Abstract

Transfer of modulation from a phase-modulated laser beam to an unmodulated, oppositely running beam occurs in a sufficiently nonlinear resonant gaseous medium. Two mechanisms account for this transfer: modulated hole burning and reflection from an induced population grating. Heterodyne detection of the transferred modulation reveals multiplet patterns that are distinct for the two mechanisms. In particular, a central dispersion feature in the dispersive phase pattern is a diagnostic indication of the reflection process.

© 1982 Optical Society of America

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References

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  1. An early example in nuclear magnetic resonance is B. Smaller, “Precise determination of the magnetic moment of the deuteron,” Phys. Rev. 83, 812 (1951).
    [Crossref]
  2. G. C. Bjorklund, “Frequency-modulation spectroscopy: a new method for measuring weak absorptions and dispersions,” Opt. Lett. 5, 15 (1980).
    [Crossref] [PubMed]
  3. J. L. Hall, L. Holberg, T. Baer, H. G. Robinson, “Optical heterodyne saturation spectroscopy,” Appl. Phys. Lett. 39, 680 (1981).
    [Crossref]
  4. G. C. Bjorklund, M. D. Levenson, “Sub-Doppler frequency-modulation spectroscopy of I2,” Phys. Rev. A 24, 166 (1981).
    [Crossref]
  5. J. J. Snyder, R. K. Raj, D. Bloch, M. Ducloy, “High-sensitivity nonlinear spectroscopy using a frequency-offset pump,” Opt. Lett. 5, 163 (1980).
    [Crossref] [PubMed]
  6. R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, M. Ducloy, “High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing,” Phys. Rev. Lett. 44, 1251 (1980).
    [Crossref]
  7. M. Ducloy, D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened media. II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems,” J. Phys. (Paris) 43, 57 (1982).
    [Crossref]
  8. W. R. Bennett, “Gaseous optical masers,” Appl. Opt. Suppl. 1, 24 (1962).
  9. J. H. Shirley, “Semiclassical theory of saturated absorption in gases,” Phys. Rev. A 8, 347 (1973).
    [Crossref]
  10. G. Camy, Ch. J. Borde, M. Ducloy, “Heterodyne saturation spectroscopy through frequency modulation of the saturating beam,” Opt. Commun. 41, 325 (1982).
    [Crossref]
  11. A. Schenzle, R. G. DeVoe, R. G. Brewer, “Phase modulation spectroscopy,” Phys. Rev. A 25, 2606 (1982).
    [Crossref]
  12. Compare the discussion in Sec. IV of J. B. Hambenne, M. Sargent, “Strong-signal laser operation. II. Specific cases,” Phys. Rev. A 13, 797 (1976).
    [Crossref]
  13. Ref. 9, Sec. IVD.
  14. Ref. 9, Sec. IVA.
  15. Ref. 9, Eqs. (46)–(51).
  16. Ref. 9, Eq. (121).

1982 (3)

M. Ducloy, D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened media. II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems,” J. Phys. (Paris) 43, 57 (1982).
[Crossref]

G. Camy, Ch. J. Borde, M. Ducloy, “Heterodyne saturation spectroscopy through frequency modulation of the saturating beam,” Opt. Commun. 41, 325 (1982).
[Crossref]

A. Schenzle, R. G. DeVoe, R. G. Brewer, “Phase modulation spectroscopy,” Phys. Rev. A 25, 2606 (1982).
[Crossref]

1981 (2)

J. L. Hall, L. Holberg, T. Baer, H. G. Robinson, “Optical heterodyne saturation spectroscopy,” Appl. Phys. Lett. 39, 680 (1981).
[Crossref]

G. C. Bjorklund, M. D. Levenson, “Sub-Doppler frequency-modulation spectroscopy of I2,” Phys. Rev. A 24, 166 (1981).
[Crossref]

1980 (3)

1976 (1)

Compare the discussion in Sec. IV of J. B. Hambenne, M. Sargent, “Strong-signal laser operation. II. Specific cases,” Phys. Rev. A 13, 797 (1976).
[Crossref]

1973 (1)

J. H. Shirley, “Semiclassical theory of saturated absorption in gases,” Phys. Rev. A 8, 347 (1973).
[Crossref]

1962 (1)

W. R. Bennett, “Gaseous optical masers,” Appl. Opt. Suppl. 1, 24 (1962).

1951 (1)

An early example in nuclear magnetic resonance is B. Smaller, “Precise determination of the magnetic moment of the deuteron,” Phys. Rev. 83, 812 (1951).
[Crossref]

Baer, T.

J. L. Hall, L. Holberg, T. Baer, H. G. Robinson, “Optical heterodyne saturation spectroscopy,” Appl. Phys. Lett. 39, 680 (1981).
[Crossref]

Bennett, W. R.

W. R. Bennett, “Gaseous optical masers,” Appl. Opt. Suppl. 1, 24 (1962).

Bjorklund, G. C.

G. C. Bjorklund, M. D. Levenson, “Sub-Doppler frequency-modulation spectroscopy of I2,” Phys. Rev. A 24, 166 (1981).
[Crossref]

G. C. Bjorklund, “Frequency-modulation spectroscopy: a new method for measuring weak absorptions and dispersions,” Opt. Lett. 5, 15 (1980).
[Crossref] [PubMed]

Bloch, D.

M. Ducloy, D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened media. II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems,” J. Phys. (Paris) 43, 57 (1982).
[Crossref]

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, M. Ducloy, “High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing,” Phys. Rev. Lett. 44, 1251 (1980).
[Crossref]

J. J. Snyder, R. K. Raj, D. Bloch, M. Ducloy, “High-sensitivity nonlinear spectroscopy using a frequency-offset pump,” Opt. Lett. 5, 163 (1980).
[Crossref] [PubMed]

Borde, Ch. J.

G. Camy, Ch. J. Borde, M. Ducloy, “Heterodyne saturation spectroscopy through frequency modulation of the saturating beam,” Opt. Commun. 41, 325 (1982).
[Crossref]

Brewer, R. G.

A. Schenzle, R. G. DeVoe, R. G. Brewer, “Phase modulation spectroscopy,” Phys. Rev. A 25, 2606 (1982).
[Crossref]

Camy, G.

G. Camy, Ch. J. Borde, M. Ducloy, “Heterodyne saturation spectroscopy through frequency modulation of the saturating beam,” Opt. Commun. 41, 325 (1982).
[Crossref]

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, M. Ducloy, “High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing,” Phys. Rev. Lett. 44, 1251 (1980).
[Crossref]

DeVoe, R. G.

A. Schenzle, R. G. DeVoe, R. G. Brewer, “Phase modulation spectroscopy,” Phys. Rev. A 25, 2606 (1982).
[Crossref]

Ducloy, M.

M. Ducloy, D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened media. II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems,” J. Phys. (Paris) 43, 57 (1982).
[Crossref]

G. Camy, Ch. J. Borde, M. Ducloy, “Heterodyne saturation spectroscopy through frequency modulation of the saturating beam,” Opt. Commun. 41, 325 (1982).
[Crossref]

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, M. Ducloy, “High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing,” Phys. Rev. Lett. 44, 1251 (1980).
[Crossref]

J. J. Snyder, R. K. Raj, D. Bloch, M. Ducloy, “High-sensitivity nonlinear spectroscopy using a frequency-offset pump,” Opt. Lett. 5, 163 (1980).
[Crossref] [PubMed]

Hall, J. L.

J. L. Hall, L. Holberg, T. Baer, H. G. Robinson, “Optical heterodyne saturation spectroscopy,” Appl. Phys. Lett. 39, 680 (1981).
[Crossref]

Hambenne, J. B.

Compare the discussion in Sec. IV of J. B. Hambenne, M. Sargent, “Strong-signal laser operation. II. Specific cases,” Phys. Rev. A 13, 797 (1976).
[Crossref]

Holberg, L.

J. L. Hall, L. Holberg, T. Baer, H. G. Robinson, “Optical heterodyne saturation spectroscopy,” Appl. Phys. Lett. 39, 680 (1981).
[Crossref]

Levenson, M. D.

G. C. Bjorklund, M. D. Levenson, “Sub-Doppler frequency-modulation spectroscopy of I2,” Phys. Rev. A 24, 166 (1981).
[Crossref]

Raj, R. K.

J. J. Snyder, R. K. Raj, D. Bloch, M. Ducloy, “High-sensitivity nonlinear spectroscopy using a frequency-offset pump,” Opt. Lett. 5, 163 (1980).
[Crossref] [PubMed]

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, M. Ducloy, “High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing,” Phys. Rev. Lett. 44, 1251 (1980).
[Crossref]

Robinson, H. G.

J. L. Hall, L. Holberg, T. Baer, H. G. Robinson, “Optical heterodyne saturation spectroscopy,” Appl. Phys. Lett. 39, 680 (1981).
[Crossref]

Sargent, M.

Compare the discussion in Sec. IV of J. B. Hambenne, M. Sargent, “Strong-signal laser operation. II. Specific cases,” Phys. Rev. A 13, 797 (1976).
[Crossref]

Schenzle, A.

A. Schenzle, R. G. DeVoe, R. G. Brewer, “Phase modulation spectroscopy,” Phys. Rev. A 25, 2606 (1982).
[Crossref]

Shirley, J. H.

J. H. Shirley, “Semiclassical theory of saturated absorption in gases,” Phys. Rev. A 8, 347 (1973).
[Crossref]

Smaller, B.

An early example in nuclear magnetic resonance is B. Smaller, “Precise determination of the magnetic moment of the deuteron,” Phys. Rev. 83, 812 (1951).
[Crossref]

Snyder, J. J.

J. J. Snyder, R. K. Raj, D. Bloch, M. Ducloy, “High-sensitivity nonlinear spectroscopy using a frequency-offset pump,” Opt. Lett. 5, 163 (1980).
[Crossref] [PubMed]

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, M. Ducloy, “High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing,” Phys. Rev. Lett. 44, 1251 (1980).
[Crossref]

Appl. Opt. Suppl. (1)

W. R. Bennett, “Gaseous optical masers,” Appl. Opt. Suppl. 1, 24 (1962).

Appl. Phys. Lett. (1)

J. L. Hall, L. Holberg, T. Baer, H. G. Robinson, “Optical heterodyne saturation spectroscopy,” Appl. Phys. Lett. 39, 680 (1981).
[Crossref]

J. Phys. (Paris) (1)

M. Ducloy, D. Bloch, “Theory of degenerate four-wave mixing in resonant Doppler-broadened media. II. Doppler-free heterodyne spectroscopy via collinear four-wave mixing in two- and three-level systems,” J. Phys. (Paris) 43, 57 (1982).
[Crossref]

Opt. Commun. (1)

G. Camy, Ch. J. Borde, M. Ducloy, “Heterodyne saturation spectroscopy through frequency modulation of the saturating beam,” Opt. Commun. 41, 325 (1982).
[Crossref]

Opt. Lett. (2)

Phys. Rev. (1)

An early example in nuclear magnetic resonance is B. Smaller, “Precise determination of the magnetic moment of the deuteron,” Phys. Rev. 83, 812 (1951).
[Crossref]

Phys. Rev. A (4)

G. C. Bjorklund, M. D. Levenson, “Sub-Doppler frequency-modulation spectroscopy of I2,” Phys. Rev. A 24, 166 (1981).
[Crossref]

J. H. Shirley, “Semiclassical theory of saturated absorption in gases,” Phys. Rev. A 8, 347 (1973).
[Crossref]

A. Schenzle, R. G. DeVoe, R. G. Brewer, “Phase modulation spectroscopy,” Phys. Rev. A 25, 2606 (1982).
[Crossref]

Compare the discussion in Sec. IV of J. B. Hambenne, M. Sargent, “Strong-signal laser operation. II. Specific cases,” Phys. Rev. A 13, 797 (1976).
[Crossref]

Phys. Rev. Lett. (1)

R. K. Raj, D. Bloch, J. J. Snyder, G. Camy, M. Ducloy, “High-frequency optically heterodyned saturation spectroscopy via resonant degenerate four-wave mixing,” Phys. Rev. Lett. 44, 1251 (1980).
[Crossref]

Other (4)

Ref. 9, Sec. IVD.

Ref. 9, Sec. IVA.

Ref. 9, Eqs. (46)–(51).

Ref. 9, Eq. (121).

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Figures (3)

Fig. 1
Fig. 1

Saturation resonances in the modulation of the saturating beam that are due to modulated hole burning by the probe beam. The modulation frequency ωm is 10 times the homogeneous linewidth 2γ2, the saturation factor S is unity, and the relaxation rates γ1 and γ2 are equal. The absorption pattern (a) and the dispersion pattern (b) differ in detection phase by 90°.

Fig. 2
Fig. 2

Saturation resonances in the modulation of the saturating beam that are due to reflection of the probe beam from an induced grating in the medium. The parameters, including detection phases, are the same as in Fig. 1, but the vertical scale is expanded four times. A difference in phase shifts between the reflection and the modulated-hole-burning processes causes the absorption pattern (a) to share some of the central dispersion of (b).

Fig. 3
Fig. 3

Combined saturation resonances in the modulation of the saturating beam (sum of Figs. 1 and 2). The inner peaks are now larger than the outer ones. The central dispersion in (b) is due solely to the reflection process.

Equations (7)

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E = E s exp ( ikz - i ω t ) + E p × j J j exp ( - ikz - i ω t + i j ω m t ) + c . c . ,
Sig ( mod hole ) = ½ ASp J 0 J 1 × [ ( L 1 - L 1 / 2 + L - 1 / 2 - L - 1 ) × cos ( ω m t + ϕ ) + ( - D 1 + D 1 / 2 + D - 1 / 2 - D - 1 ) × sin ( ω m t + ϕ ) ] .
Sig ( probe ) = ASQ - 1 ( Q + 1 ) - 1 J 0 J 1 × ( L ¯ 1 / 2 - L ¯ - 1 / 2 ) cos ω m t + ( - D ¯ 1 / 2 + 2 D ¯ 0 - D ¯ - 1 / 2 ) sin ω m t ] ,
Sig ( sat corr ) = ASp ( 2 γ 2 / ω m ) Q - 1 ( Q + 1 ) - 1 J 0 J 1 × [ ( - D ¯ 1 / 2 + 2 D ¯ 0 - D ¯ - 1 / 2 ) cos ( ω m t + ϕ ) + ( - L ¯ 1 / 2 + L ¯ - 1 / 2 ) sin ( ω m t + ϕ ) ] .
Sig ( refl ) = A S 2 p Q - 1 ( Q + 1 ) - 1 [ Q + ( γ 1 / 2 γ 2 ) ] - 1 J 0 J 1 × [ ( - L 1 / 2 + L - 1 / 2 ) cos ( ω m t + ϕ ) + ( D 1 / 2 - 2 D 0 + D - 1 / 2 ) sin ( ω m t + ϕ ) ] ,
L j + i D j = ( L ¯ j + i D ¯ j ) ( 1 + L ¯ j + i D ¯ j ) / 2 q j ,
Sig ( 2 nd mod hold ) = ½ ASp J 1 J 2 × [ ( L 3 / 2 - L - 3 / 2 ) cos ( ω m t + ϕ ) + ( - D 3 / 2 + 2 D 0 - D - 3 / 2 ) × sin ( ω m t + ϕ ) ] ,

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