Abstract

The design of a Faraday isolator that uses a short glass rotator rod and produces highly uniform rotation across its clear aperture is presented. The rotator rod is 19.5 mm long, and at a wavelength of 633 nm the rotation angle is 45 deg and the isolation ratio is >45 dB.

© 1986 Optical Society of America

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References

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  1. S. D. Jacobs, K. J. Teegarden, R. K. Ahrenkeil, Appl. Opt. 13, 2313 (1974); H. C. Meyer, G. A. Tanton, S. S. Mitra, J. D. Stettler, Appl. Phys. 13, 307 (1977); F. Keilmann, R. L. Sheffield, M. S. Feld, A. Javan, Appl. Phys. Lett. 23, 612 (1973).
    [CrossRef] [PubMed]
  2. L. J. Aplet, J. W. Carson, Appl. Opt. 3, 544 (1963); L. G. DeShazer, E. A. Maunders, Rev. Sci. Instrum. 38, 248 (1967).
    [CrossRef]
  3. C. F. Padula, C. G. Young, IEEE J. Quantum Electron. QE-3, 483, (1967); O.C. Barr, J. M. McMahon, J. B. Trenholme, IEEE J. Quantum Electron. QE-9, 1124 (1973); P. J. Brannon, F. R. Franklin, G. C. Hauser, J. W. Lavasek, E. D. Jones, Appl. Opt. 13, 1555 (1974).
    [CrossRef] [PubMed]
  4. N. F. Borrelli, J. Chem. Phys. 44, 3289 (1964).
    [CrossRef]
  5. J. J. Becker, J. Appl. Phys. 41, 1055 (1970).
    [CrossRef]
  6. H. Iwamura, S. Hayashi, H. Iwasaki, Opt. Quantum Electron. 10, 398 (1978); F. J. Sansalone, Appl. Opt. 10, 2329 (1971).
    [CrossRef] [PubMed]
  7. K. P. Birch, Opt. Commun. 43, 79 (1982).
    [CrossRef]
  8. K. Shiraishi, F. Tajima, S. Kawakami, Opt. Lett. 11, 82 (1986).
    [CrossRef] [PubMed]
  9. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), Sec. 3.3.
  10. Electron Energy Company, P.O. Box 458, Landisville, Pa. 17538.
  11. Kigre, Inc., 5333 Secor Road, Toledo, Ohio 43623.
  12. Karl Lambrecht Company, 4202 North Lincoln Avenue, Chicago, Ill. 60618.

1986 (1)

1982 (1)

K. P. Birch, Opt. Commun. 43, 79 (1982).
[CrossRef]

1978 (1)

H. Iwamura, S. Hayashi, H. Iwasaki, Opt. Quantum Electron. 10, 398 (1978); F. J. Sansalone, Appl. Opt. 10, 2329 (1971).
[CrossRef] [PubMed]

1974 (1)

1970 (1)

J. J. Becker, J. Appl. Phys. 41, 1055 (1970).
[CrossRef]

1967 (1)

C. F. Padula, C. G. Young, IEEE J. Quantum Electron. QE-3, 483, (1967); O.C. Barr, J. M. McMahon, J. B. Trenholme, IEEE J. Quantum Electron. QE-9, 1124 (1973); P. J. Brannon, F. R. Franklin, G. C. Hauser, J. W. Lavasek, E. D. Jones, Appl. Opt. 13, 1555 (1974).
[CrossRef] [PubMed]

1964 (1)

N. F. Borrelli, J. Chem. Phys. 44, 3289 (1964).
[CrossRef]

1963 (1)

Ahrenkeil, R. K.

Aplet, L. J.

Becker, J. J.

J. J. Becker, J. Appl. Phys. 41, 1055 (1970).
[CrossRef]

Birch, K. P.

K. P. Birch, Opt. Commun. 43, 79 (1982).
[CrossRef]

Borrelli, N. F.

N. F. Borrelli, J. Chem. Phys. 44, 3289 (1964).
[CrossRef]

Carson, J. W.

Hayashi, S.

H. Iwamura, S. Hayashi, H. Iwasaki, Opt. Quantum Electron. 10, 398 (1978); F. J. Sansalone, Appl. Opt. 10, 2329 (1971).
[CrossRef] [PubMed]

Iwamura, H.

H. Iwamura, S. Hayashi, H. Iwasaki, Opt. Quantum Electron. 10, 398 (1978); F. J. Sansalone, Appl. Opt. 10, 2329 (1971).
[CrossRef] [PubMed]

Iwasaki, H.

H. Iwamura, S. Hayashi, H. Iwasaki, Opt. Quantum Electron. 10, 398 (1978); F. J. Sansalone, Appl. Opt. 10, 2329 (1971).
[CrossRef] [PubMed]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), Sec. 3.3.

Jacobs, S. D.

Kawakami, S.

Padula, C. F.

C. F. Padula, C. G. Young, IEEE J. Quantum Electron. QE-3, 483, (1967); O.C. Barr, J. M. McMahon, J. B. Trenholme, IEEE J. Quantum Electron. QE-9, 1124 (1973); P. J. Brannon, F. R. Franklin, G. C. Hauser, J. W. Lavasek, E. D. Jones, Appl. Opt. 13, 1555 (1974).
[CrossRef] [PubMed]

Shiraishi, K.

Tajima, F.

Teegarden, K. J.

Young, C. G.

C. F. Padula, C. G. Young, IEEE J. Quantum Electron. QE-3, 483, (1967); O.C. Barr, J. M. McMahon, J. B. Trenholme, IEEE J. Quantum Electron. QE-9, 1124 (1973); P. J. Brannon, F. R. Franklin, G. C. Hauser, J. W. Lavasek, E. D. Jones, Appl. Opt. 13, 1555 (1974).
[CrossRef] [PubMed]

Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

C. F. Padula, C. G. Young, IEEE J. Quantum Electron. QE-3, 483, (1967); O.C. Barr, J. M. McMahon, J. B. Trenholme, IEEE J. Quantum Electron. QE-9, 1124 (1973); P. J. Brannon, F. R. Franklin, G. C. Hauser, J. W. Lavasek, E. D. Jones, Appl. Opt. 13, 1555 (1974).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

J. J. Becker, J. Appl. Phys. 41, 1055 (1970).
[CrossRef]

J. Chem. Phys. (1)

N. F. Borrelli, J. Chem. Phys. 44, 3289 (1964).
[CrossRef]

Opt. Commun. (1)

K. P. Birch, Opt. Commun. 43, 79 (1982).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

H. Iwamura, S. Hayashi, H. Iwasaki, Opt. Quantum Electron. 10, 398 (1978); F. J. Sansalone, Appl. Opt. 10, 2329 (1971).
[CrossRef] [PubMed]

Other (4)

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), Sec. 3.3.

Electron Energy Company, P.O. Box 458, Landisville, Pa. 17538.

Kigre, Inc., 5333 Secor Road, Toledo, Ohio 43623.

Karl Lambrecht Company, 4202 North Lincoln Avenue, Chicago, Ill. 60618.

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Figures (4)

Fig. 1
Fig. 1

(a) Cross-sectional view of the permanent-magnet Faraday isolator. The rotator rod of length Lr is located at the center of a hole of diameter 2a in a magnetic stack. The stack is composed of a central magnet of length L and two auxiliary magnets of length L′ whose magnetization is anti-parallel to that of the central magnet. The coordinate system is used in the calculation presented in the text. (b) The axial component of the magnetic intensity produced by the magnetic stack as a function of position along the symmetry axis. The dashed curve shows the field in the absence of the two auxiliary magnets.

Fig. 2
Fig. 2

Integrated on-axis magnetic intensity (proportional to the rotation) (a) as a function of the length L′ of the auxiliary magnet for b = 16.5 mm and (b) as a function of the radius b of the magnets for L′ = 7.6 mm, for various values of the rod length Lr, which is held equal to the length L of the central magnet. In both cases, the radius of the hole is a = 2.8 mm and the residual inductance is 104 G.

Fig. 3
Fig. 3

Integrated on-axis magnetic intensity and fractional difference in the rotation angle between the axis and at a distance of 2.5 mm from the axis as a function of the length L of the central magnet. The length of the rotator rod is held fixed at 19.5 mm, and a = 2.8 mm, b = 16.5 mm, L′ = 7.6 mm, and the residual inductance is equal to 104 G.

Fig. 4
Fig. 4

Measured rotation angle as a function of the displacement of the rotator rod from its central position for various wavelengths given in the legend. At any position, the rotation decreases with increasing wavelength. The solid lines are theoretical curves calculated using the tabulated value of the Verdet constant.

Equations (7)

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Θ = V H z d z ,
2 Φ = 4 π · M .
Φ ( r , θ ) = l = 0 [ A l r l + B l r - ( l + 1 ) ] P l ( cos θ )
Φ ( r , θ ) = 0 R 0 2 π M r d r d ϕ ( r 2 + r 2 ) 1 / 2 = 2 π M [ ( r 2 + R 2 ) 1 / 2 - r ] ,
Φ ( r , θ ) = 2 π M [ R - r cos ( θ ) + R × l = 0 P 2 ( l + 1 ) ( cos θ ) ( 2 l ) ! ( - 1 ) l 2 2 l + 1 l ! ( l + 1 ) ! [ r R ] 2 ( l + 1 ) ] ,             r < R .
Φ ( r , θ ) = 2 π M r l = 0 P 2 l ( cos θ ) ( 2 l ) ! ( - 1 ) l 2 2 l + 1 l ! ( l + 1 ) ! [ R r ] 2 ( l + 1 ) ,             r > R .
Φ ( z , 0 ) = 2 π M [ 2 ( z 1 2 + a 2 ) 1 / 2 - 2 ( z 1 2 + b 2 ) 1 / 2 + 2 ( z 2 2 + a 2 ) 1 / 2 2 ( z 2 2 + b 2 ) 1 / 2 + ( z 3 2 + b 2 ) 1 / 2 - ( z 3 2 + a 2 ) 1 / 2 + ( z 4 2 + a 2 ) 1 / 2 - ( z 4 2 + b 2 ) 1 / 2 ] ,

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