Abstract

Transmission spectroscopy in an ultrathin vapor cell, which has been recently demonstrated as a new method of sub-Doppler spectroscopy in the optical domain, is revisited. We show that, because of an unavoidable Fabry–Perot effect, the observed signal—in transmission spectroscopy and selective reflection spectroscopy as well—is actually an interferometric mixture of the optical responses as provided in transmission and in reflection by a long macroscopic cell. After the derivation of a very general solution, we restrict ourselves to the case of a linear interaction with the resonant laser. We finally discuss the application to a two-level atom for which analytical expressions are given, in the large Doppler limit, for FM transmission and reflection signals.

© 2003 Optical Society of America

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  1. M. F. H. Schuurmans, “Spectral narrowing of selective reflection,” J. Phys. (Paris) 37, 469–485 (1976).
    [CrossRef]
  2. A. Ch. Izmailov, “On the possibility of sub-Doppler structure of spectral lines of gas particles by a single travelling monochromatic wave,” Laser Phys. 2, 762–763 (1992).
  3. A. Ch. Izmailov, “Manifestations of sub-Doppler structure of the spectral lines of gas particles in the radiation of a travelling monochromatic pump wave,” Opt. Spektrosk. 74, 41–48 (1993) [Opt. Spectrosc. 74, 25–29 (1993)].
  4. T. A. Vartanyan and D. L. Lin, “Enhanced selective reflection from a thin layer of a dilute gaseous medium,” Phys. Rev. A 51, 1959–1964 (1995).
    [CrossRef] [PubMed]
  5. B. Zambon and G. Nienhuis, “Reflection and transmission of light by thin vapor layers,” Opt. Commun. 143, 308–314 (1997).
    [CrossRef]
  6. S. Briaudeau, D. Bloch, and M. Ducloy, “Detection of slow atoms in laser spectroscopy of a thin vapor film,” Europhys. Lett. 35, 337–342 (1996).
    [CrossRef]
  7. S. Briaudeau, S. Saltiel, G. Nienhuis, D. Bloch, and M. Ducloy, “Coherent Doppler narrowing in a thin vapor cell: Observation of the Dicke regime in the optical domain,” Phys. Rev. A 57, R3169–3172 (1998).
    [CrossRef]
  8. S. Briaudeau, D. Bloch, and M. Ducloy, “Sub-Doppler spectroscopy in a thin film of resonant vapor,” Phys. Rev. A 59, 3723–3735 (1999).
    [CrossRef]
  9. S. Briaudeau, “Spectroscopie à haute résolution en vapeur confinée,” thèse de doctorat, Laboratoire de Physique des Lasers, Université Paris 13 (1998) (unpublished).
  10. S. Briaudeau, S. Saltiel, J. R. R. Leite, M. Oria, A. Bramati, A. Weis, D. Bloch, and M. Ducloy, “Recent developments in sub-Doppler spectroscopy in a thin cell,” J. Phys. IV 10, Pr. 8, 145–146 (2000).
  11. D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, “Sub-Doppler spectroscopy by sub-micron thin Cs-vapor layer,” Opt. Commun. 200, 201–208 (2001).
    [CrossRef]
  12. G. Nienhuis, F. Schuller, and M. Ducloy, “Nonlinear selec-tive reflection from an atomic vapor at arbitrary incidence angle,” Phys. Rev. A 38, 5197–5205 (1988).
    [CrossRef] [PubMed]
  13. F. Schuller, G. Nienhuis, and M. Ducloy, “Selective reflection from an atomic vapor in a pump-probe scheme,” Phys. Rev. A 43, 443–454 (1991).
    [CrossRef] [PubMed]
  14. M. Chevrollier, M. Oria, J. G. De Souza, D. Bloch, M. Fichet, and M. Ducloy, “Selective reflection spectroscopy of a resonant vapor at the interface with a metallic layer,” Phys. Rev. E 63, 046610 (2001).
    [CrossRef]
  15. Note that r1 is an amplitude reflection coefficient usually not much smaller than unity; in recent experiments (see Ref. 11) performed with a narrow cell with yttrium aluminum garnet (YAG) windows, one has n1=1.82, i.e., r1= 0.29. Note also that even with an antireflection coating, one usually has r1, 2≥0.1.
  16. The difficulties typical of the optically thick medium in comparable problems have been analysed in the appendix of Ref. 1 and in T. Vartanyan, D. Bloch, and M. Ducloy, “Blue shift paradox in selective reflection,” in Spectral Line Shapes, A. D. May, J. R. Drummond, eds., AIP Conference Proceedings 328 (American Institute of Physics, New York, 1995), pp. 249–250.
  17. M. Ducloy and M. Fichet, “General theory of frequency modulated selective reflection. Influence of atom surface interactions,” J. Phys. II 1, 1429–1446 (1991).
  18. F. Schuller, O. Gorceix, and M. Ducloy, “Nonlinear selectivereflection in cascade three-level atomic systems,” Phys. Rev. A 47, 519–528 (1993).
    [CrossRef] [PubMed]
  19. G. Nienhuis and F. Schuller, “Selective reflection from a vapor of three-level atoms,” Phys. Rev. A 50, 1586–1592 (1994).
    [CrossRef] [PubMed]
  20. M. Gorris-Neveux, P. Monnot, S. Saltiel, R. Barbé, J. C. Keller, and M. Ducloy, “Two-photon selective reflection,” Phys. Rev. A 54, 3386–3393 (1996).
    [CrossRef] [PubMed]
  21. F. Schuller, A. Amy-Klein, and S. Saltiel, “Saturation effects in three-level selective reflection,” Phys. Rev. A 53, 3647–3651 (1996).
    [CrossRef] [PubMed]
  22. H. van Kampen, V. A. Sautenkov, E. R. Eliel, and J. P. Woerdman, “Probing the spatial dispersion in a dense atomic vapor near a dielectric interface,” Phys. Rev. A 58, 4473–4478 (1998).
    [CrossRef]
  23. D. Petrosyan and Yu. P. Malakyan, “Electromagnetically induced transparency in a thin vapor film,” Phys. Rev. A 61, 053820 (2000).
    [CrossRef]
  24. Note that the restriction to a finite cell length may intro-duce some additional changes relative to most common SR theories, as elaborated for various atomic models.
  25. R. H. Romer and R. H. Dicke, “New technique of high-resolution microwave spectroscopy,” Phys. Rev. 99, 532–536 (1955).
    [CrossRef]
  26. The essential dispersive response of SR spectroscopy in a long cell results only from the SR spatial averaging, which washes out the atomic response close to the (remote) second window. It should be recalled also that because of the symmetry breakdown occurring between arriving and departing atoms, and because of the atom–surface interaction, SR spectra in a long cell commonly include, in the vicinity of line center, a mixture of absorptive and dispersive responses—see notably the discussions in M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. II 2, 631–657 (1992); conversely, and as noted in Section 3 herein, the transmission through a relatively long cell exhibits simply absorption-like properties as long as the medium remains optically thin.
  27. A. M. Akul’shin, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, E. K. Yurkin, and N. V. Senkov, “Collisional broadening of intra-Doppler resonances of selective reflection of the D2 of cesium,” JETP Lett. 36, 303–306 (1982).
  28. G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, “Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy,” Europhys. Lett. (to be published).

2001 (2)

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, “Sub-Doppler spectroscopy by sub-micron thin Cs-vapor layer,” Opt. Commun. 200, 201–208 (2001).
[CrossRef]

M. Chevrollier, M. Oria, J. G. De Souza, D. Bloch, M. Fichet, and M. Ducloy, “Selective reflection spectroscopy of a resonant vapor at the interface with a metallic layer,” Phys. Rev. E 63, 046610 (2001).
[CrossRef]

2000 (2)

S. Briaudeau, S. Saltiel, J. R. R. Leite, M. Oria, A. Bramati, A. Weis, D. Bloch, and M. Ducloy, “Recent developments in sub-Doppler spectroscopy in a thin cell,” J. Phys. IV 10, Pr. 8, 145–146 (2000).

D. Petrosyan and Yu. P. Malakyan, “Electromagnetically induced transparency in a thin vapor film,” Phys. Rev. A 61, 053820 (2000).
[CrossRef]

1999 (1)

S. Briaudeau, D. Bloch, and M. Ducloy, “Sub-Doppler spectroscopy in a thin film of resonant vapor,” Phys. Rev. A 59, 3723–3735 (1999).
[CrossRef]

1998 (2)

S. Briaudeau, S. Saltiel, G. Nienhuis, D. Bloch, and M. Ducloy, “Coherent Doppler narrowing in a thin vapor cell: Observation of the Dicke regime in the optical domain,” Phys. Rev. A 57, R3169–3172 (1998).
[CrossRef]

H. van Kampen, V. A. Sautenkov, E. R. Eliel, and J. P. Woerdman, “Probing the spatial dispersion in a dense atomic vapor near a dielectric interface,” Phys. Rev. A 58, 4473–4478 (1998).
[CrossRef]

1997 (1)

B. Zambon and G. Nienhuis, “Reflection and transmission of light by thin vapor layers,” Opt. Commun. 143, 308–314 (1997).
[CrossRef]

1996 (3)

S. Briaudeau, D. Bloch, and M. Ducloy, “Detection of slow atoms in laser spectroscopy of a thin vapor film,” Europhys. Lett. 35, 337–342 (1996).
[CrossRef]

M. Gorris-Neveux, P. Monnot, S. Saltiel, R. Barbé, J. C. Keller, and M. Ducloy, “Two-photon selective reflection,” Phys. Rev. A 54, 3386–3393 (1996).
[CrossRef] [PubMed]

F. Schuller, A. Amy-Klein, and S. Saltiel, “Saturation effects in three-level selective reflection,” Phys. Rev. A 53, 3647–3651 (1996).
[CrossRef] [PubMed]

1995 (1)

T. A. Vartanyan and D. L. Lin, “Enhanced selective reflection from a thin layer of a dilute gaseous medium,” Phys. Rev. A 51, 1959–1964 (1995).
[CrossRef] [PubMed]

1994 (1)

G. Nienhuis and F. Schuller, “Selective reflection from a vapor of three-level atoms,” Phys. Rev. A 50, 1586–1592 (1994).
[CrossRef] [PubMed]

1993 (1)

F. Schuller, O. Gorceix, and M. Ducloy, “Nonlinear selectivereflection in cascade three-level atomic systems,” Phys. Rev. A 47, 519–528 (1993).
[CrossRef] [PubMed]

1992 (2)

A. Ch. Izmailov, “On the possibility of sub-Doppler structure of spectral lines of gas particles by a single travelling monochromatic wave,” Laser Phys. 2, 762–763 (1992).

The essential dispersive response of SR spectroscopy in a long cell results only from the SR spatial averaging, which washes out the atomic response close to the (remote) second window. It should be recalled also that because of the symmetry breakdown occurring between arriving and departing atoms, and because of the atom–surface interaction, SR spectra in a long cell commonly include, in the vicinity of line center, a mixture of absorptive and dispersive responses—see notably the discussions in M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. II 2, 631–657 (1992); conversely, and as noted in Section 3 herein, the transmission through a relatively long cell exhibits simply absorption-like properties as long as the medium remains optically thin.

1991 (2)

F. Schuller, G. Nienhuis, and M. Ducloy, “Selective reflection from an atomic vapor in a pump-probe scheme,” Phys. Rev. A 43, 443–454 (1991).
[CrossRef] [PubMed]

M. Ducloy and M. Fichet, “General theory of frequency modulated selective reflection. Influence of atom surface interactions,” J. Phys. II 1, 1429–1446 (1991).

1988 (1)

G. Nienhuis, F. Schuller, and M. Ducloy, “Nonlinear selec-tive reflection from an atomic vapor at arbitrary incidence angle,” Phys. Rev. A 38, 5197–5205 (1988).
[CrossRef] [PubMed]

1982 (1)

A. M. Akul’shin, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, E. K. Yurkin, and N. V. Senkov, “Collisional broadening of intra-Doppler resonances of selective reflection of the D2 of cesium,” JETP Lett. 36, 303–306 (1982).

1976 (1)

M. F. H. Schuurmans, “Spectral narrowing of selective reflection,” J. Phys. (Paris) 37, 469–485 (1976).
[CrossRef]

1955 (1)

R. H. Romer and R. H. Dicke, “New technique of high-resolution microwave spectroscopy,” Phys. Rev. 99, 532–536 (1955).
[CrossRef]

Akul’shin, A. M.

A. M. Akul’shin, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, E. K. Yurkin, and N. V. Senkov, “Collisional broadening of intra-Doppler resonances of selective reflection of the D2 of cesium,” JETP Lett. 36, 303–306 (1982).

Amy-Klein, A.

F. Schuller, A. Amy-Klein, and S. Saltiel, “Saturation effects in three-level selective reflection,” Phys. Rev. A 53, 3647–3651 (1996).
[CrossRef] [PubMed]

Barbé, R.

M. Gorris-Neveux, P. Monnot, S. Saltiel, R. Barbé, J. C. Keller, and M. Ducloy, “Two-photon selective reflection,” Phys. Rev. A 54, 3386–3393 (1996).
[CrossRef] [PubMed]

Bloch, D.

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, “Sub-Doppler spectroscopy by sub-micron thin Cs-vapor layer,” Opt. Commun. 200, 201–208 (2001).
[CrossRef]

M. Chevrollier, M. Oria, J. G. De Souza, D. Bloch, M. Fichet, and M. Ducloy, “Selective reflection spectroscopy of a resonant vapor at the interface with a metallic layer,” Phys. Rev. E 63, 046610 (2001).
[CrossRef]

S. Briaudeau, S. Saltiel, J. R. R. Leite, M. Oria, A. Bramati, A. Weis, D. Bloch, and M. Ducloy, “Recent developments in sub-Doppler spectroscopy in a thin cell,” J. Phys. IV 10, Pr. 8, 145–146 (2000).

S. Briaudeau, D. Bloch, and M. Ducloy, “Sub-Doppler spectroscopy in a thin film of resonant vapor,” Phys. Rev. A 59, 3723–3735 (1999).
[CrossRef]

S. Briaudeau, S. Saltiel, G. Nienhuis, D. Bloch, and M. Ducloy, “Coherent Doppler narrowing in a thin vapor cell: Observation of the Dicke regime in the optical domain,” Phys. Rev. A 57, R3169–3172 (1998).
[CrossRef]

S. Briaudeau, D. Bloch, and M. Ducloy, “Detection of slow atoms in laser spectroscopy of a thin vapor film,” Europhys. Lett. 35, 337–342 (1996).
[CrossRef]

The essential dispersive response of SR spectroscopy in a long cell results only from the SR spatial averaging, which washes out the atomic response close to the (remote) second window. It should be recalled also that because of the symmetry breakdown occurring between arriving and departing atoms, and because of the atom–surface interaction, SR spectra in a long cell commonly include, in the vicinity of line center, a mixture of absorptive and dispersive responses—see notably the discussions in M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. II 2, 631–657 (1992); conversely, and as noted in Section 3 herein, the transmission through a relatively long cell exhibits simply absorption-like properties as long as the medium remains optically thin.

Bramati, A.

S. Briaudeau, S. Saltiel, J. R. R. Leite, M. Oria, A. Bramati, A. Weis, D. Bloch, and M. Ducloy, “Recent developments in sub-Doppler spectroscopy in a thin cell,” J. Phys. IV 10, Pr. 8, 145–146 (2000).

Briaudeau, S.

S. Briaudeau, S. Saltiel, J. R. R. Leite, M. Oria, A. Bramati, A. Weis, D. Bloch, and M. Ducloy, “Recent developments in sub-Doppler spectroscopy in a thin cell,” J. Phys. IV 10, Pr. 8, 145–146 (2000).

S. Briaudeau, D. Bloch, and M. Ducloy, “Sub-Doppler spectroscopy in a thin film of resonant vapor,” Phys. Rev. A 59, 3723–3735 (1999).
[CrossRef]

S. Briaudeau, S. Saltiel, G. Nienhuis, D. Bloch, and M. Ducloy, “Coherent Doppler narrowing in a thin vapor cell: Observation of the Dicke regime in the optical domain,” Phys. Rev. A 57, R3169–3172 (1998).
[CrossRef]

S. Briaudeau, D. Bloch, and M. Ducloy, “Detection of slow atoms in laser spectroscopy of a thin vapor film,” Europhys. Lett. 35, 337–342 (1996).
[CrossRef]

Chevrollier, M.

M. Chevrollier, M. Oria, J. G. De Souza, D. Bloch, M. Fichet, and M. Ducloy, “Selective reflection spectroscopy of a resonant vapor at the interface with a metallic layer,” Phys. Rev. E 63, 046610 (2001).
[CrossRef]

The essential dispersive response of SR spectroscopy in a long cell results only from the SR spatial averaging, which washes out the atomic response close to the (remote) second window. It should be recalled also that because of the symmetry breakdown occurring between arriving and departing atoms, and because of the atom–surface interaction, SR spectra in a long cell commonly include, in the vicinity of line center, a mixture of absorptive and dispersive responses—see notably the discussions in M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. II 2, 631–657 (1992); conversely, and as noted in Section 3 herein, the transmission through a relatively long cell exhibits simply absorption-like properties as long as the medium remains optically thin.

De Souza, J. G.

M. Chevrollier, M. Oria, J. G. De Souza, D. Bloch, M. Fichet, and M. Ducloy, “Selective reflection spectroscopy of a resonant vapor at the interface with a metallic layer,” Phys. Rev. E 63, 046610 (2001).
[CrossRef]

Dicke, R. H.

R. H. Romer and R. H. Dicke, “New technique of high-resolution microwave spectroscopy,” Phys. Rev. 99, 532–536 (1955).
[CrossRef]

Ducloy, M.

M. Chevrollier, M. Oria, J. G. De Souza, D. Bloch, M. Fichet, and M. Ducloy, “Selective reflection spectroscopy of a resonant vapor at the interface with a metallic layer,” Phys. Rev. E 63, 046610 (2001).
[CrossRef]

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, “Sub-Doppler spectroscopy by sub-micron thin Cs-vapor layer,” Opt. Commun. 200, 201–208 (2001).
[CrossRef]

S. Briaudeau, S. Saltiel, J. R. R. Leite, M. Oria, A. Bramati, A. Weis, D. Bloch, and M. Ducloy, “Recent developments in sub-Doppler spectroscopy in a thin cell,” J. Phys. IV 10, Pr. 8, 145–146 (2000).

S. Briaudeau, D. Bloch, and M. Ducloy, “Sub-Doppler spectroscopy in a thin film of resonant vapor,” Phys. Rev. A 59, 3723–3735 (1999).
[CrossRef]

S. Briaudeau, S. Saltiel, G. Nienhuis, D. Bloch, and M. Ducloy, “Coherent Doppler narrowing in a thin vapor cell: Observation of the Dicke regime in the optical domain,” Phys. Rev. A 57, R3169–3172 (1998).
[CrossRef]

S. Briaudeau, D. Bloch, and M. Ducloy, “Detection of slow atoms in laser spectroscopy of a thin vapor film,” Europhys. Lett. 35, 337–342 (1996).
[CrossRef]

M. Gorris-Neveux, P. Monnot, S. Saltiel, R. Barbé, J. C. Keller, and M. Ducloy, “Two-photon selective reflection,” Phys. Rev. A 54, 3386–3393 (1996).
[CrossRef] [PubMed]

F. Schuller, O. Gorceix, and M. Ducloy, “Nonlinear selectivereflection in cascade three-level atomic systems,” Phys. Rev. A 47, 519–528 (1993).
[CrossRef] [PubMed]

The essential dispersive response of SR spectroscopy in a long cell results only from the SR spatial averaging, which washes out the atomic response close to the (remote) second window. It should be recalled also that because of the symmetry breakdown occurring between arriving and departing atoms, and because of the atom–surface interaction, SR spectra in a long cell commonly include, in the vicinity of line center, a mixture of absorptive and dispersive responses—see notably the discussions in M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. II 2, 631–657 (1992); conversely, and as noted in Section 3 herein, the transmission through a relatively long cell exhibits simply absorption-like properties as long as the medium remains optically thin.

M. Ducloy and M. Fichet, “General theory of frequency modulated selective reflection. Influence of atom surface interactions,” J. Phys. II 1, 1429–1446 (1991).

F. Schuller, G. Nienhuis, and M. Ducloy, “Selective reflection from an atomic vapor in a pump-probe scheme,” Phys. Rev. A 43, 443–454 (1991).
[CrossRef] [PubMed]

G. Nienhuis, F. Schuller, and M. Ducloy, “Nonlinear selec-tive reflection from an atomic vapor at arbitrary incidence angle,” Phys. Rev. A 38, 5197–5205 (1988).
[CrossRef] [PubMed]

Eliel, E. R.

H. van Kampen, V. A. Sautenkov, E. R. Eliel, and J. P. Woerdman, “Probing the spatial dispersion in a dense atomic vapor near a dielectric interface,” Phys. Rev. A 58, 4473–4478 (1998).
[CrossRef]

Fichet, M.

M. Chevrollier, M. Oria, J. G. De Souza, D. Bloch, M. Fichet, and M. Ducloy, “Selective reflection spectroscopy of a resonant vapor at the interface with a metallic layer,” Phys. Rev. E 63, 046610 (2001).
[CrossRef]

The essential dispersive response of SR spectroscopy in a long cell results only from the SR spatial averaging, which washes out the atomic response close to the (remote) second window. It should be recalled also that because of the symmetry breakdown occurring between arriving and departing atoms, and because of the atom–surface interaction, SR spectra in a long cell commonly include, in the vicinity of line center, a mixture of absorptive and dispersive responses—see notably the discussions in M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. II 2, 631–657 (1992); conversely, and as noted in Section 3 herein, the transmission through a relatively long cell exhibits simply absorption-like properties as long as the medium remains optically thin.

M. Ducloy and M. Fichet, “General theory of frequency modulated selective reflection. Influence of atom surface interactions,” J. Phys. II 1, 1429–1446 (1991).

Gorceix, O.

F. Schuller, O. Gorceix, and M. Ducloy, “Nonlinear selectivereflection in cascade three-level atomic systems,” Phys. Rev. A 47, 519–528 (1993).
[CrossRef] [PubMed]

Gorris-Neveux, M.

M. Gorris-Neveux, P. Monnot, S. Saltiel, R. Barbé, J. C. Keller, and M. Ducloy, “Two-photon selective reflection,” Phys. Rev. A 54, 3386–3393 (1996).
[CrossRef] [PubMed]

Izmailov, A. Ch.

A. Ch. Izmailov, “On the possibility of sub-Doppler structure of spectral lines of gas particles by a single travelling monochromatic wave,” Laser Phys. 2, 762–763 (1992).

Keller, J. C.

M. Gorris-Neveux, P. Monnot, S. Saltiel, R. Barbé, J. C. Keller, and M. Ducloy, “Two-photon selective reflection,” Phys. Rev. A 54, 3386–3393 (1996).
[CrossRef] [PubMed]

Leite, J. R. R.

S. Briaudeau, S. Saltiel, J. R. R. Leite, M. Oria, A. Bramati, A. Weis, D. Bloch, and M. Ducloy, “Recent developments in sub-Doppler spectroscopy in a thin cell,” J. Phys. IV 10, Pr. 8, 145–146 (2000).

Lin, D. L.

T. A. Vartanyan and D. L. Lin, “Enhanced selective reflection from a thin layer of a dilute gaseous medium,” Phys. Rev. A 51, 1959–1964 (1995).
[CrossRef] [PubMed]

Malakyan, Yu. P.

D. Petrosyan and Yu. P. Malakyan, “Electromagnetically induced transparency in a thin vapor film,” Phys. Rev. A 61, 053820 (2000).
[CrossRef]

Monnot, P.

M. Gorris-Neveux, P. Monnot, S. Saltiel, R. Barbé, J. C. Keller, and M. Ducloy, “Two-photon selective reflection,” Phys. Rev. A 54, 3386–3393 (1996).
[CrossRef] [PubMed]

Nienhuis, G.

S. Briaudeau, S. Saltiel, G. Nienhuis, D. Bloch, and M. Ducloy, “Coherent Doppler narrowing in a thin vapor cell: Observation of the Dicke regime in the optical domain,” Phys. Rev. A 57, R3169–3172 (1998).
[CrossRef]

B. Zambon and G. Nienhuis, “Reflection and transmission of light by thin vapor layers,” Opt. Commun. 143, 308–314 (1997).
[CrossRef]

G. Nienhuis and F. Schuller, “Selective reflection from a vapor of three-level atoms,” Phys. Rev. A 50, 1586–1592 (1994).
[CrossRef] [PubMed]

F. Schuller, G. Nienhuis, and M. Ducloy, “Selective reflection from an atomic vapor in a pump-probe scheme,” Phys. Rev. A 43, 443–454 (1991).
[CrossRef] [PubMed]

G. Nienhuis, F. Schuller, and M. Ducloy, “Nonlinear selec-tive reflection from an atomic vapor at arbitrary incidence angle,” Phys. Rev. A 38, 5197–5205 (1988).
[CrossRef] [PubMed]

Nikitin, V. V.

A. M. Akul’shin, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, E. K. Yurkin, and N. V. Senkov, “Collisional broadening of intra-Doppler resonances of selective reflection of the D2 of cesium,” JETP Lett. 36, 303–306 (1982).

Oria, M.

M. Chevrollier, M. Oria, J. G. De Souza, D. Bloch, M. Fichet, and M. Ducloy, “Selective reflection spectroscopy of a resonant vapor at the interface with a metallic layer,” Phys. Rev. E 63, 046610 (2001).
[CrossRef]

S. Briaudeau, S. Saltiel, J. R. R. Leite, M. Oria, A. Bramati, A. Weis, D. Bloch, and M. Ducloy, “Recent developments in sub-Doppler spectroscopy in a thin cell,” J. Phys. IV 10, Pr. 8, 145–146 (2000).

The essential dispersive response of SR spectroscopy in a long cell results only from the SR spatial averaging, which washes out the atomic response close to the (remote) second window. It should be recalled also that because of the symmetry breakdown occurring between arriving and departing atoms, and because of the atom–surface interaction, SR spectra in a long cell commonly include, in the vicinity of line center, a mixture of absorptive and dispersive responses—see notably the discussions in M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. II 2, 631–657 (1992); conversely, and as noted in Section 3 herein, the transmission through a relatively long cell exhibits simply absorption-like properties as long as the medium remains optically thin.

Papoyan, A.

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, “Sub-Doppler spectroscopy by sub-micron thin Cs-vapor layer,” Opt. Commun. 200, 201–208 (2001).
[CrossRef]

Petrosyan, D.

D. Petrosyan and Yu. P. Malakyan, “Electromagnetically induced transparency in a thin vapor film,” Phys. Rev. A 61, 053820 (2000).
[CrossRef]

Rahmat, G.

The essential dispersive response of SR spectroscopy in a long cell results only from the SR spatial averaging, which washes out the atomic response close to the (remote) second window. It should be recalled also that because of the symmetry breakdown occurring between arriving and departing atoms, and because of the atom–surface interaction, SR spectra in a long cell commonly include, in the vicinity of line center, a mixture of absorptive and dispersive responses—see notably the discussions in M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. II 2, 631–657 (1992); conversely, and as noted in Section 3 herein, the transmission through a relatively long cell exhibits simply absorption-like properties as long as the medium remains optically thin.

Romer, R. H.

R. H. Romer and R. H. Dicke, “New technique of high-resolution microwave spectroscopy,” Phys. Rev. 99, 532–536 (1955).
[CrossRef]

Saltiel, S.

S. Briaudeau, S. Saltiel, J. R. R. Leite, M. Oria, A. Bramati, A. Weis, D. Bloch, and M. Ducloy, “Recent developments in sub-Doppler spectroscopy in a thin cell,” J. Phys. IV 10, Pr. 8, 145–146 (2000).

S. Briaudeau, S. Saltiel, G. Nienhuis, D. Bloch, and M. Ducloy, “Coherent Doppler narrowing in a thin vapor cell: Observation of the Dicke regime in the optical domain,” Phys. Rev. A 57, R3169–3172 (1998).
[CrossRef]

M. Gorris-Neveux, P. Monnot, S. Saltiel, R. Barbé, J. C. Keller, and M. Ducloy, “Two-photon selective reflection,” Phys. Rev. A 54, 3386–3393 (1996).
[CrossRef] [PubMed]

F. Schuller, A. Amy-Klein, and S. Saltiel, “Saturation effects in three-level selective reflection,” Phys. Rev. A 53, 3647–3651 (1996).
[CrossRef] [PubMed]

Sarkisyan, D.

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, “Sub-Doppler spectroscopy by sub-micron thin Cs-vapor layer,” Opt. Commun. 200, 201–208 (2001).
[CrossRef]

Sautenkov, V. A.

H. van Kampen, V. A. Sautenkov, E. R. Eliel, and J. P. Woerdman, “Probing the spatial dispersion in a dense atomic vapor near a dielectric interface,” Phys. Rev. A 58, 4473–4478 (1998).
[CrossRef]

A. M. Akul’shin, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, E. K. Yurkin, and N. V. Senkov, “Collisional broadening of intra-Doppler resonances of selective reflection of the D2 of cesium,” JETP Lett. 36, 303–306 (1982).

Schuller, F.

F. Schuller, A. Amy-Klein, and S. Saltiel, “Saturation effects in three-level selective reflection,” Phys. Rev. A 53, 3647–3651 (1996).
[CrossRef] [PubMed]

G. Nienhuis and F. Schuller, “Selective reflection from a vapor of three-level atoms,” Phys. Rev. A 50, 1586–1592 (1994).
[CrossRef] [PubMed]

F. Schuller, O. Gorceix, and M. Ducloy, “Nonlinear selectivereflection in cascade three-level atomic systems,” Phys. Rev. A 47, 519–528 (1993).
[CrossRef] [PubMed]

F. Schuller, G. Nienhuis, and M. Ducloy, “Selective reflection from an atomic vapor in a pump-probe scheme,” Phys. Rev. A 43, 443–454 (1991).
[CrossRef] [PubMed]

G. Nienhuis, F. Schuller, and M. Ducloy, “Nonlinear selec-tive reflection from an atomic vapor at arbitrary incidence angle,” Phys. Rev. A 38, 5197–5205 (1988).
[CrossRef] [PubMed]

Schuurmans, M. F. H.

M. F. H. Schuurmans, “Spectral narrowing of selective reflection,” J. Phys. (Paris) 37, 469–485 (1976).
[CrossRef]

Senkov, N. V.

A. M. Akul’shin, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, E. K. Yurkin, and N. V. Senkov, “Collisional broadening of intra-Doppler resonances of selective reflection of the D2 of cesium,” JETP Lett. 36, 303–306 (1982).

van Kampen, H.

H. van Kampen, V. A. Sautenkov, E. R. Eliel, and J. P. Woerdman, “Probing the spatial dispersion in a dense atomic vapor near a dielectric interface,” Phys. Rev. A 58, 4473–4478 (1998).
[CrossRef]

Vartanyan, T. A.

T. A. Vartanyan and D. L. Lin, “Enhanced selective reflection from a thin layer of a dilute gaseous medium,” Phys. Rev. A 51, 1959–1964 (1995).
[CrossRef] [PubMed]

Velichanskii, V. L.

A. M. Akul’shin, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, E. K. Yurkin, and N. V. Senkov, “Collisional broadening of intra-Doppler resonances of selective reflection of the D2 of cesium,” JETP Lett. 36, 303–306 (1982).

Weis, A.

S. Briaudeau, S. Saltiel, J. R. R. Leite, M. Oria, A. Bramati, A. Weis, D. Bloch, and M. Ducloy, “Recent developments in sub-Doppler spectroscopy in a thin cell,” J. Phys. IV 10, Pr. 8, 145–146 (2000).

Woerdman, J. P.

H. van Kampen, V. A. Sautenkov, E. R. Eliel, and J. P. Woerdman, “Probing the spatial dispersion in a dense atomic vapor near a dielectric interface,” Phys. Rev. A 58, 4473–4478 (1998).
[CrossRef]

Yurkin, E. K.

A. M. Akul’shin, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, E. K. Yurkin, and N. V. Senkov, “Collisional broadening of intra-Doppler resonances of selective reflection of the D2 of cesium,” JETP Lett. 36, 303–306 (1982).

Zambon, B.

B. Zambon and G. Nienhuis, “Reflection and transmission of light by thin vapor layers,” Opt. Commun. 143, 308–314 (1997).
[CrossRef]

Zibrov, A. S.

A. M. Akul’shin, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, E. K. Yurkin, and N. V. Senkov, “Collisional broadening of intra-Doppler resonances of selective reflection of the D2 of cesium,” JETP Lett. 36, 303–306 (1982).

Europhys. Lett. (1)

S. Briaudeau, D. Bloch, and M. Ducloy, “Detection of slow atoms in laser spectroscopy of a thin vapor film,” Europhys. Lett. 35, 337–342 (1996).
[CrossRef]

J. Phys. (Paris) (1)

M. F. H. Schuurmans, “Spectral narrowing of selective reflection,” J. Phys. (Paris) 37, 469–485 (1976).
[CrossRef]

J. Phys. II (2)

M. Ducloy and M. Fichet, “General theory of frequency modulated selective reflection. Influence of atom surface interactions,” J. Phys. II 1, 1429–1446 (1991).

The essential dispersive response of SR spectroscopy in a long cell results only from the SR spatial averaging, which washes out the atomic response close to the (remote) second window. It should be recalled also that because of the symmetry breakdown occurring between arriving and departing atoms, and because of the atom–surface interaction, SR spectra in a long cell commonly include, in the vicinity of line center, a mixture of absorptive and dispersive responses—see notably the discussions in M. Chevrollier, M. Fichet, M. Oria, G. Rahmat, D. Bloch, and M. Ducloy, “High resolution selective reflection spectroscopy as a probe of long-range surface interaction: measurement of the surface van der Waals attraction exerted on excited Cs atoms,” J. Phys. II 2, 631–657 (1992); conversely, and as noted in Section 3 herein, the transmission through a relatively long cell exhibits simply absorption-like properties as long as the medium remains optically thin.

J. Phys. IV (1)

S. Briaudeau, S. Saltiel, J. R. R. Leite, M. Oria, A. Bramati, A. Weis, D. Bloch, and M. Ducloy, “Recent developments in sub-Doppler spectroscopy in a thin cell,” J. Phys. IV 10, Pr. 8, 145–146 (2000).

JETP Lett. (1)

A. M. Akul’shin, V. L. Velichanskii, A. S. Zibrov, V. V. Nikitin, V. A. Sautenkov, E. K. Yurkin, and N. V. Senkov, “Collisional broadening of intra-Doppler resonances of selective reflection of the D2 of cesium,” JETP Lett. 36, 303–306 (1982).

Laser Phys. (1)

A. Ch. Izmailov, “On the possibility of sub-Doppler structure of spectral lines of gas particles by a single travelling monochromatic wave,” Laser Phys. 2, 762–763 (1992).

Opt. Commun. (2)

B. Zambon and G. Nienhuis, “Reflection and transmission of light by thin vapor layers,” Opt. Commun. 143, 308–314 (1997).
[CrossRef]

D. Sarkisyan, D. Bloch, A. Papoyan, and M. Ducloy, “Sub-Doppler spectroscopy by sub-micron thin Cs-vapor layer,” Opt. Commun. 200, 201–208 (2001).
[CrossRef]

Phys. Rev. (1)

R. H. Romer and R. H. Dicke, “New technique of high-resolution microwave spectroscopy,” Phys. Rev. 99, 532–536 (1955).
[CrossRef]

Phys. Rev. A (11)

G. Nienhuis, F. Schuller, and M. Ducloy, “Nonlinear selec-tive reflection from an atomic vapor at arbitrary incidence angle,” Phys. Rev. A 38, 5197–5205 (1988).
[CrossRef] [PubMed]

F. Schuller, G. Nienhuis, and M. Ducloy, “Selective reflection from an atomic vapor in a pump-probe scheme,” Phys. Rev. A 43, 443–454 (1991).
[CrossRef] [PubMed]

T. A. Vartanyan and D. L. Lin, “Enhanced selective reflection from a thin layer of a dilute gaseous medium,” Phys. Rev. A 51, 1959–1964 (1995).
[CrossRef] [PubMed]

S. Briaudeau, S. Saltiel, G. Nienhuis, D. Bloch, and M. Ducloy, “Coherent Doppler narrowing in a thin vapor cell: Observation of the Dicke regime in the optical domain,” Phys. Rev. A 57, R3169–3172 (1998).
[CrossRef]

S. Briaudeau, D. Bloch, and M. Ducloy, “Sub-Doppler spectroscopy in a thin film of resonant vapor,” Phys. Rev. A 59, 3723–3735 (1999).
[CrossRef]

F. Schuller, O. Gorceix, and M. Ducloy, “Nonlinear selectivereflection in cascade three-level atomic systems,” Phys. Rev. A 47, 519–528 (1993).
[CrossRef] [PubMed]

G. Nienhuis and F. Schuller, “Selective reflection from a vapor of three-level atoms,” Phys. Rev. A 50, 1586–1592 (1994).
[CrossRef] [PubMed]

M. Gorris-Neveux, P. Monnot, S. Saltiel, R. Barbé, J. C. Keller, and M. Ducloy, “Two-photon selective reflection,” Phys. Rev. A 54, 3386–3393 (1996).
[CrossRef] [PubMed]

F. Schuller, A. Amy-Klein, and S. Saltiel, “Saturation effects in three-level selective reflection,” Phys. Rev. A 53, 3647–3651 (1996).
[CrossRef] [PubMed]

H. van Kampen, V. A. Sautenkov, E. R. Eliel, and J. P. Woerdman, “Probing the spatial dispersion in a dense atomic vapor near a dielectric interface,” Phys. Rev. A 58, 4473–4478 (1998).
[CrossRef]

D. Petrosyan and Yu. P. Malakyan, “Electromagnetically induced transparency in a thin vapor film,” Phys. Rev. A 61, 053820 (2000).
[CrossRef]

Phys. Rev. E (1)

M. Chevrollier, M. Oria, J. G. De Souza, D. Bloch, M. Fichet, and M. Ducloy, “Selective reflection spectroscopy of a resonant vapor at the interface with a metallic layer,” Phys. Rev. E 63, 046610 (2001).
[CrossRef]

Other (6)

Note that r1 is an amplitude reflection coefficient usually not much smaller than unity; in recent experiments (see Ref. 11) performed with a narrow cell with yttrium aluminum garnet (YAG) windows, one has n1=1.82, i.e., r1= 0.29. Note also that even with an antireflection coating, one usually has r1, 2≥0.1.

The difficulties typical of the optically thick medium in comparable problems have been analysed in the appendix of Ref. 1 and in T. Vartanyan, D. Bloch, and M. Ducloy, “Blue shift paradox in selective reflection,” in Spectral Line Shapes, A. D. May, J. R. Drummond, eds., AIP Conference Proceedings 328 (American Institute of Physics, New York, 1995), pp. 249–250.

G. Dutier, A. Yarovitski, S. Saltiel, A. Papoyan, D. Sarkisyan, D. Bloch, and M. Ducloy, “Collapse and revival of a Dicke-type coherent narrowing in a sub-micron thick vapor cell transmission spectroscopy,” Europhys. Lett. (to be published).

Note that the restriction to a finite cell length may intro-duce some additional changes relative to most common SR theories, as elaborated for various atomic models.

S. Briaudeau, “Spectroscopie à haute résolution en vapeur confinée,” thèse de doctorat, Laboratoire de Physique des Lasers, Université Paris 13 (1998) (unpublished).

A. Ch. Izmailov, “Manifestations of sub-Doppler structure of the spectral lines of gas particles in the radiation of a travelling monochromatic pump wave,” Opt. Spektrosk. 74, 41–48 (1993) [Opt. Spectrosc. 74, 25–29 (1993)].

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Figures (3)

Fig. 1
Fig. 1

Thin layer (thickness L) of a (resonant) atomic medium sandwiched between two parallel, transparent, dielectric windows with index of refraction n1 for z<0, and n2 for z>L.

Fig. 2
Fig. 2

Theoretical line shapes for a two-level system in the linear regime as evaluated for various cell lengths (as indicated): the T values for (a), (b), (e), (f) and R values for (c), (d), (g), (h) correspond to the respective resonant modifications of the transmitted amplitude and of the reflected amplitude. These values naturally account for the FP resonance through the F factor appearing in Eqs. (20) and (21) and coefficient C. For purposes of comparison, a single vertical scale (in arbitrary units) has been used. The various line shapes permit one to compare, respectively, a cell with two identical windows [(a)–(d) with r1=r2=0.29] and a cell whose output window has an antireflection coating [(e)–(h) with r1=0.29, r2=0]. The spectra are calculated with γ/ku=0.025. It is recalled that in a macroscopic cell, the transmission linewidth is an absorption Voigt profile that can be approximated, as long as γku, by the Gaussian line shape represented in (a) by the dashed curve for L→∞ (arbitrary vertical scale, half-width at 1/e : ku).

Fig. 3
Fig. 3

Theoretical transmission dT/dω (solid curve) and reflection dR/dω (dashed curve) spectra in the FM regime for different cell lengths as indicated, assuming two identical windows (r1=r2=0.29). A single vertical scale has been used, and the signal amplitudes account for the FP resonance through the F factor appearing in Eqs. (47) and (48) and coefficient C.

Equations (52)

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Ein(z, t)=12Einexp[-i(ωt-kn1z)]+c.c.
Et(z, t)=12Etexp[-i(ωt-kn2z+ϕ)]+c.c.,
Er(z, t)=12Erexp[-i(ωt+kn1z)]+c.c.
Eo(z, t)=12Eo(z)exp[-i(ωt-kz)]+c.c.,
Po(z, t)=12Po(z)exp[-i(ωt-kz)]+c.c.
Ein+Er=Eo(0),
in1k(Ein-Er)=ikEo(0)+Eoz (0),
Eo(L)=Et,
ikEo(L)+Eoz (L)=in2 kEt.
2Eo(z)z2+2ik Eo(z)z=-(k2/εo)Po(z).
zexp(2ikz) Eo(z)z=-(k2/εo)Po(z)exp(2ikz).
Eoz (L)-Eoz (0)+2ik[Eo(L)-Eo(0)]=2ikIf,
Eoz (L)exp(2ikL)-Eoz (0)=2ikIb.
If=ik/2εo0LPo(z)dz,
Ib=ik/2εo0LPo(z)exp(2ikz)dz.
Et=t02 t10Ein/F,
Er=[r1-r2exp(2ikL)]Ein/F,
Et=t02(If-r1Ib)/F,
Er=t01[Ib-r2Ifexp(i2kL)]/F.
r1=n1-1n1+1,r2=n2-1n2+1,
t10=2n1n1+1,t01=2n1+1,
t02=2n2+1,
andF=1-r1r2exp(2ikL).
St2t10t022EinRe(If-r1Ib)/|F|2,
Sr2t01EinRe{[r1-r2exp(-2ikL)]×[Ib-r2Ifexp(2ikL)]}/|F|2.
Sr=|Ib-rIf|2(1+r)2.
Eo(z)=Eint10{1-r2exp[-2ik(z-L)]}/F.
Eo=12Eo+exp[-i(ωt-kz)]+12Eo-exp[-i(ωt+kz)]+c.c.,
Po=12Po+(z)exp[-i(ωt-kz)]+12Po-(z)exp[-i(ωt+kz)]+c.c.,
Eo+=Eint10/F
Eo-=-Eint10r2exp(2ikL)/F=-r2exp(2ikL)Eo+,
Po(z)=Po+(z)+Po-(z)exp(-2ikz).
Po-(L-z)Eo-=Po+(z)Eo+.
ITlin=ik/2εo0LPo+(z)dz,
ISRlin=ik/2εo0LPo+(z)exp(2ikz)dz.
If=ITlin-r2ISRlin,
Ib=ISRlin-r2exp(2ikL)ITlin.
IT=If-r1Ib=[1+r1r2exp(2ikL)]ITlin-[r1+r2]ISRlin,
ISR=Ib-r2Ifexp(2ikL)=[1+r22exp(2ikL)]ISRlin-2[r2exp(2ikL)]ITlin.
ITlin=C-+W(v)g(ω-ωo, v, L)dv,
ISRlin=C-+W(v)h(ω-ωo, v, L)dv,
g(ω-ωo, v, L)=-kΛ+L-|v|Λ+×1-exp-Λ+L|v|,
Λ±=γ-i(ω-ωo)±ikv,
h(ω-ωo, v, L)=h±(ω-ωo, v, L)=12i1Λ-exp(2ikL)Λ±-k|v|Λ+Λ-exp-ΛL|v|.
C=Nμ2t10Ein4Fεo.
dPo+dω (z)=2εoC [exp(ikL-ikz)-exp(-ikz)][γ-i(ω-ωo)]kuπ,
dITlindω=-4ikuπ C sin2(kL/2)γ-i(ω-ωo),
dISRlindω=dITlindωexp(ikL).
dITdω=-4ikuπ C[1-r exp(ikL)]2×sin2(kL/2)γ-i(ω-ωo),
dISRdω=dITdωexp(ikL).
dStdω=2(1-r)(1-r2)Ein|F|2RedITdω,
dSrdω=-4(1-r)rEinsin(kL)|F|2ImdITdω.

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