Abstract

The resolution of a practical Faraday effect device is limited by birefringence. The case where both Faraday effect and birefringence are small is treated. Means for obtaining a high degree of linearity between Faraday rotation and applied magnetic field are investigated. With a method requiring two nearly identical sensors, a very significant over-all improvement is achieved. A second method of compensation, which acts on the polarization of the incoming light, gives an improvement for low fields only. A slight mismatch between the two sensors may be almost completely offset by superimposing the first and second compensation methods.

© 1972 Optical Society of America

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References

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  1. F. Pockels, Lehrbuch der Kristalloptik (Teubner, Berlin, 1906), p. 307.
  2. R. C. Jones, J. Opt. Soc. Am. 31, 500 (1941).
    [CrossRef]
  3. S. Chandrasekhar, Proc. Ind. Acad. Sci. 37, 468 (1953).
  4. W. J. Tabor, F. S. Chen, J. Appl. Phys. 40, 2760 (1969).
    [CrossRef]
  5. W. J. Tabor, A. W. Anderson, L. G. Van Uitert, J. Appl. Phys. 41, 3018 (1970).
    [CrossRef]
  6. A. A. Jaecklin, M. Lietz, J. Appl. Math. Phys. (ZAMP) 20, 565 (1969).
  7. N. F. Borrelli, J. Chem. Phys. 41, 3289 (1964).
    [CrossRef]
  8. C. C. Robinson, Appl. Opt. 3, 1163 (1964).
    [CrossRef]
  9. A. A. Jaecklin, Laser Focus No.6, 35 (1970).
  10. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 30.
  11. C. J. Peters, Proc. IEEE 53, 455 (1965).
    [CrossRef]

1970 (1)

W. J. Tabor, A. W. Anderson, L. G. Van Uitert, J. Appl. Phys. 41, 3018 (1970).
[CrossRef]

1969 (2)

A. A. Jaecklin, M. Lietz, J. Appl. Math. Phys. (ZAMP) 20, 565 (1969).

W. J. Tabor, F. S. Chen, J. Appl. Phys. 40, 2760 (1969).
[CrossRef]

1965 (1)

C. J. Peters, Proc. IEEE 53, 455 (1965).
[CrossRef]

1964 (2)

N. F. Borrelli, J. Chem. Phys. 41, 3289 (1964).
[CrossRef]

C. C. Robinson, Appl. Opt. 3, 1163 (1964).
[CrossRef]

1953 (1)

S. Chandrasekhar, Proc. Ind. Acad. Sci. 37, 468 (1953).

1941 (1)

Anderson, A. W.

W. J. Tabor, A. W. Anderson, L. G. Van Uitert, J. Appl. Phys. 41, 3018 (1970).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 30.

Borrelli, N. F.

N. F. Borrelli, J. Chem. Phys. 41, 3289 (1964).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Proc. Ind. Acad. Sci. 37, 468 (1953).

Chen, F. S.

W. J. Tabor, F. S. Chen, J. Appl. Phys. 40, 2760 (1969).
[CrossRef]

Jaecklin, A. A.

A. A. Jaecklin, M. Lietz, J. Appl. Math. Phys. (ZAMP) 20, 565 (1969).

A. A. Jaecklin, Laser Focus No.6, 35 (1970).

Jones, R. C.

Lietz, M.

A. A. Jaecklin, M. Lietz, J. Appl. Math. Phys. (ZAMP) 20, 565 (1969).

Peters, C. J.

C. J. Peters, Proc. IEEE 53, 455 (1965).
[CrossRef]

Pockels, F.

F. Pockels, Lehrbuch der Kristalloptik (Teubner, Berlin, 1906), p. 307.

Robinson, C. C.

Tabor, W. J.

W. J. Tabor, A. W. Anderson, L. G. Van Uitert, J. Appl. Phys. 41, 3018 (1970).
[CrossRef]

W. J. Tabor, F. S. Chen, J. Appl. Phys. 40, 2760 (1969).
[CrossRef]

Van Uitert, L. G.

W. J. Tabor, A. W. Anderson, L. G. Van Uitert, J. Appl. Phys. 41, 3018 (1970).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 30.

Appl. Opt. (1)

J. Appl. Math. Phys. (ZAMP) (1)

A. A. Jaecklin, M. Lietz, J. Appl. Math. Phys. (ZAMP) 20, 565 (1969).

J. Appl. Phys. (2)

W. J. Tabor, F. S. Chen, J. Appl. Phys. 40, 2760 (1969).
[CrossRef]

W. J. Tabor, A. W. Anderson, L. G. Van Uitert, J. Appl. Phys. 41, 3018 (1970).
[CrossRef]

J. Chem. Phys. (1)

N. F. Borrelli, J. Chem. Phys. 41, 3289 (1964).
[CrossRef]

J. Opt. Soc. Am. (1)

Proc. IEEE (1)

C. J. Peters, Proc. IEEE 53, 455 (1965).
[CrossRef]

Proc. Ind. Acad. Sci. (1)

S. Chandrasekhar, Proc. Ind. Acad. Sci. 37, 468 (1953).

Other (3)

A. A. Jaecklin, Laser Focus No.6, 35 (1970).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 30.

F. Pockels, Lehrbuch der Kristalloptik (Teubner, Berlin, 1906), p. 307.

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Figures (6)

Fig. 1
Fig. 1

Experimental setup. Analyzer setting: 35.5° for Iυ, 101.4° for Iy.

Fig. 2
Fig. 2

Detection angle ψ vs normalized applied field κ. Solid line: incident light linearly polarized with polarization parallel to axis of birefringence. Dashed line: optimum polarization adjustment of incident light. Dashdotted line: ideal case (ψ = ϕκ). Note that the initial slope of the dashed line coincides with the ideal case.

Fig. 3
Fig. 3

Calculated relative error of detection angle ψ for twofold and eightfold compensation. The incident light is linearly polarized, with polarization parallel to axis of birefringence.

Fig. 4
Fig. 4

Locus in uncompensated glass slab with both coordinate systems (Iυ;Iy) and (V;Y), and ψ as defined in Eq. (9). (a) Experiment, (b) theory.

Fig. 5
Fig. 5

Locus for ten passes with optimum adjustment of the polarization of the incoming light (α = −45°, δ = 67°). (a) Experiment, (b) theory.

Fig. 6
Fig. 6

Locus for ten passes with two slabs compensating each other, (a) Polarization of incoming light not adjusted, (b) polarization adjusted (α = −45°, δ = 0°).

Equations (7)

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( E x 0 ; E y 0 ) = ( cos α ; e i δ sin α ) e i ω t .
k + = 2 π n / λ ; k = ( π / λ n ) ( 2 + ¯ 2 ) 1 2 ,
I y = 1 2 | E y | 2 and I υ = 1 2 | ( E 2 + E y ) / 2 | 2 ,
V = 4 I υ 1 Y = 4 I y 1.
ϕ = ( 2 π / λ ) z Δ n , ν = / ¯ = V 0 λ H / π Δ n .
d ψ / d ν = ϕ + c ν + O ( ν 2 ) ,
α = ± 45 ° t g δ = ( ϕ cos ϕ sin ϕ ) / ( 1 cos ϕ ϕ sin ϕ ) ,

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