Abstract

The anomalous dispersion of the Faraday rotation near optical resonance lines can be employed to build extremely narrowband filters (0.01 Å) with a very wide field of view (±45°). This paper investigates the properties of these filters.

© 1982 Optical Society of America

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References

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  1. P. Yeh, Opt. Commun. 35, 9 (1980).
    [CrossRef]
  2. P. Yeh, Opt. Commun. 35, 15 (1980).
    [CrossRef]
  3. P. Yeh, Opt. Commun. 37, 153 (1981).
    [CrossRef]
  4. P. Yeh, J. Tracy, “Theory of Dispersive Birefringent Filters,” at SPIE Technical Symposium, Los Angeles, 9–13 Feb. 1981, paper 268-08.
  5. J. F. Lotspeich, IEEE J. Quantum Electron. QE-15, 904 (1979).
    [CrossRef]
  6. J. B. Marling, J. Nilsen, L. C. West, L. L. Wood, J. Appl. Phys. 50, 610 (1979).
    [CrossRef]
  7. R. Burhnam, private communication.
  8. D. Macaluso, O. M. Corbino, C. R. Acad. Sci., 127, 548 (1898).
  9. A. Righi, C. R. Acad. Sci. 127, 216 (1898).
  10. A. Righi, C. R. Acad. Sci. 128, 45 (1899).
  11. W. Voigt, Magneto-und Elektrooptik (Tuebner, Leipzig, 1908).
  12. B. M. Schmidt, J. M. Williams, D. Williams, J. Opt. Soc. Am. 54, 454 (1964).
    [CrossRef]
  13. T. Hadeishi, Appl. Phys. Lett. 21, 438 (1972).
    [CrossRef]
  14. D. A. Church, T. Hadeishi, Appl. Phys. Lett. 24, 185 (1974).
    [CrossRef]
  15. G. A. Tanton, H. C. Meyer, J. Opt. Soc. Am. 65, 1261 (1975).
    [CrossRef]
  16. H. A. Bomke, M. Harmatz, Appl. Opt. 16, 751 (1977).
    [CrossRef] [PubMed]
  17. K. G. Kessler, W. G. Schweitzer, J. Opt. Soc. Am. 55, 284 (1965).
    [CrossRef]
  18. M. Cimino, A. Cacciani, N. Sopranzi, Appl. Opt. 7, 1654 (1968).
    [CrossRef] [PubMed]
  19. Y. Ohman, Stockholm Obs. Ann. 19, No. 4, 3 (1956).
  20. J. M. Beckers, Appl. Opt. 9, 595 (1970).
    [CrossRef] [PubMed]
  21. A. Corney, B. P. Kibble, G. W. Series, Proc. Soc. London Ser. A 293, 70 (1966).
    [CrossRef]
  22. M. Yamamoto, S. Murayama, J. Opt. Soc. Am. 69, 781 (1979).
    [CrossRef]
  23. R. Burhnam, private communication.
  24. L. Melamed, J. Opt. Soc. Am. 52, 1316 (1962).
  25. See, for example, A. S. Davydov, Quantum Mechanics (Pergamon, London, 1965), Sec. 81, p. 316–321.
  26. See, for example, H. E. White, Introduction to Atomic Spectra (McGraw-Hill, New York, 1934).
  27. See, for example, E. U. Condon, G. H. Shortley, The Theory of Atomic Spectra (Cambridge U. P., New York, 1957).
  28. M. Abramowitz, I. A. Stegun, Eds. Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 7.
  29. N. A. Lange, Handbook of Chemistry (McGraw-Hill, New York, 1967), p. 1436.
  30. P. M. Stone, Phys. Rev. 127, 1151 (1962).
    [CrossRef]

1981

P. Yeh, Opt. Commun. 37, 153 (1981).
[CrossRef]

1980

P. Yeh, Opt. Commun. 35, 9 (1980).
[CrossRef]

P. Yeh, Opt. Commun. 35, 15 (1980).
[CrossRef]

1979

J. F. Lotspeich, IEEE J. Quantum Electron. QE-15, 904 (1979).
[CrossRef]

J. B. Marling, J. Nilsen, L. C. West, L. L. Wood, J. Appl. Phys. 50, 610 (1979).
[CrossRef]

M. Yamamoto, S. Murayama, J. Opt. Soc. Am. 69, 781 (1979).
[CrossRef]

1977

1975

1974

D. A. Church, T. Hadeishi, Appl. Phys. Lett. 24, 185 (1974).
[CrossRef]

1972

T. Hadeishi, Appl. Phys. Lett. 21, 438 (1972).
[CrossRef]

1970

1968

1966

A. Corney, B. P. Kibble, G. W. Series, Proc. Soc. London Ser. A 293, 70 (1966).
[CrossRef]

1965

1964

1962

L. Melamed, J. Opt. Soc. Am. 52, 1316 (1962).

P. M. Stone, Phys. Rev. 127, 1151 (1962).
[CrossRef]

1956

Y. Ohman, Stockholm Obs. Ann. 19, No. 4, 3 (1956).

1899

A. Righi, C. R. Acad. Sci. 128, 45 (1899).

1898

D. Macaluso, O. M. Corbino, C. R. Acad. Sci., 127, 548 (1898).

A. Righi, C. R. Acad. Sci. 127, 216 (1898).

Beckers, J. M.

Bomke, H. A.

Burhnam, R.

R. Burhnam, private communication.

R. Burhnam, private communication.

Cacciani, A.

Church, D. A.

D. A. Church, T. Hadeishi, Appl. Phys. Lett. 24, 185 (1974).
[CrossRef]

Cimino, M.

Condon, E. U.

See, for example, E. U. Condon, G. H. Shortley, The Theory of Atomic Spectra (Cambridge U. P., New York, 1957).

Corbino, O. M.

D. Macaluso, O. M. Corbino, C. R. Acad. Sci., 127, 548 (1898).

Corney, A.

A. Corney, B. P. Kibble, G. W. Series, Proc. Soc. London Ser. A 293, 70 (1966).
[CrossRef]

Davydov, A. S.

See, for example, A. S. Davydov, Quantum Mechanics (Pergamon, London, 1965), Sec. 81, p. 316–321.

Hadeishi, T.

D. A. Church, T. Hadeishi, Appl. Phys. Lett. 24, 185 (1974).
[CrossRef]

T. Hadeishi, Appl. Phys. Lett. 21, 438 (1972).
[CrossRef]

Harmatz, M.

Kessler, K. G.

Kibble, B. P.

A. Corney, B. P. Kibble, G. W. Series, Proc. Soc. London Ser. A 293, 70 (1966).
[CrossRef]

Lange, N. A.

N. A. Lange, Handbook of Chemistry (McGraw-Hill, New York, 1967), p. 1436.

Lotspeich, J. F.

J. F. Lotspeich, IEEE J. Quantum Electron. QE-15, 904 (1979).
[CrossRef]

Macaluso, D.

D. Macaluso, O. M. Corbino, C. R. Acad. Sci., 127, 548 (1898).

Marling, J. B.

J. B. Marling, J. Nilsen, L. C. West, L. L. Wood, J. Appl. Phys. 50, 610 (1979).
[CrossRef]

Melamed, L.

L. Melamed, J. Opt. Soc. Am. 52, 1316 (1962).

Meyer, H. C.

Murayama, S.

Nilsen, J.

J. B. Marling, J. Nilsen, L. C. West, L. L. Wood, J. Appl. Phys. 50, 610 (1979).
[CrossRef]

Ohman, Y.

Y. Ohman, Stockholm Obs. Ann. 19, No. 4, 3 (1956).

Righi, A.

A. Righi, C. R. Acad. Sci. 128, 45 (1899).

A. Righi, C. R. Acad. Sci. 127, 216 (1898).

Schmidt, B. M.

Schweitzer, W. G.

Series, G. W.

A. Corney, B. P. Kibble, G. W. Series, Proc. Soc. London Ser. A 293, 70 (1966).
[CrossRef]

Shortley, G. H.

See, for example, E. U. Condon, G. H. Shortley, The Theory of Atomic Spectra (Cambridge U. P., New York, 1957).

Sopranzi, N.

Stone, P. M.

P. M. Stone, Phys. Rev. 127, 1151 (1962).
[CrossRef]

Tanton, G. A.

Tracy, J.

P. Yeh, J. Tracy, “Theory of Dispersive Birefringent Filters,” at SPIE Technical Symposium, Los Angeles, 9–13 Feb. 1981, paper 268-08.

Voigt, W.

W. Voigt, Magneto-und Elektrooptik (Tuebner, Leipzig, 1908).

West, L. C.

J. B. Marling, J. Nilsen, L. C. West, L. L. Wood, J. Appl. Phys. 50, 610 (1979).
[CrossRef]

White, H. E.

See, for example, H. E. White, Introduction to Atomic Spectra (McGraw-Hill, New York, 1934).

Williams, D.

Williams, J. M.

Wood, L. L.

J. B. Marling, J. Nilsen, L. C. West, L. L. Wood, J. Appl. Phys. 50, 610 (1979).
[CrossRef]

Yamamoto, M.

Yeh, P.

P. Yeh, Opt. Commun. 37, 153 (1981).
[CrossRef]

P. Yeh, Opt. Commun. 35, 9 (1980).
[CrossRef]

P. Yeh, Opt. Commun. 35, 15 (1980).
[CrossRef]

P. Yeh, J. Tracy, “Theory of Dispersive Birefringent Filters,” at SPIE Technical Symposium, Los Angeles, 9–13 Feb. 1981, paper 268-08.

Appl. Opt.

Appl. Phys. Lett.

T. Hadeishi, Appl. Phys. Lett. 21, 438 (1972).
[CrossRef]

D. A. Church, T. Hadeishi, Appl. Phys. Lett. 24, 185 (1974).
[CrossRef]

C. R. Acad. Sci.

D. Macaluso, O. M. Corbino, C. R. Acad. Sci., 127, 548 (1898).

A. Righi, C. R. Acad. Sci. 127, 216 (1898).

A. Righi, C. R. Acad. Sci. 128, 45 (1899).

IEEE J. Quantum Electron.

J. F. Lotspeich, IEEE J. Quantum Electron. QE-15, 904 (1979).
[CrossRef]

J. Appl. Phys.

J. B. Marling, J. Nilsen, L. C. West, L. L. Wood, J. Appl. Phys. 50, 610 (1979).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

P. Yeh, Opt. Commun. 35, 9 (1980).
[CrossRef]

P. Yeh, Opt. Commun. 35, 15 (1980).
[CrossRef]

P. Yeh, Opt. Commun. 37, 153 (1981).
[CrossRef]

Phys. Rev.

P. M. Stone, Phys. Rev. 127, 1151 (1962).
[CrossRef]

Proc. Soc. London Ser. A

A. Corney, B. P. Kibble, G. W. Series, Proc. Soc. London Ser. A 293, 70 (1966).
[CrossRef]

Stockholm Obs. Ann.

Y. Ohman, Stockholm Obs. Ann. 19, No. 4, 3 (1956).

Other

R. Burhnam, private communication.

P. Yeh, J. Tracy, “Theory of Dispersive Birefringent Filters,” at SPIE Technical Symposium, Los Angeles, 9–13 Feb. 1981, paper 268-08.

W. Voigt, Magneto-und Elektrooptik (Tuebner, Leipzig, 1908).

R. Burhnam, private communication.

See, for example, A. S. Davydov, Quantum Mechanics (Pergamon, London, 1965), Sec. 81, p. 316–321.

See, for example, H. E. White, Introduction to Atomic Spectra (McGraw-Hill, New York, 1934).

See, for example, E. U. Condon, G. H. Shortley, The Theory of Atomic Spectra (Cambridge U. P., New York, 1957).

M. Abramowitz, I. A. Stegun, Eds. Handbook of Mathematical Functions (Dover, New York, 1972), Chap. 7.

N. A. Lange, Handbook of Chemistry (McGraw-Hill, New York, 1967), p. 1436.

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Figures (7)

Fig. 1
Fig. 1

Schematic drawing of the magnetooptic filter structure.

Fig. 2
Fig. 2

Zeeman splitting of the energy levels.

Fig. 3
Fig. 3

Mean absorption coefficient α ̅, rotatory power ρ, and transmission Tmax at the line center (ν = 0) as functions of the Zeeman splitting ΔνB.

Fig. 4
Fig. 4

Typical transmission spectrum of a cesium vapor filter with a passband at the line center.

Fig. 5
Fig. 5

Typical transmission spectrum of a cesium vapor filter with a passband at the wings.

Fig. 6
Fig. 6

Schematic drawing of a two-stage magnetooptic filter.

Fig. 7
Fig. 7

Coordinate system for studying the FOV of magnetooptic filters.

Equations (74)

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E = ½ E 0 exp [ i ( k · r ω t ) ] + c . c . ,
d = e 2 1 | r | 2 [ E 0 · 2 | r | 1 ] 2 ( ω 0 ω i Γ / 2 ) exp [ i ( k · r ω t ) ] + c . c . ,
Γ = 1 / t spont ,
d = ½ χ 0 E 0 exp [ i ( k · r ω t ) ] + c . c . ,
Δ E = g M J e 2 m B ,
e ̂ + = 1 2 ( x ̂ + i y ̂ ) e ̂ = 1 2 ( x ̂ i y ̂ ) e ̂ 0 = z ̂
χ + + = e 2 | 1 / 2 , 1 / 2 | 1 2 ( x + iy ) | 1 / 2 , 1 / 2 | 2 2 0 ( ω 0 + Δ ω s ω i Γ / 2 ) ,
χ = e 2 | 1 / 2 , 1 / 2 | 1 2 ( x iy ) | 1 / 2 , 1 / 2 | 2 2 0 ( ω 0 Δ ω s ω i Γ / 2 ) ,
χ 00 = e 2 | 1 / 2 , 1 / 2 | z | 1 / 2 , 1 / 2 | 2 2 0 ( ω 0 + Δ ω p ω i Γ / 2 ) + e 2 | 1 / 2 , 1 / 2 | z | 1 / 2 , 1 / 2 | 2 2 0 ( ω 0 Δ ω p ω i Γ / 2 ) ,
Δ ω s = 4 3 · e 2 m B Δ ω p = 2 3 · e 2 m B .
f ± = 2 m ω 0 | 1 / 2 , ± 1 / 2 | 1 2 ( x ± iy ) | 1 / 2 , 1 / 2 | 2 ,
f 0 = 2 m ω 0 | 1 / 2 , ± 1 / 2 | z | 1 / 2 , ± 1 / 2 | 2 ,
f = 2 m ω 0 3 · 1 2 J + 1 M , M | J M | r | JM | 2
f + = f = 2 f f 0 = f .
χ + + = e 2 f 2 m ω 0 0 1 ( ω 0 + Δ ω s ω i Γ / 2 ) ,
χ = e 2 f 2 m ω 0 0 1 ( ω 0 + Δ ω s ω i Γ / 2 ) ,
χ 00 = e 2 f 4 m ω 0 0 [ 1 ( ω 0 + Δ ω p ω i Γ / 2 ) + 1 ( ω 0 Δ ω p ω i Γ / 2 ) ] .
f ( υ ) d υ = N ( M 2 π k T ) 1 / 2 exp ( m υ 2 / 2 k T ) d υ
a = Γ Δ ω D ln 2 = Δ ν N Δ ν D ln 2 ,
ν = 2 ( ω ω 0 ) Δ ω D ln 2 = 2 ( ν ν 0 ) Δ ν D ln 2 ,
ν s = 2 Δ ω s Δ ω D ln 2 = 2 Δ ν s Δ ν D ln 2 ,
ν p = 2 Δ ω p Δ ω D ln 2 = 2 Δ ν p Δ ν D ln 2 ,
χ + + = Ne 2 f 2 m ω 0 0 ln 2 π · i Δ ν D W ( ν ν s + ia ) ,
χ = Ne 2 f 2 m ω 0 0 ln 2 π · i Δ ν D W ( ν + ν s + ia ) ,
χ 00 = Ne 2 f 4 m ω 0 0 ln 2 π · i Δ ν D [ W ( ν ν p + ia ) + W ( ν + ν p + ia ) ] ,
W ( x + iy ) = i π exp ( t 2 ) x + iy t dt W Re + i W Im ,
Δ ν D = 2 ln 2 · ν 0 c 2 k T M .
Δ ν D = 0.0405 T GHz ,
= 0 + 0 { χ + + 0 0 0 χ 0 0 0 χ 00 } .
n ̂ + = ( 1 + χ + + ) 1 / 2 1 + ½ χ + + , n ̂ = ( 1 + χ ) 1 / 2 1 + ½ χ ,
E = 1 2 E 0 [ e ̂ + exp ( ik + z ) + e ̂ exp ( ik z ) ] exp ( i ω t )
k ± = ω c n ̂ ± = ω c n ± + i 2 α ± ,
E t = i 2 E 0 y ̂ [ exp ( i k + z ) exp ( i k z ) ] exp ( i ω t ) .
T = ¼ { exp ( α + L ) + exp ( α L ) 2 exp [ ( α + + α ) L / 2 ] × cos [ ω c ( n + n ) L ] } .
α ̅ = ½ ( α + + α ) = ω 2 c Im ( χ + + + χ ) ,
Δ α = ½ ( α + α ) = ω 2 c Im ( χ + + χ ) ,
ρ = ω c 1 2 ( n + n ) = ω 4 c Re ( χ + + χ ) ,
T = ½ exp ( α ̅ L ) [ cosh ( Δ α L ) cos ( 2 ρ L ) ] .
α ̅ = ln 2 π N e 2 f 4 mc 0 Δ ν D [ W Re ( ν + ν s + ia ) + W Re ( ν ν s + ia ) ] ,
Δ α = ln 2 π N e 2 f 4 mc 0 Δ ν D [ W Re ( ν ν s + ia ) W Re ( ν + ν s + ia ) ] ,
ρ = ln 2 π N e 2 f 4 m c 0 Δ ν D [ W Im ( ν + ν s + i a ) W Im ( ν ν s + i a ) ] .
α 0 = ln 2 π N e 2 f 2 mc 0 Δ ν D ,
α + = α 0 W Re ( ν ν s + ia ) ,
α = α 0 W Re ( ν + ν s + ia ) ,
ρ = ¼ α 0 [ W Im ( ν + ν s + ia ) W Im ( ν ν s + i ) ] .
α + = α 0 exp [ ( ν ν s ) 2 ] ,
α = α 0 exp [ ( ν + ν s ) 2 ] ,
ρ = ¼ α 0 [ W Im ( ν + ν s ) W Im ( ν ν s ) ] ,
W Im ( x ) = 2 π exp ( x ) 2 0 x exp ( t 2 ) d t .
T ( ν = 0 ) = exp ( α ̅ L ) sin 2 ρ L .
α ̅ = α 0 exp ( ν s 2 ) ,
ρ = α 0 π exp ( ν s 2 ) 0 ν s exp ( t 2 ) dt .
ρ α = 1 π 0 ν s exp ( t 2 ) dt .
tan ρ L = 2 ρ α ̅ = 2 π 0 ν s e t 2 d t
T max ( ν = 0 ) = [ ( 2 ρ α ̅ ) ] 2 1 + [ ( 2 ρ α ̅ ) ] 2 exp [ α ̅ ρ tan 1 ( 2 ρ α ̅ ) ] .
T π 2 4 ( ν s ν ) 4 ,
Δ ν 1 2 3 ν s Δ ν 2 2 3 ν s
Δ ν 1 = 4 3 π 3 · e 2 m B Δ ν 2 = 4 π 3 · e 2 m B .
T = sin 2 ρ L
ρ = α 0 4 π ( 1 ν + ν s 1 ν ν s ) = α 0 4 π ( 2 ν s ν 2 ν s 2 ) ,
ν = ( ν s 2 + α 0 L π 3 / 2 | ν s | ) 1 / 2
δ ν 1 / 2 = ( ν s 2 + 2 α 0 L π 3 / 2 | ν s | ) 1 / 2 ( ν s 2 + 2 α 0 L 3 π 3 / 2 | ν s | ) 1 / 2
ν = ( α 0 L π 3 / 2 | ν s | ) 1 / 2
δ ν 1 / 2 0.6 ν .
χ x x = ½ ( χ + + + χ ) ,
χ y y = ½ cos 2 θ ( χ + + + χ ) + sin 2 θ χ 00 ,
χ x y = i 2 cos θ ( χ + + χ ) ,
χ y χ = i 2 cos θ ( χ + + χ ) ,
T = sin 2 ρ L [ 1 + ( β ρ tan θ ) 2 ] 1 / 2 1 + ( β ρ tan θ ) 2
β = ω 4 c Re ( χ + + + χ 2 χ 00 ) ,
β = α 0 [ W Im ( ν ν p ) + W Im ( ν + ν p ) W Im ( ν ν s ) W Im ( ν + ν s ) ] ,
β = α 0 8 π ( 1 ν ν p + 1 ν + ν p 1 ν ν s 1 ν + ν s ) .
θ tan 1 ( ρ / β ) ,
θ tan 1 ( 8 ν 3 ν s ) ,

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