (1975).
[CrossRef]

IEEE J. Quantum Electron.

R. F. Leheny, J. Shah, IEEE J. Quantum Electron. 11, 70 (1975).
[CrossRef]

J. Appl. Phys.

O. G. Peterson, J. P. Webb, W. C. McColgin, J. H. Eberly, J. Appl. Phys. 42, 1917 (1971).
[CrossRef]

J. Chem. Phys.

R. P. Drucker, W. M. McClain, J. Chem. Phys. 61, 2609, 2616 (1974).
[CrossRef]

J. Opt. Soc. Am.

Jpn. J. Appl. Phys.

K. Kato, Jpn. J. Appl. Phys. 11, 912 (1972).
[CrossRef]

Opt. Commun.

E. E. Marinero, A. M. Angus, M. J. Colles, Opt. Commun. 14, 226 (1975).
[CrossRef]

R. Wallenstein, T. W. Hänsch, Opt. Commun. 14, 353 (1975).
[CrossRef]

Opt. Eng.

G. K. Klauminzer, Opt. Eng. 13, 528 (1974).
[CrossRef]

Other

T. W. Hänsch, “Applications of Dye Lasers,” in Dye Lasers: Topics in Applied Physics, F. P. Schäfer, Ed. (Springer, Berlin, 1973), Vol. 1, pp. 194–259.

F. P. Schäfer, “Principles of Dye Laser Operation,” in Ref. 1, pp. 1–85.

B. B. Snavely, “Continuous-Wave Dye Lasers,” in Ref. 1, pp. 86–120.

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Figures (2)

Fig. 1
Fig. 1

Zero-gain surface of rhodamine 6G (showing the relative excited-state population n*/n at threshold as a function of the wavelength λ and the normalized extrinsic loss factor r/n). Also shown is a surface representing a dispersive element, tuned to the wavelength λ0, and characterized by a Gaussian-type dispersive loss function r(λ). The intersection of both surfaces has a minimum at wavelength λm which is shifted from λ0 by an amount δλ.

Fig. 2
Fig. 2

(a) The output of a flashlamp pumped rhodamine 6G laser (solid curve, arbitrary units) and calculated relative shifts δλ/we for two values of the effective bandwidth of the tuning element: we = 0.1 nm (dashed curve); we = 0.01 nm (dot–dash curve). (b) Normalized wavelength shifts δλ/Lwe2 for three concentrations of rhodamine 6G. (c) Normalized wavelength shifts δλ/Lwe2 for three values of the intersystem crossing rate kSTτ = 0, 1, and 2. In (b) and (c) physically meaningful limits of the absolute shifts δλ < we/2 are indicated for we = 1 nm (solid curve), we = 0.1 nm (dashed curve), and we = 0.01 nm (dot–dash curve).

Equations (17)

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G ( λ ) = γ n * - σ S 0 n - r ,
γ ( λ ) = σ e m + σ S 0 + k S T τ ( σ S 0 - σ T 1 ) .
r = - ( 1 / 2 L ) ln ( r 1 r 2 t 1 t 2 ) ,
r 1 = r 1 ( λ ) = A exp [ - ( λ - λ 0 ) 2 / w e 2 ] ,
G ( λ ) = 0 , r = r ( λ ) , [ ( n * / n ) ] / λ = 0 ,
r ( λ ) u ( λ ) - r ( λ ) / λ + v ( λ ) = 0 ,
u ( λ ) = ( 1 / λ ) ( γ / λ ) , v ( λ ) = n [ σ S 0 u ( λ ) - σ S 0 / λ ] .
r ( λ ) = - ( 1 / 2 L ) ln { r 2 t 1 t 2 A exp [ - ( λ - λ 0 ) 2 / w e 2 ] } = r 0 + ( 1 / 2 L ) ( λ - λ 0 ) 2 / w e 2 ,
u ( λ ) u ( λ 0 ) = u 0 , v ( λ ) v ( λ 0 ) = v 0 .
r ( λ ) u 0 - r ( λ ) / λ + v 0 = 0.
( λ - λ 0 ) 2 - 2 ( λ - λ 0 ) / u 0 + 2 L w e 2 ( r 0 u 0 + v 0 ) / u 0 = 0
δ λ = λ m - λ 0 = ( 1 / u 0 ) { 1 ± [ 1 - 2 u 0 L w e 2 ( r 0 u 0 + v 0 ) ] 1 / 2 } ,
δ λ = L w e 2 ( r 0 u 0 + v 0 ) .
P ( λ ) = ( 1 / w a π ) exp [ - ( λ - λ m ) 2 / w a 2 ] ,
u 0 - r ( λ ) P ( λ ) d λ - - [ r ( λ ) / λ ] P ( λ ) d λ + v 0 = 0 .
r ( λ ) = - [ r 0 + ( 1 / 2 L ) ( λ - λ 0 ) 2 / w e 2 ] ( w a π ) - 1 × exp [ - ( λ - λ m ) 2 / w a 2 ] d λ = r 0 + ( λ - λ 0 ) 2 / 2 L w e 2 + w a 2 / 4 L w e 2 .
r 0 * = r 0 + w a 2 / 4 L w e 2 ,

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