Abstract

We develop a three-level theoretical model for atomic optical filters based on optical anisotropy induced by the circularly polarized pump field. Calculative results are in good agreement with experimental results reported previously [Opt. Lett 27, 500 (2002) ]. The filtering characteristics such as the functions of pump intensity, pump detuning, and cell temperature are studied, respectively. The theoretical analysis presented here is expected to be useful in investigating atomic optical filters and polarization spectroscopy.

© 2009 Optical Society of America

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  1. J. Tang, Q. Wang, Y. Li, L. Zhang, J. Gan, M. Duan, J. Kong, and L. Zheng, “Experimental study of a model digital space optical communication system with new quantum devices,” Appl. Opt. 34, 2619-2622 (1995).
    [CrossRef]
  2. H. Chen, M. A. White, David. A. Krugger, and C. Y. She, “Daytime mesopause temperature measurements with a sodium-vapor dispersive Faraday filter in a lidar receiver,” Opt. Lett. 21, 1093-1095 (1996).
    [CrossRef] [PubMed]
  3. C. Fricke-Begemann, M. Alpers, and J. Höffner, “Daylight rejection with a new receiver for potassium resonance temperature lidars,” Opt. Lett. 27, 1932-1934 (2002).
    [CrossRef]
  4. J. Höffner and C. Fricke-Begemann, “Accurate lidar temperature with narrowband filters,” Opt. Lett. 30, 890-892 (2005).
    [CrossRef] [PubMed]
  5. J. Menders, K. Benson, S. H. Bloom, C. S. Liu, and E. Korevaar, “Ultranarrow line filtering using a Cs Faraday filter at 852 nm,” Opt. Lett. 16, 846-848 (1991).
    [CrossRef] [PubMed]
  6. D. J. Dick and T. M. Shay, “Ultrahigh-noise rejection optical filter,” Opt. Lett. 16, 867-869 (1991).
    [CrossRef] [PubMed]
  7. R. I. Billmers, S. K. Gayen, M. F. Squicciarini, V. M. Contarino, W. J. Scharpf, and D. M. Allocca, “Experimental demonstration of an excited-state Faraday filter operating at 532 nm,” Opt. Lett. 20, 106-108 (1995).
    [CrossRef] [PubMed]
  8. Y. Peng, “Transmission characteristics of an excited-state Faraday optical filter at 532 nm,” J. Phys. B 30, 5123-5129 (1997).
    [CrossRef]
  9. Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Potassium Faraday optical filter in line-center operation,” Opt. Commun. 194, 147-150 (2001).
    [CrossRef]
  10. Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Optical filtering characteristic of potassium Faraday optical filter,” IEEE J. Quantum Electron. 37, 372-375 (2001).
    [CrossRef]
  11. L. Zhang and J. Tang, “Experimental study on optimization of the working conditions of excited state Faraday filter,” Opt. Commun. 152, 275-279 (1998).
    [CrossRef]
  12. S. K. Gayen, R. I. Billmers, V. M. Contarino, M. F. Squicciarini, W. J. Scharpf, G. Yang, P. R. Herczfeld, and D. M. Allocca, “Induced-dichroism-excited atomic line filter at 532 nm,” Opt. Lett. 20, 1427-1429 (1995).
    [CrossRef] [PubMed]
  13. L. D. Turner, V. Karaganov, P. J. O. Teubner, and R. E. Scholten, “Sub-Doppler bandwidth atomic optical filter,” Opt. Lett. 27, 500-502 (2002).
    [CrossRef]
  14. Z. He, Y. Zhang, S. Liu, and P. Yuan, “Transmission characteristics of an excited-state induced dispersion optical filter of rubidium at 775.9 nm,” Chin. Opt. Lett. 5, 252-254 (2007).
  15. A. Cere, V. Parigi, M. Abad, F. Wolfgramm, A. Predojevic, and W. Mitchell, “Narrowband tunable filter based on velocity-selective optical pumping in an atomic vapor,” Opt. Lett. 34, 1012-1014 (2009).
    [CrossRef] [PubMed]
  16. K.-A. Suominen, S. Stenholm, and B. Stahlberg, “Laser-induced dispersion in a three-level system,” J. Opt. Soc. Am. B 8, 1899-1906 (1991).
    [CrossRef]
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    [CrossRef] [PubMed]
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  19. J. Huennekens, R. K. Namiotka, J. Sagle, and Z. J. Jabbour, “Thermalization of velocity-selected excited-state population by resonance exchange collisions and radiation trapping,” Phys. Rev. A 51, 4472-4482 (1995).
    [CrossRef] [PubMed]
  20. R. K. Namiotka, J. Huennekens, and M. Allegrini, “Energy-pooling collisions in potassium: 4P(J)+4P(J)−4S+nI(nI=5P,6S,4D),” Phys. Rev. A 56, 514-520 (1997).
    [CrossRef]

2009

2007

2005

2002

2001

Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Potassium Faraday optical filter in line-center operation,” Opt. Commun. 194, 147-150 (2001).
[CrossRef]

Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Optical filtering characteristic of potassium Faraday optical filter,” IEEE J. Quantum Electron. 37, 372-375 (2001).
[CrossRef]

1998

L. Zhang and J. Tang, “Experimental study on optimization of the working conditions of excited state Faraday filter,” Opt. Commun. 152, 275-279 (1998).
[CrossRef]

1997

R. K. Namiotka, J. Huennekens, and M. Allegrini, “Energy-pooling collisions in potassium: 4P(J)+4P(J)−4S+nI(nI=5P,6S,4D),” Phys. Rev. A 56, 514-520 (1997).
[CrossRef]

Y. Peng, “Transmission characteristics of an excited-state Faraday optical filter at 532 nm,” J. Phys. B 30, 5123-5129 (1997).
[CrossRef]

1996

1995

1991

1982

Abad, M.

Allegrini, M.

R. K. Namiotka, J. Huennekens, and M. Allegrini, “Energy-pooling collisions in potassium: 4P(J)+4P(J)−4S+nI(nI=5P,6S,4D),” Phys. Rev. A 56, 514-520 (1997).
[CrossRef]

Allocca, D. M.

Alpers, M.

Benson, K.

Billmers, R. I.

Bloom, S. H.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003), pp. 283-293.

Cere, A.

Chen, H.

Contarino, V. M.

Dick, D. J.

Duan, M.

Fricke-Begemann, C.

Gan, J.

Gayen, S. K.

He, Z.

Herczfeld, P. R.

Höffner, J.

Huennekens, J.

R. K. Namiotka, J. Huennekens, and M. Allegrini, “Energy-pooling collisions in potassium: 4P(J)+4P(J)−4S+nI(nI=5P,6S,4D),” Phys. Rev. A 56, 514-520 (1997).
[CrossRef]

J. Huennekens, R. K. Namiotka, J. Sagle, and Z. J. Jabbour, “Thermalization of velocity-selected excited-state population by resonance exchange collisions and radiation trapping,” Phys. Rev. A 51, 4472-4482 (1995).
[CrossRef] [PubMed]

Jabbour, Z. J.

J. Huennekens, R. K. Namiotka, J. Sagle, and Z. J. Jabbour, “Thermalization of velocity-selected excited-state population by resonance exchange collisions and radiation trapping,” Phys. Rev. A 51, 4472-4482 (1995).
[CrossRef] [PubMed]

Jia, X.

Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Potassium Faraday optical filter in line-center operation,” Opt. Commun. 194, 147-150 (2001).
[CrossRef]

Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Optical filtering characteristic of potassium Faraday optical filter,” IEEE J. Quantum Electron. 37, 372-375 (2001).
[CrossRef]

Karaganov, V.

Kong, J.

Korevaar, E.

Krugger, David. A.

Li, Y.

Liu, C. S.

Liu, S.

Ma, Z.

Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Optical filtering characteristic of potassium Faraday optical filter,” IEEE J. Quantum Electron. 37, 372-375 (2001).
[CrossRef]

Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Potassium Faraday optical filter in line-center operation,” Opt. Commun. 194, 147-150 (2001).
[CrossRef]

Menders, J.

Mitchell, W.

Namiotka, R. K.

R. K. Namiotka, J. Huennekens, and M. Allegrini, “Energy-pooling collisions in potassium: 4P(J)+4P(J)−4S+nI(nI=5P,6S,4D),” Phys. Rev. A 56, 514-520 (1997).
[CrossRef]

J. Huennekens, R. K. Namiotka, J. Sagle, and Z. J. Jabbour, “Thermalization of velocity-selected excited-state population by resonance exchange collisions and radiation trapping,” Phys. Rev. A 51, 4472-4482 (1995).
[CrossRef] [PubMed]

Parigi, V.

Peng, Y.

Y. Peng, “Transmission characteristics of an excited-state Faraday optical filter at 532 nm,” J. Phys. B 30, 5123-5129 (1997).
[CrossRef]

Predojevic, A.

Sagle, J.

J. Huennekens, R. K. Namiotka, J. Sagle, and Z. J. Jabbour, “Thermalization of velocity-selected excited-state population by resonance exchange collisions and radiation trapping,” Phys. Rev. A 51, 4472-4482 (1995).
[CrossRef] [PubMed]

Scharpf, W. J.

Scholten, R. E.

Shay, T. M.

She, C. Y.

Squicciarini, M. F.

Stahlberg, B.

Stenholm, S.

Suominen, K.-A.

Tang, J.

L. Zhang and J. Tang, “Experimental study on optimization of the working conditions of excited state Faraday filter,” Opt. Commun. 152, 275-279 (1998).
[CrossRef]

J. Tang, Q. Wang, Y. Li, L. Zhang, J. Gan, M. Duan, J. Kong, and L. Zheng, “Experimental study of a model digital space optical communication system with new quantum devices,” Appl. Opt. 34, 2619-2622 (1995).
[CrossRef]

Teubner, P. J. O.

Turner, L. D.

Wang, Q.

Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Potassium Faraday optical filter in line-center operation,” Opt. Commun. 194, 147-150 (2001).
[CrossRef]

Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Optical filtering characteristic of potassium Faraday optical filter,” IEEE J. Quantum Electron. 37, 372-375 (2001).
[CrossRef]

J. Tang, Q. Wang, Y. Li, L. Zhang, J. Gan, M. Duan, J. Kong, and L. Zheng, “Experimental study of a model digital space optical communication system with new quantum devices,” Appl. Opt. 34, 2619-2622 (1995).
[CrossRef]

White, M. A.

Wolfgramm, F.

Yang, G.

Yeh, P.

Yuan, P.

Zhang, L.

L. Zhang and J. Tang, “Experimental study on optimization of the working conditions of excited state Faraday filter,” Opt. Commun. 152, 275-279 (1998).
[CrossRef]

J. Tang, Q. Wang, Y. Li, L. Zhang, J. Gan, M. Duan, J. Kong, and L. Zheng, “Experimental study of a model digital space optical communication system with new quantum devices,” Appl. Opt. 34, 2619-2622 (1995).
[CrossRef]

Zhang, Y.

Z. He, Y. Zhang, S. Liu, and P. Yuan, “Transmission characteristics of an excited-state induced dispersion optical filter of rubidium at 775.9 nm,” Chin. Opt. Lett. 5, 252-254 (2007).

Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Optical filtering characteristic of potassium Faraday optical filter,” IEEE J. Quantum Electron. 37, 372-375 (2001).
[CrossRef]

Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Potassium Faraday optical filter in line-center operation,” Opt. Commun. 194, 147-150 (2001).
[CrossRef]

Zheng, L.

Appl. Opt.

Chin. Opt. Lett.

IEEE J. Quantum Electron.

Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Optical filtering characteristic of potassium Faraday optical filter,” IEEE J. Quantum Electron. 37, 372-375 (2001).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

Y. Peng, “Transmission characteristics of an excited-state Faraday optical filter at 532 nm,” J. Phys. B 30, 5123-5129 (1997).
[CrossRef]

Opt. Commun.

Y. Zhang, X. Jia, Z. Ma, and Q. Wang, “Potassium Faraday optical filter in line-center operation,” Opt. Commun. 194, 147-150 (2001).
[CrossRef]

L. Zhang and J. Tang, “Experimental study on optimization of the working conditions of excited state Faraday filter,” Opt. Commun. 152, 275-279 (1998).
[CrossRef]

Opt. Lett.

J. Menders, K. Benson, S. H. Bloom, C. S. Liu, and E. Korevaar, “Ultranarrow line filtering using a Cs Faraday filter at 852 nm,” Opt. Lett. 16, 846-848 (1991).
[CrossRef] [PubMed]

D. J. Dick and T. M. Shay, “Ultrahigh-noise rejection optical filter,” Opt. Lett. 16, 867-869 (1991).
[CrossRef] [PubMed]

L. D. Turner, V. Karaganov, P. J. O. Teubner, and R. E. Scholten, “Sub-Doppler bandwidth atomic optical filter,” Opt. Lett. 27, 500-502 (2002).
[CrossRef]

C. Fricke-Begemann, M. Alpers, and J. Höffner, “Daylight rejection with a new receiver for potassium resonance temperature lidars,” Opt. Lett. 27, 1932-1934 (2002).
[CrossRef]

J. Höffner and C. Fricke-Begemann, “Accurate lidar temperature with narrowband filters,” Opt. Lett. 30, 890-892 (2005).
[CrossRef] [PubMed]

R. I. Billmers, S. K. Gayen, M. F. Squicciarini, V. M. Contarino, W. J. Scharpf, and D. M. Allocca, “Experimental demonstration of an excited-state Faraday filter operating at 532 nm,” Opt. Lett. 20, 106-108 (1995).
[CrossRef] [PubMed]

S. K. Gayen, R. I. Billmers, V. M. Contarino, M. F. Squicciarini, W. J. Scharpf, G. Yang, P. R. Herczfeld, and D. M. Allocca, “Induced-dichroism-excited atomic line filter at 532 nm,” Opt. Lett. 20, 1427-1429 (1995).
[CrossRef] [PubMed]

H. Chen, M. A. White, David. A. Krugger, and C. Y. She, “Daytime mesopause temperature measurements with a sodium-vapor dispersive Faraday filter in a lidar receiver,” Opt. Lett. 21, 1093-1095 (1996).
[CrossRef] [PubMed]

A. Cere, V. Parigi, M. Abad, F. Wolfgramm, A. Predojevic, and W. Mitchell, “Narrowband tunable filter based on velocity-selective optical pumping in an atomic vapor,” Opt. Lett. 34, 1012-1014 (2009).
[CrossRef] [PubMed]

Phys. Rev. A

J. Huennekens, R. K. Namiotka, J. Sagle, and Z. J. Jabbour, “Thermalization of velocity-selected excited-state population by resonance exchange collisions and radiation trapping,” Phys. Rev. A 51, 4472-4482 (1995).
[CrossRef] [PubMed]

R. K. Namiotka, J. Huennekens, and M. Allegrini, “Energy-pooling collisions in potassium: 4P(J)+4P(J)−4S+nI(nI=5P,6S,4D),” Phys. Rev. A 56, 514-520 (1997).
[CrossRef]

Other

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003), pp. 283-293.

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Figures (8)

Fig. 1
Fig. 1

Relevant energy levels of K 39 4 S 1 2 4 P 3 2 6 S 1 2 system.

Fig. 2
Fig. 2

Calculated filter characteristics versus probe detuning from resonance with 4 P 3 2 F = 3 6 S 1 2 F = 2 transition. (a) Transmission, (b) rotation angle, and (c) absorption coefficient. The pump field is resonant with 4 S 1 2 F = 2 4 P 3 2 F = 3 transition. I pump = 330 mW cm 2 , T = 383 K , and L = 7.5 cm .

Fig. 3
Fig. 3

Experimental transmittance spectrum obtained by Turner [13] at 694 nm of 4 P 3 2 F = 3 6 S 1 2 F = 2 transition. The pump field is resonant with 4 S 1 2 F = 2 4 P 3 2 F = 3 transition. I pump = 330 mW cm 2 , T = 383 K , and L = 7.5 cm .

Fig. 4
Fig. 4

Calculated peak transmission and FWHM of probe transmittance spectrum as a function of pump intensity at 383 K . The pump field is resonant with 4 S 1 2 F = 2 4 P 3 2 F = 3 transition. The probe field is resonance with 4 P 3 2 F = 3 6 S 1 2 F = 2 transition. L = 7.5 cm .

Fig. 5
Fig. 5

Calculated transmission of probe field versus probe detuning from resonance with 4 P 3 2 F = 3 6 S 1 2 F = 2 transition at different pump intensities. (a) 0.5 W cm 2 , (b) 1 W cm 2 , (c) 5 W cm 2 , (d) 10 W cm 2 . The pump field is resonant with 4 S 1 2 F = 2 4 P 3 2 F = 3 transition. T = 383 K and L = 7.5 cm .

Fig. 6
Fig. 6

Dependence of peak transmission and peak shift for probe field on pump detuning. I pump = 330 mW cm 2 , T = 383 K , and L = 7.5 cm .

Fig. 7
Fig. 7

Dependence of peak transmission and FWHM for probe field on pump detuning. I pump = 330 mW cm 2 , T = 383 K , and L = 7.5 cm .

Fig. 8
Fig. 8

Peak transmission and FWHM of probe field as a function of cell temperature. The pump field is resonant with 4 S 1 2 F = 2 4 P 3 2 F = 3 transition. I pump = 330 mW cm 2 and L = 7.5 cm .

Equations (22)

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E 1 ( z , t ) = 1 2 E + ( 1 ) ( z , t ) e ̂ + exp [ i ( k 1 z ω 1 t ) ] + c.c ,
E 2 ( z , t ) = 1 2 [ E + ( 2 ) ( z , t ) e ̑ + + E ( 2 ) ( z , t ) e ̑ ] exp [ i ( k 2 z ω 2 t ) ] + c.c ,
H = ( ω 11 1 | e r E 1 | 2 0 2 | e r E 1 | 1 ω 22 2 | e r E 2 | 3 0 3 | e r E 2 | 2 ω 33 ) ,
i d ρ n m d t = s ( H n s ρ s m ρ n s H s m ) i γ n m ρ n m ,
ρ ̃ 21 = ρ 21 exp [ i ( k 1 z ω 1 t ) ] ,
ρ ̃ 32 = ρ 32 exp [ i ( k 2 z ω 2 t ) ] ,
ρ ̃ 31 = ρ 31 exp { i [ ( k 1 + k 2 ) z ( ω 1 + ω 2 ) t ] } .
ρ ̇ 11 = γ 2 ρ 22 + [ i Ω 1 ( ρ ̃ 21 ρ ̃ 12 ) ] 2 ,
ρ ̇ 22 = γ 3 ρ 33 γ 2 ρ 22 + [ i Ω 1 ( ρ ̃ 12 ρ ̃ 21 ) + i Ω 2 ( ρ ̃ 32 ρ ̃ 23 ) ] 2 ,
ρ ̇ 33 = γ 3 ρ 33 + [ i Ω 2 ( ρ ̃ 23 ρ ̃ 32 ) ] 2 ,
ρ ̃ ̇ 21 = ρ ̃ 21 ( i Δ 1 i k 1 υ γ 21 ) + [ i Ω 1 ( ρ 11 ρ 22 ) + i Ω 2 ρ ̃ 31 ] 2 ,
ρ ̃ ̇ 32 = ρ ̃ 32 ( i Δ 2 i k 2 υ γ 32 ) + [ i Ω 2 ( ρ 22 ρ 33 ) i Ω 1 ρ ̃ 31 ] 2 ,
ρ ̃ ̇ 31 = ρ ̃ 31 ( i Δ 3 i k 3 υ γ 31 ) + ( i Ω 2 ρ ̃ 21 i Ω 1 ρ ̃ 32 ) 2 ,
ρ ̃ 32 ( 2 ) = Ω 2 [ 2 Ω 1 2 γ 21 ( Δ 3 + k 3 υ i γ 31 ) Ω 1 2 γ 2 ( Δ 1 + k 1 υ + i γ 21 ) ] { γ 2 [ ( Δ 1 + k 1 υ ) 2 + γ 21 2 ] + Ω 1 2 γ 21 } [ 8 ( Δ 2 + k 2 υ i γ 32 ) ( Δ 3 + k 3 υ i γ 31 ) 2 Ω 1 2 ] .
P ( z , t ) = 1 2 ε 0 χ E ( 2 ) ( z , t ) e ̂ exp [ i ( k 2 z ω 2 t ) ] + c.c ,
= N 0 ( μ 2 ρ 32 e ̂ + c.c ) .
χ = 2 μ 2 2 N 0 ρ ̃ 32 ( ε 0 Ω 2 ) ,
T r = 1 2 exp ( α L ) [ cosh ( Δ α L ) cos ( 2 φ ) ] ,
α = 1 2 ( α + + α ) = ω 2 2 c Im ( χ + + χ ) ,
Δ α = 1 2 ( α + α ) = ω 2 2 c Im ( χ + χ ) ,
φ = ω 2 L 2 c ( n + n ) = ω 2 L 4 c Re ( χ + χ ) ,
f ( T ) = c 1 + a ( N 0 ( T ) N 0 ( T 0 ) ) b .

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