Abstract

A bichromatic sodium guide star based on two-photon coherent excitation followed by cascade emission is considered. Results of density matrix computations, including Doppler averaging, are presented for both a three-level model and the full hyperfine structure of the sodium 3S, 3P, and 4S levels. These results indicate that the proposed scheme for a bichromatic guide star is feasible.

© 2000 Optical Society of America

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  1. R. Foy, A. Migus, F. Biraben, G. Grynberg, P. McCullough, and M. Tallon, Astron. Astrophys. Suppl. 111, 569 (1995).
  2. J.-C. Diels and S. Besnainou, J. Chem. Phys. 85, 6347 (1986).
  3. R. C. Weast, ed., CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, Fla., 1985–1986), Chap. E, p. E-370.
  4. M. Schöck, R. Foy, J.-P. Pique, M. Tallon, P. Segonds, M. Laubscher, and O. Peillet, Proc. SPIE 3762, 321 (1999).
    [CrossRef]
  5. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif., 1995).
  6. L. Lapidus and J. Seinfield, Numerical Solution of Ordinary Differential Equations (Academic, San Diego, Calif., 1971).
  7. J. Biegert, V. Kubecek, and J.-C. Diels, in Encyclopedia of Electrical and Electronics Engineering, J. G. Webster, ed. (Institute of Electrical and Electronics Engineers, New York, 1998), p. 446–545.
  8. J.-C. Diels, Phys. Rev. A 13, 1520 (1976).
    [CrossRef]
  9. J.-C. Diels, Opt. Quantum Electron. 8, 513 (1976).
    [CrossRef]
  10. D. Grischkowsky, M. M. T. Loy, and P. F. Liao, Phys. Rev. A 12, 2514 (1975).
    [CrossRef]
  11. R. D. Cowan, The Theory of Atomic Structure and Spectra (U. California Press, Berkeley, Calif., 1981).
  12. C. W. Allen, Astrophysical Quantities (Athlone, London, 1973).
  13. H. Eicher, IEEE J. Quantum Electron. 11, 121 (1975).
    [CrossRef]
  14. R. H. Dicke, Phys. Rev. 93, 99 (1954).
    [CrossRef]

1999

M. Schöck, R. Foy, J.-P. Pique, M. Tallon, P. Segonds, M. Laubscher, and O. Peillet, Proc. SPIE 3762, 321 (1999).
[CrossRef]

1995

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. McCullough, and M. Tallon, Astron. Astrophys. Suppl. 111, 569 (1995).

1986

J.-C. Diels and S. Besnainou, J. Chem. Phys. 85, 6347 (1986).

1976

J.-C. Diels, Phys. Rev. A 13, 1520 (1976).
[CrossRef]

J.-C. Diels, Opt. Quantum Electron. 8, 513 (1976).
[CrossRef]

1975

D. Grischkowsky, M. M. T. Loy, and P. F. Liao, Phys. Rev. A 12, 2514 (1975).
[CrossRef]

H. Eicher, IEEE J. Quantum Electron. 11, 121 (1975).
[CrossRef]

1954

R. H. Dicke, Phys. Rev. 93, 99 (1954).
[CrossRef]

Allen, C. W.

C. W. Allen, Astrophysical Quantities (Athlone, London, 1973).

Besnainou, S.

J.-C. Diels and S. Besnainou, J. Chem. Phys. 85, 6347 (1986).

Biegert, J.

J. Biegert, V. Kubecek, and J.-C. Diels, in Encyclopedia of Electrical and Electronics Engineering, J. G. Webster, ed. (Institute of Electrical and Electronics Engineers, New York, 1998), p. 446–545.

Biraben, F.

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. McCullough, and M. Tallon, Astron. Astrophys. Suppl. 111, 569 (1995).

Cowan, R. D.

R. D. Cowan, The Theory of Atomic Structure and Spectra (U. California Press, Berkeley, Calif., 1981).

Dicke, R. H.

R. H. Dicke, Phys. Rev. 93, 99 (1954).
[CrossRef]

Diels, J.-C.

J.-C. Diels and S. Besnainou, J. Chem. Phys. 85, 6347 (1986).

J.-C. Diels, Phys. Rev. A 13, 1520 (1976).
[CrossRef]

J.-C. Diels, Opt. Quantum Electron. 8, 513 (1976).
[CrossRef]

J. Biegert, V. Kubecek, and J.-C. Diels, in Encyclopedia of Electrical and Electronics Engineering, J. G. Webster, ed. (Institute of Electrical and Electronics Engineers, New York, 1998), p. 446–545.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif., 1995).

Eicher, H.

H. Eicher, IEEE J. Quantum Electron. 11, 121 (1975).
[CrossRef]

Foy, R.

M. Schöck, R. Foy, J.-P. Pique, M. Tallon, P. Segonds, M. Laubscher, and O. Peillet, Proc. SPIE 3762, 321 (1999).
[CrossRef]

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. McCullough, and M. Tallon, Astron. Astrophys. Suppl. 111, 569 (1995).

Grischkowsky, D.

D. Grischkowsky, M. M. T. Loy, and P. F. Liao, Phys. Rev. A 12, 2514 (1975).
[CrossRef]

Grynberg, G.

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. McCullough, and M. Tallon, Astron. Astrophys. Suppl. 111, 569 (1995).

Kubecek, V.

J. Biegert, V. Kubecek, and J.-C. Diels, in Encyclopedia of Electrical and Electronics Engineering, J. G. Webster, ed. (Institute of Electrical and Electronics Engineers, New York, 1998), p. 446–545.

Lapidus, L.

L. Lapidus and J. Seinfield, Numerical Solution of Ordinary Differential Equations (Academic, San Diego, Calif., 1971).

Laubscher, M.

M. Schöck, R. Foy, J.-P. Pique, M. Tallon, P. Segonds, M. Laubscher, and O. Peillet, Proc. SPIE 3762, 321 (1999).
[CrossRef]

Liao, P. F.

D. Grischkowsky, M. M. T. Loy, and P. F. Liao, Phys. Rev. A 12, 2514 (1975).
[CrossRef]

Loy, M. M. T.

D. Grischkowsky, M. M. T. Loy, and P. F. Liao, Phys. Rev. A 12, 2514 (1975).
[CrossRef]

McCullough, P.

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. McCullough, and M. Tallon, Astron. Astrophys. Suppl. 111, 569 (1995).

Migus, A.

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. McCullough, and M. Tallon, Astron. Astrophys. Suppl. 111, 569 (1995).

Peillet, O.

M. Schöck, R. Foy, J.-P. Pique, M. Tallon, P. Segonds, M. Laubscher, and O. Peillet, Proc. SPIE 3762, 321 (1999).
[CrossRef]

Pique, J.-P.

M. Schöck, R. Foy, J.-P. Pique, M. Tallon, P. Segonds, M. Laubscher, and O. Peillet, Proc. SPIE 3762, 321 (1999).
[CrossRef]

Rudolph, W.

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif., 1995).

Schöck, M.

M. Schöck, R. Foy, J.-P. Pique, M. Tallon, P. Segonds, M. Laubscher, and O. Peillet, Proc. SPIE 3762, 321 (1999).
[CrossRef]

Segonds, P.

M. Schöck, R. Foy, J.-P. Pique, M. Tallon, P. Segonds, M. Laubscher, and O. Peillet, Proc. SPIE 3762, 321 (1999).
[CrossRef]

Seinfield, J.

L. Lapidus and J. Seinfield, Numerical Solution of Ordinary Differential Equations (Academic, San Diego, Calif., 1971).

Tallon, M.

M. Schöck, R. Foy, J.-P. Pique, M. Tallon, P. Segonds, M. Laubscher, and O. Peillet, Proc. SPIE 3762, 321 (1999).
[CrossRef]

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. McCullough, and M. Tallon, Astron. Astrophys. Suppl. 111, 569 (1995).

Astron. Astrophys. Suppl.

R. Foy, A. Migus, F. Biraben, G. Grynberg, P. McCullough, and M. Tallon, Astron. Astrophys. Suppl. 111, 569 (1995).

IEEE J. Quantum Electron.

H. Eicher, IEEE J. Quantum Electron. 11, 121 (1975).
[CrossRef]

J. Chem. Phys.

J.-C. Diels and S. Besnainou, J. Chem. Phys. 85, 6347 (1986).

Opt. Quantum Electron.

J.-C. Diels, Opt. Quantum Electron. 8, 513 (1976).
[CrossRef]

Phys. Rev.

R. H. Dicke, Phys. Rev. 93, 99 (1954).
[CrossRef]

Phys. Rev. A

J.-C. Diels, Phys. Rev. A 13, 1520 (1976).
[CrossRef]

D. Grischkowsky, M. M. T. Loy, and P. F. Liao, Phys. Rev. A 12, 2514 (1975).
[CrossRef]

Proc. SPIE

M. Schöck, R. Foy, J.-P. Pique, M. Tallon, P. Segonds, M. Laubscher, and O. Peillet, Proc. SPIE 3762, 321 (1999).
[CrossRef]

Other

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Academic, San Diego, Calif., 1995).

L. Lapidus and J. Seinfield, Numerical Solution of Ordinary Differential Equations (Academic, San Diego, Calif., 1971).

J. Biegert, V. Kubecek, and J.-C. Diels, in Encyclopedia of Electrical and Electronics Engineering, J. G. Webster, ed. (Institute of Electrical and Electronics Engineers, New York, 1998), p. 446–545.

R. D. Cowan, The Theory of Atomic Structure and Spectra (U. California Press, Berkeley, Calif., 1981).

C. W. Allen, Astrophysical Quantities (Athlone, London, 1973).

R. C. Weast, ed., CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, Fla., 1985–1986), Chap. E, p. E-370.

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Figures (3)

Fig. 1
Fig. 1

Evolution of the elements of the density matrix shown as a function of time for an excitation consisting of a sequence of two bichromatic pulses. Each of the two (identical) exciting pulses, which are separated by 650 ps, has a duration of 100 ps. For each pulse, the fluences at the shorter and longer wavelengths are, respectively 0.90 and 2.2 µJ/cm2. The detunings (as defined in the text) are Δ1=0.092 and Δ2=0.015 rad/ps. Crosses, result of the calculation for the three-level approximation. Solid curves, result of the calculation with the complete hyperfine level structure of sodium taken into account.

Fig. 2
Fig. 2

Calculation of the upper-level population as a function of radial coordinate for the bichromatic two-pulse sequence used in Fig. 1. The ordinate to the right shows the fluence in the sequence that corresponds to the pulse profile. The ordinate to the left shows the population of the upper level at the end of the pulse sequence as a function of the radial coordinate. The peak intensity on the axis of the pulse was chosen 10% above the value for optimum excitation.

Fig. 3
Fig. 3

Upper state (ρ22, solid curve), lower state (ρ00, dotted curve), and intermediate state (ρ11, dotted–dashed curve) population as a function of time. The Doppler broadening corresponds to a temperature of mesospheric sodium of 190 K.

Tables (1)

Tables Icon

Table 1 Total Laser Power Required for a Bichromatic Laser Beacon to Correct for Differential Tilt at a Wavelength λca

Equations (3)

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|Ψt=c0t|Ψ0+c1texp-iωl,1t|Ψ1+c2texp-iωl,1+ωl,2t|Ψ2.
ddtc0c1c2=01/2E˜10-1/2E˜1*-iΔ11/2E˜20-1/2E˜2*-iΔ2c0c1c2.
c·0,F,m=i2F,mp10,F,m,F,mE˜1c1,F,m,  c·1,F,m=-iΔ1c1,F,m+i2×F,mp01,F,m,F,m+E˜1c0,F,m+F,mp21,F,m,F,mE˜2c2,F,m,  c·2,F,m=-iΔ2c2,F,m+i2F,mp12,F,m,F,m+E˜2c1,F,m,

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