Abstract

A model for the Faraday anomalous dispersion optical filter is presented. Our model predicts a bandwidth of 0.6 GHz and a transmission peak of 0.98 for a filter operating on the Cs (D2) line. The model includes hyper-fine effects and is valid for arbitrary magnetic fields.

© 1991 Optical Society of America

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References

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  1. D. J. Dick, T. M. Shay, Opt. Lett. 16, 867 (1991).
    [CrossRef] [PubMed]
  2. D. M. Camm, F. L. Curzon, Can. J. Phys. 50, 2866 (1972).
    [CrossRef]
  3. G. J. Roberts, P. E. G. Baird, M. W. S. M. Brimicombe, P. G. H. Sandars, D. R. Selby, D. N. Stacey, J. Phys. B 13, 1389 (1980).
    [CrossRef]
  4. A. D. Kersey, J. B. Dawson, D. J. Ellis, Spectrochim. Acta 35B, 865 (1980).
  5. P. Yeh, Appl. Opt. 21, 2069 (1982).
    [CrossRef] [PubMed]
  6. X. Chen, V. L. Telegdi, A. Wis, J. Phys. B 20, 5653 (1987).
    [CrossRef]
  7. We calculated the saturation intensity in the filter transmission band to be 1.8 kW/cm2. This is four orders of magnitude higher than the total solar intensity at the Earth’s surface.
  8. R. D. Cowan, Theory of Atomic Structure and Spectra (U. of California Press, Berkeley, Calif., 1981), p. 497.
  9. I. I. Sobelman, Atomic Spectra and Radiative Transition (Springer-Verlag, Berlin, 1979), p. 194.
  10. B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, New York, 1990), Vol. 2, p. 1426.
  11. E. Arimonodo, M. Inguscio, P. Violino, Rev. Mod. Phys. 49, 31 (1977).
    [CrossRef]
  12. S. Rydberg, S. Svanberg, Phys. Scr. 5, 209 (1972).
    [CrossRef]
  13. C. L. Chen, A. V. Phelps, Phys. Rev. 173, 62 (1968).
    [CrossRef]
  14. J. Menders, K. Benson, S. H. Bloom, C. S. Liu, E. Korevaar, Opt. Lett. 16, 846 (1991).
    [CrossRef] [PubMed]

1991 (2)

1987 (1)

X. Chen, V. L. Telegdi, A. Wis, J. Phys. B 20, 5653 (1987).
[CrossRef]

1982 (1)

1980 (2)

G. J. Roberts, P. E. G. Baird, M. W. S. M. Brimicombe, P. G. H. Sandars, D. R. Selby, D. N. Stacey, J. Phys. B 13, 1389 (1980).
[CrossRef]

A. D. Kersey, J. B. Dawson, D. J. Ellis, Spectrochim. Acta 35B, 865 (1980).

1977 (1)

E. Arimonodo, M. Inguscio, P. Violino, Rev. Mod. Phys. 49, 31 (1977).
[CrossRef]

1972 (2)

S. Rydberg, S. Svanberg, Phys. Scr. 5, 209 (1972).
[CrossRef]

D. M. Camm, F. L. Curzon, Can. J. Phys. 50, 2866 (1972).
[CrossRef]

1968 (1)

C. L. Chen, A. V. Phelps, Phys. Rev. 173, 62 (1968).
[CrossRef]

Arimonodo, E.

E. Arimonodo, M. Inguscio, P. Violino, Rev. Mod. Phys. 49, 31 (1977).
[CrossRef]

Baird, P. E. G.

G. J. Roberts, P. E. G. Baird, M. W. S. M. Brimicombe, P. G. H. Sandars, D. R. Selby, D. N. Stacey, J. Phys. B 13, 1389 (1980).
[CrossRef]

Benson, K.

Bloom, S. H.

Brimicombe, M. W. S. M.

G. J. Roberts, P. E. G. Baird, M. W. S. M. Brimicombe, P. G. H. Sandars, D. R. Selby, D. N. Stacey, J. Phys. B 13, 1389 (1980).
[CrossRef]

Camm, D. M.

D. M. Camm, F. L. Curzon, Can. J. Phys. 50, 2866 (1972).
[CrossRef]

Chen, C. L.

C. L. Chen, A. V. Phelps, Phys. Rev. 173, 62 (1968).
[CrossRef]

Chen, X.

X. Chen, V. L. Telegdi, A. Wis, J. Phys. B 20, 5653 (1987).
[CrossRef]

Cowan, R. D.

R. D. Cowan, Theory of Atomic Structure and Spectra (U. of California Press, Berkeley, Calif., 1981), p. 497.

Curzon, F. L.

D. M. Camm, F. L. Curzon, Can. J. Phys. 50, 2866 (1972).
[CrossRef]

Dawson, J. B.

A. D. Kersey, J. B. Dawson, D. J. Ellis, Spectrochim. Acta 35B, 865 (1980).

Dick, D. J.

Ellis, D. J.

A. D. Kersey, J. B. Dawson, D. J. Ellis, Spectrochim. Acta 35B, 865 (1980).

Inguscio, M.

E. Arimonodo, M. Inguscio, P. Violino, Rev. Mod. Phys. 49, 31 (1977).
[CrossRef]

Kersey, A. D.

A. D. Kersey, J. B. Dawson, D. J. Ellis, Spectrochim. Acta 35B, 865 (1980).

Korevaar, E.

Liu, C. S.

Menders, J.

Phelps, A. V.

C. L. Chen, A. V. Phelps, Phys. Rev. 173, 62 (1968).
[CrossRef]

Roberts, G. J.

G. J. Roberts, P. E. G. Baird, M. W. S. M. Brimicombe, P. G. H. Sandars, D. R. Selby, D. N. Stacey, J. Phys. B 13, 1389 (1980).
[CrossRef]

Rydberg, S.

S. Rydberg, S. Svanberg, Phys. Scr. 5, 209 (1972).
[CrossRef]

Sandars, P. G. H.

G. J. Roberts, P. E. G. Baird, M. W. S. M. Brimicombe, P. G. H. Sandars, D. R. Selby, D. N. Stacey, J. Phys. B 13, 1389 (1980).
[CrossRef]

Selby, D. R.

G. J. Roberts, P. E. G. Baird, M. W. S. M. Brimicombe, P. G. H. Sandars, D. R. Selby, D. N. Stacey, J. Phys. B 13, 1389 (1980).
[CrossRef]

Shay, T. M.

Shore, B. W.

B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, New York, 1990), Vol. 2, p. 1426.

Sobelman, I. I.

I. I. Sobelman, Atomic Spectra and Radiative Transition (Springer-Verlag, Berlin, 1979), p. 194.

Stacey, D. N.

G. J. Roberts, P. E. G. Baird, M. W. S. M. Brimicombe, P. G. H. Sandars, D. R. Selby, D. N. Stacey, J. Phys. B 13, 1389 (1980).
[CrossRef]

Svanberg, S.

S. Rydberg, S. Svanberg, Phys. Scr. 5, 209 (1972).
[CrossRef]

Telegdi, V. L.

X. Chen, V. L. Telegdi, A. Wis, J. Phys. B 20, 5653 (1987).
[CrossRef]

Violino, P.

E. Arimonodo, M. Inguscio, P. Violino, Rev. Mod. Phys. 49, 31 (1977).
[CrossRef]

Wis, A.

X. Chen, V. L. Telegdi, A. Wis, J. Phys. B 20, 5653 (1987).
[CrossRef]

Yeh, P.

Appl. Opt. (1)

Can. J. Phys. (1)

D. M. Camm, F. L. Curzon, Can. J. Phys. 50, 2866 (1972).
[CrossRef]

J. Phys. B (2)

G. J. Roberts, P. E. G. Baird, M. W. S. M. Brimicombe, P. G. H. Sandars, D. R. Selby, D. N. Stacey, J. Phys. B 13, 1389 (1980).
[CrossRef]

X. Chen, V. L. Telegdi, A. Wis, J. Phys. B 20, 5653 (1987).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. (1)

C. L. Chen, A. V. Phelps, Phys. Rev. 173, 62 (1968).
[CrossRef]

Phys. Scr. (1)

S. Rydberg, S. Svanberg, Phys. Scr. 5, 209 (1972).
[CrossRef]

Rev. Mod. Phys. (1)

E. Arimonodo, M. Inguscio, P. Violino, Rev. Mod. Phys. 49, 31 (1977).
[CrossRef]

Spectrochim. Acta (1)

A. D. Kersey, J. B. Dawson, D. J. Ellis, Spectrochim. Acta 35B, 865 (1980).

Other (4)

We calculated the saturation intensity in the filter transmission band to be 1.8 kW/cm2. This is four orders of magnitude higher than the total solar intensity at the Earth’s surface.

R. D. Cowan, Theory of Atomic Structure and Spectra (U. of California Press, Berkeley, Calif., 1981), p. 497.

I. I. Sobelman, Atomic Spectra and Radiative Transition (Springer-Verlag, Berlin, 1979), p. 194.

B. W. Shore, The Theory of Coherent Atomic Excitation (Wiley, New York, 1990), Vol. 2, p. 1426.

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Figures (4)

Fig. 1
Fig. 1

Faraday anomalous dispersion optical filter. P1 and P2 are the crossed polarizers.

Fig. 2
Fig. 2

Cs(62P3/2) energy levels versus the magnetic field.

Fig. 3
Fig. 3

(a) Cs FADOF rotation angles and (b) vapor cell absorption at T = 85°C and Bz = 100 G.

Fig. 4
Fig. 4

Cs(852) FADOF theoretical transmission at T = 85°C and Bz = 100 G.

Equations (20)

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I J F M H I J F M = Δ E F δ ( F , F ) + ( μ B z ( - 1 ) M + J + 1 + I ( g j - g I ) [ J ( J + 1 ) ( 2 J + 1 ) ( 2 F + 1 ) ( 2 F + 1 ) ] 1 / 2 × { J 1 J F I F } [ F 1 F - M 0 M ] ) ,
Δ E F = ( 1 / 2 ) h A K + h B [ ( 3 / 2 ) K ( K + 1 ) - 2 I ( I + 1 ) J ( J + 1 ) ] / [ 2 I ( 2 I - 1 ) × 2 J ( 2 J - 1 ) ] ,
S ± 1 / 2 ( F M , F M ) = β β Y β F M γ β F M d ± β F M × Y β F M γ
β F M d ± β F M = ( - 1 ) F - M [ F 1 F - M ± 1 M ] × β F | | d | | β F ,
β F | | d | | β F = ( - 1 ) J + I + F + 1 × ( 2 F + 1 ) ( 2 F + 1 ) × [ J I F F 1 J ] J | | d | | J ,
γ F M = β Y β F M γ β F M .
J | | d | | J 2 = 3 h λ 3 / [ ( 2 π ) 4 τ ] ,
ϕ ( ω ) = ( ω L / 2 c ) Re [ n + ( ω ) - n - ( ω ) ] ,
n ± ( ω ) = F , F , M n ± ( ω , F M , F M ) .
n ± ( ω , F M , F M ) - 1 = C S ± ( F M , F M ) W ( ξ F M , F M ) ,
C = ( 2 π / h ) N ( F ) / [ ( 2 J + 1 ) ( 2 I + 1 ) Δ ν D ] .
N ( F ) N exp [ - E ( F ) / k T ] / F ( 2 F + 1 ) × exp [ - E ( F ) / k T ] ,
N = 9.66 × 10 18 p / T             ( atoms - cm - 3 ) ,
log [ p ] = 11.0531 - 4041 / T - 1.35 log [ T ] ,
W ( ξ F M , F M ) = ( 1 / π ) - exp ( - x 2 ) / ( x - ξ F M , F M ) d x ,
ξ F M , F M = ( ln 2 / π Δ ν D ) ( ω - ω F M , F M + i π / τ ) ,
k ± ( ω ) = ( 2 ω / c ) Im [ n ± ( ω ) ] .
a ( ω ) = 0.5 [ exp ( - k + L ) + exp ( - k - L ) ] .
T ( ω ) = 0.25 { exp ( - k + L ) + exp ( - k - L ) - 2 cos ( 2 ϕ ) exp [ - ( k + L + k - L ) / 2 ] } .
ENBW [ - T ( ω ) d ω ] / T max .

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