Abstract

It is shown that there exists an optimal cavity length which should minimize the frequency shifts induced by lenslike effects in intracavity saturated absorption lasers. Ideas are developed which provide a satisfactory explanation for the dispersion in modulation shifts observed in some recent laser intercomparisons.

© 1983 Optical Society of America

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References

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  1. J. Helmcke, F. Bayer-Helms, PTB Ber. Me-17, 111 (May1977).
  2. A. N. Titov, Opt. Commun. 43, 419 (1982).
    [CrossRef]
  3. A. Le Floch, R. Le Naour, J. M. Lenormand, J. P. Taché, Phys. Rev. Lett. 45, 544 (1980).
    [CrossRef]
  4. P. Cérez, A. Brillet, Metrologia 13, 29 (1977).
    [CrossRef]
  5. A. Le Floch, J. M. Lenormand, R. Le Naour, J. P. Taché, J. Phys. Lett. (Paris) 43, L493 (1982).
    [CrossRef]
  6. V. S. Letokhov, V. P. Chebotayev. Nonlinear Laser Spectroscopy (Springer, New York, 1977), Vol. 4, p. 64.
  7. P. Baues, Optoelectronics 1, 103 (1969).
  8. J. L. Hall, C. J. Bordé, Appl. Phys. Lett. 29, 788 (1976).
    [CrossRef]
  9. H. Greenstein, J. Appl. Phys. 43, 1732 (1972).
    [CrossRef]
  10. A. J. Wallard, J. Phys. E 5, 927 (1972).
    [CrossRef]
  11. P. Cérez, S. J. Bennett, Appl. Opt. 18, 1079 (1979).
    [CrossRef] [PubMed]
  12. F. Bertinetto, P. Cordiale, G. B. Picotto, J.-M. Chartier, R. Felder, M. Gläser, IEEE Trans. Instrum. Meas. (CPEM) (1983); in press.
  13. R. Felder, F. Bertinetto, Rapport BIPM-82/4.
  14. J.-M. Chartier, J. Helmcke, A. J. Wallard, IEEE Trans. Instrum. Meas. IM-25, 450 (Dec.1976).
    [CrossRef]
  15. J.-M. Chartier, Bureau International des Poids et Mesures; private communication.
  16. H. P. Layer, W. R. C. Rowley, B. R. Marx, Opt. Lett. 6, 188 (1981).
    [CrossRef] [PubMed]
  17. N. B. Koshelyaevskii, A. Oboukhov, V. M. Tatarenkov, A. N. Titov, J.-M. Chartier, R. Felder, Metrologia 17, 3 (1981).
    [CrossRef]
  18. J. B. Cole, C. F. Bruce, Appl. Opt. 14, 1303 (1975).
    [CrossRef] [PubMed]
  19. P. Cérez, A. Brillet, C. N. Man-Pichot, R. Felder, IEEE Trans. Instrum. Meas. IM-29, 352 (1980).
    [CrossRef]
  20. “Fundamental and Applied Laser Physics,” in Proceedings, Esfahan Symposium (Wiley, New York, 1971), p. 463.

1982 (2)

A. N. Titov, Opt. Commun. 43, 419 (1982).
[CrossRef]

A. Le Floch, J. M. Lenormand, R. Le Naour, J. P. Taché, J. Phys. Lett. (Paris) 43, L493 (1982).
[CrossRef]

1981 (2)

N. B. Koshelyaevskii, A. Oboukhov, V. M. Tatarenkov, A. N. Titov, J.-M. Chartier, R. Felder, Metrologia 17, 3 (1981).
[CrossRef]

H. P. Layer, W. R. C. Rowley, B. R. Marx, Opt. Lett. 6, 188 (1981).
[CrossRef] [PubMed]

1980 (2)

P. Cérez, A. Brillet, C. N. Man-Pichot, R. Felder, IEEE Trans. Instrum. Meas. IM-29, 352 (1980).
[CrossRef]

A. Le Floch, R. Le Naour, J. M. Lenormand, J. P. Taché, Phys. Rev. Lett. 45, 544 (1980).
[CrossRef]

1979 (1)

1977 (2)

P. Cérez, A. Brillet, Metrologia 13, 29 (1977).
[CrossRef]

J. Helmcke, F. Bayer-Helms, PTB Ber. Me-17, 111 (May1977).

1976 (2)

J.-M. Chartier, J. Helmcke, A. J. Wallard, IEEE Trans. Instrum. Meas. IM-25, 450 (Dec.1976).
[CrossRef]

J. L. Hall, C. J. Bordé, Appl. Phys. Lett. 29, 788 (1976).
[CrossRef]

1975 (1)

1972 (2)

H. Greenstein, J. Appl. Phys. 43, 1732 (1972).
[CrossRef]

A. J. Wallard, J. Phys. E 5, 927 (1972).
[CrossRef]

1969 (1)

P. Baues, Optoelectronics 1, 103 (1969).

Baues, P.

P. Baues, Optoelectronics 1, 103 (1969).

Bayer-Helms, F.

J. Helmcke, F. Bayer-Helms, PTB Ber. Me-17, 111 (May1977).

Bennett, S. J.

Bertinetto, F.

F. Bertinetto, P. Cordiale, G. B. Picotto, J.-M. Chartier, R. Felder, M. Gläser, IEEE Trans. Instrum. Meas. (CPEM) (1983); in press.

R. Felder, F. Bertinetto, Rapport BIPM-82/4.

Bordé, C. J.

J. L. Hall, C. J. Bordé, Appl. Phys. Lett. 29, 788 (1976).
[CrossRef]

Brillet, A.

P. Cérez, A. Brillet, C. N. Man-Pichot, R. Felder, IEEE Trans. Instrum. Meas. IM-29, 352 (1980).
[CrossRef]

P. Cérez, A. Brillet, Metrologia 13, 29 (1977).
[CrossRef]

Bruce, C. F.

Cérez, P.

P. Cérez, A. Brillet, C. N. Man-Pichot, R. Felder, IEEE Trans. Instrum. Meas. IM-29, 352 (1980).
[CrossRef]

P. Cérez, S. J. Bennett, Appl. Opt. 18, 1079 (1979).
[CrossRef] [PubMed]

P. Cérez, A. Brillet, Metrologia 13, 29 (1977).
[CrossRef]

Chartier, J.-M.

N. B. Koshelyaevskii, A. Oboukhov, V. M. Tatarenkov, A. N. Titov, J.-M. Chartier, R. Felder, Metrologia 17, 3 (1981).
[CrossRef]

J.-M. Chartier, J. Helmcke, A. J. Wallard, IEEE Trans. Instrum. Meas. IM-25, 450 (Dec.1976).
[CrossRef]

F. Bertinetto, P. Cordiale, G. B. Picotto, J.-M. Chartier, R. Felder, M. Gläser, IEEE Trans. Instrum. Meas. (CPEM) (1983); in press.

J.-M. Chartier, Bureau International des Poids et Mesures; private communication.

Chebotayev, V. P.

V. S. Letokhov, V. P. Chebotayev. Nonlinear Laser Spectroscopy (Springer, New York, 1977), Vol. 4, p. 64.

Cole, J. B.

Cordiale, P.

F. Bertinetto, P. Cordiale, G. B. Picotto, J.-M. Chartier, R. Felder, M. Gläser, IEEE Trans. Instrum. Meas. (CPEM) (1983); in press.

Felder, R.

N. B. Koshelyaevskii, A. Oboukhov, V. M. Tatarenkov, A. N. Titov, J.-M. Chartier, R. Felder, Metrologia 17, 3 (1981).
[CrossRef]

P. Cérez, A. Brillet, C. N. Man-Pichot, R. Felder, IEEE Trans. Instrum. Meas. IM-29, 352 (1980).
[CrossRef]

F. Bertinetto, P. Cordiale, G. B. Picotto, J.-M. Chartier, R. Felder, M. Gläser, IEEE Trans. Instrum. Meas. (CPEM) (1983); in press.

R. Felder, F. Bertinetto, Rapport BIPM-82/4.

Gläser, M.

F. Bertinetto, P. Cordiale, G. B. Picotto, J.-M. Chartier, R. Felder, M. Gläser, IEEE Trans. Instrum. Meas. (CPEM) (1983); in press.

Greenstein, H.

H. Greenstein, J. Appl. Phys. 43, 1732 (1972).
[CrossRef]

Hall, J. L.

J. L. Hall, C. J. Bordé, Appl. Phys. Lett. 29, 788 (1976).
[CrossRef]

Helmcke, J.

J. Helmcke, F. Bayer-Helms, PTB Ber. Me-17, 111 (May1977).

J.-M. Chartier, J. Helmcke, A. J. Wallard, IEEE Trans. Instrum. Meas. IM-25, 450 (Dec.1976).
[CrossRef]

Koshelyaevskii, N. B.

N. B. Koshelyaevskii, A. Oboukhov, V. M. Tatarenkov, A. N. Titov, J.-M. Chartier, R. Felder, Metrologia 17, 3 (1981).
[CrossRef]

Layer, H. P.

Le Floch, A.

A. Le Floch, J. M. Lenormand, R. Le Naour, J. P. Taché, J. Phys. Lett. (Paris) 43, L493 (1982).
[CrossRef]

A. Le Floch, R. Le Naour, J. M. Lenormand, J. P. Taché, Phys. Rev. Lett. 45, 544 (1980).
[CrossRef]

Le Naour, R.

A. Le Floch, J. M. Lenormand, R. Le Naour, J. P. Taché, J. Phys. Lett. (Paris) 43, L493 (1982).
[CrossRef]

A. Le Floch, R. Le Naour, J. M. Lenormand, J. P. Taché, Phys. Rev. Lett. 45, 544 (1980).
[CrossRef]

Lenormand, J. M.

A. Le Floch, J. M. Lenormand, R. Le Naour, J. P. Taché, J. Phys. Lett. (Paris) 43, L493 (1982).
[CrossRef]

A. Le Floch, R. Le Naour, J. M. Lenormand, J. P. Taché, Phys. Rev. Lett. 45, 544 (1980).
[CrossRef]

Letokhov, V. S.

V. S. Letokhov, V. P. Chebotayev. Nonlinear Laser Spectroscopy (Springer, New York, 1977), Vol. 4, p. 64.

Man-Pichot, C. N.

P. Cérez, A. Brillet, C. N. Man-Pichot, R. Felder, IEEE Trans. Instrum. Meas. IM-29, 352 (1980).
[CrossRef]

Marx, B. R.

Oboukhov, A.

N. B. Koshelyaevskii, A. Oboukhov, V. M. Tatarenkov, A. N. Titov, J.-M. Chartier, R. Felder, Metrologia 17, 3 (1981).
[CrossRef]

Picotto, G. B.

F. Bertinetto, P. Cordiale, G. B. Picotto, J.-M. Chartier, R. Felder, M. Gläser, IEEE Trans. Instrum. Meas. (CPEM) (1983); in press.

Rowley, W. R. C.

Taché, J. P.

A. Le Floch, J. M. Lenormand, R. Le Naour, J. P. Taché, J. Phys. Lett. (Paris) 43, L493 (1982).
[CrossRef]

A. Le Floch, R. Le Naour, J. M. Lenormand, J. P. Taché, Phys. Rev. Lett. 45, 544 (1980).
[CrossRef]

Tatarenkov, V. M.

N. B. Koshelyaevskii, A. Oboukhov, V. M. Tatarenkov, A. N. Titov, J.-M. Chartier, R. Felder, Metrologia 17, 3 (1981).
[CrossRef]

Titov, A. N.

A. N. Titov, Opt. Commun. 43, 419 (1982).
[CrossRef]

N. B. Koshelyaevskii, A. Oboukhov, V. M. Tatarenkov, A. N. Titov, J.-M. Chartier, R. Felder, Metrologia 17, 3 (1981).
[CrossRef]

Wallard, A. J.

J.-M. Chartier, J. Helmcke, A. J. Wallard, IEEE Trans. Instrum. Meas. IM-25, 450 (Dec.1976).
[CrossRef]

A. J. Wallard, J. Phys. E 5, 927 (1972).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. L. Hall, C. J. Bordé, Appl. Phys. Lett. 29, 788 (1976).
[CrossRef]

IEEE Trans. Instrum. Meas. (2)

J.-M. Chartier, J. Helmcke, A. J. Wallard, IEEE Trans. Instrum. Meas. IM-25, 450 (Dec.1976).
[CrossRef]

P. Cérez, A. Brillet, C. N. Man-Pichot, R. Felder, IEEE Trans. Instrum. Meas. IM-29, 352 (1980).
[CrossRef]

J. Appl. Phys. (1)

H. Greenstein, J. Appl. Phys. 43, 1732 (1972).
[CrossRef]

J. Phys. E (1)

A. J. Wallard, J. Phys. E 5, 927 (1972).
[CrossRef]

J. Phys. Lett. (Paris) (1)

A. Le Floch, J. M. Lenormand, R. Le Naour, J. P. Taché, J. Phys. Lett. (Paris) 43, L493 (1982).
[CrossRef]

Metrologia (2)

N. B. Koshelyaevskii, A. Oboukhov, V. M. Tatarenkov, A. N. Titov, J.-M. Chartier, R. Felder, Metrologia 17, 3 (1981).
[CrossRef]

P. Cérez, A. Brillet, Metrologia 13, 29 (1977).
[CrossRef]

Opt. Commun. (1)

A. N. Titov, Opt. Commun. 43, 419 (1982).
[CrossRef]

Opt. Lett. (1)

Optoelectronics (1)

P. Baues, Optoelectronics 1, 103 (1969).

Phys. Rev. Lett. (1)

A. Le Floch, R. Le Naour, J. M. Lenormand, J. P. Taché, Phys. Rev. Lett. 45, 544 (1980).
[CrossRef]

PTB Ber. (1)

J. Helmcke, F. Bayer-Helms, PTB Ber. Me-17, 111 (May1977).

Other (5)

F. Bertinetto, P. Cordiale, G. B. Picotto, J.-M. Chartier, R. Felder, M. Gläser, IEEE Trans. Instrum. Meas. (CPEM) (1983); in press.

R. Felder, F. Bertinetto, Rapport BIPM-82/4.

“Fundamental and Applied Laser Physics,” in Proceedings, Esfahan Symposium (Wiley, New York, 1971), p. 463.

V. S. Letokhov, V. P. Chebotayev. Nonlinear Laser Spectroscopy (Springer, New York, 1977), Vol. 4, p. 64.

J.-M. Chartier, Bureau International des Poids et Mesures; private communication.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Dimensionless convergence of the absorber per unit length as a function of detuning; the parameter is S (saturated absorption parameter).

Fig. 3
Fig. 3

Dimensionless amplitude of the saturated absorption peak as a function of the ratio gain/losses. The parameters are a and b.

Fig. 4
Fig. 4

(a) Normalized Lorentzian feature as a function of the detuning. (b) Dispersion-type parasitic signal due to the gas–lens effect of the absorber when F1 ≤ 0 and when S ≥ 2.45. (c) Addition of curves a and b (we can observe a frequency shift toward lower frequencies). (d) Evolution of (1 + S)(∂ca/∂Ω)Ω=0 as a function of S. (e) Expected behavior of the frequency shift induced by power variations; a negative gradient is observed.

Tables (2)

Tables Icon

Table I Values of the Cavity Length (Optimal Length) Which Cancel the Beam Spot Size Variations on the Mirror M2 for Three Usual Configurations

Tables Icon

Table II Characteristics of the Lasers Described in Ref. 13.

Equations (34)

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n s = 1 + α 0 2 k Ω [ 1 ( A / B ) ] [ ( A + B ) 2 4 Ω 2 ] 1 / 2 ;
Ω = ω ω 0 , A = ( Ω 2 + Γ 2 ) 1 / 2 , B = [ Ω 2 + Γ 2 ( 1 + 2 S ) ] 1 / 2 ;
S = S 0 exp ( 2 r 2 / w 2 ) ,
d 2 r d z 2 = 1 n d n d r d n s d r = n s S · S r = 4 r w 2 S n s S .
d 2 r d z 2 = c a · r ,
c a = 4 S w 2 ( α 0 2 k ) Γ 2 Ω [ ( A + B ) 2 4 Ω 2 ] 3 / 2 × [ A · [ ( A + B ) 2 4 Ω 2 ] B 3 1 + A 2 B 2 ] .
( A B C D ) absorber = ( 1 l a c a l a 1 ) .
( A B C D ) gain = ( 1 l g + c g l g 1 ) .
( A B C D ) = ( 1 0 1 / R 1 1 ) ( 1 l 0 0 1 ) ( 1 l a c a l a 1 ) ( 1 l i 0 1 ) ( 1 l g c g l g 1 ) ( 1 l t 0 1 ) ( 1 0 1 / R 2 1 ) .
w 4 = λ 2 π 2 B D A C .
w 0 4 = λ 2 π 2 B 0 D 0 A 0 C 0 .
4 Δ w / w A 0 C 0 B D B 0 D 0 A C A 0 B 0 C 0 D 0 .
Δ w / w = c a F 1 + c g F 2 ,
F 1 = l a 4 × L 2 R 2 [ 1 + 2 l 0 ( l 0 + l a ) R 1 2 ( l a + 2 l 0 ) R 1 ] L ( 1 L R 1 ) ( 1 L R 2 ) [ 1 R 1 ( 1 L R 2 ) + 1 R 2 ] l a 4 × L [ 1 ( l a + 2 l 0 ) R 1 + 2 l 0 ( l 0 + l a ) R 1 2 + 2 l 0 ( l 0 + l a ) R 1 R 2 ] l 0 ( l 0 + l a ) ( 1 R 1 + 1 R 2 ) L ( 1 L R 1 ) ( 1 L R 2 ) [ 1 R 1 ( 1 L R 2 ) + 1 R 2 ] ,
F 2 = l g × L 3 R 1 R 2 ( 1 2 L 0 R 1 ) + L 2 [ 3 L 0 l t R 1 R 2 1 R 1 1 R 2 + 2 L 0 R 1 2 ( 1 + l t R 2 ) ] D l g × L [ l t 2 L 0 R 1 L 0 R 2 2 l t L 0 R 1 ( 1 R 1 + 1 R 2 ) + 1 ] + l t L 0 ( 1 R 1 + 1 R 2 ) D ,
( Δ w / w ) c a = F 1 = 0 ,
G 0 1 + a S = P 0 + α 0 l a [ 1 1 + S ( 1 1 + S 1 1 + 2 S ) ( S , Ω ) ] .
( S , Ω ) = Γ 2 ( 1 + S ) Ω 2 + Γ 2 ( 1 + S )
Δ I max = 2 a ( α 0 l a P 0 ) × ( 1 + S 1 ) 1 / 2 ( 1 + 2 S 1 ) 1 / 2 a ( G 0 P 0 ) ( 1 + a S 1 ) 3 / 2 2 α 0 l a P 0 ( 1 + 2 S 1 ) 3 / 2 ,
( G 0 P 0 ) ( 1 + a S 1 ) 1 / 2 = 1 + α 0 l a P 0 ( 1 + S 1 ) 1 / 2 .
α 0 l a P 0 ( 1 + S 1 ) 1 / 2 1 ;
Δ I max = f ( m , a , α 0 l a G 0 ) .
P D = P D 0 [ 1 2 ( Δ w / w ) log P D 0 ] .
Δ P / P = exp ( 2 a 2 / w 2 ) .
P 0 = P 00 [ 1 2 P D 0 P 00 ( Δ w / w ) log P D 0 ] .
m = G 0 P 00 [ 1 + 2 ( P D 0 / P 00 ) ( Δ w / w ) log P D 0 ] = m 0 + Δ m .
Δ I = Δ I max × Γ 2 ( 1 + m 2 1 a ) Ω 2 + Γ 2 ( 1 + m 2 1 a ) .
d ( Δ I ) d Δ I max × Γ 2 ( 1 + m 0 2 1 a ) Ω 2 + Γ 2 ( 1 + m 0 2 1 a ) .
d ( Δ I ) = ( d Δ I max d m ) m = m 0 × 2 G 0 P 00 × P D 0 P 00 × ( Δ w / w ) log P D 0 × .
P = L ( 1 · F 1 · c a ) .
δ Ω = F 1 × Γ 2 ( 1 + S ) × ( c a Ω ) Ω = 0 4 .
( 1 + S ) × ( c a Ω ) Ω = 0 .
( δ Ω ) M = δ Ω × [ 1 + F ( M ) ] ,
( δ Ω M ) 1 / ( δ Ω M ) 1 = F 1 / F 1 ,

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