Abstract

This paper gives both theoretical and experimental proof of elliptical polarization and nonorthogonality of Zeeman laser output. It verifies that the polarized modes of the output have 4–7° orthogonal error which is induced by anisotropy in the laser cavity. A new formula for calculation of this orthogonal error has been derived which also provides a way to measure the anisotropy of the laser cavity. We also discuss the influence of nonorthogonality on the spectrum of the laser.

© 1989 Optical Society of America

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References

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  1. M. A. Zumberge, “Frequency Stability of a Zeeman-Stabilized Laser,” Appl. Opt. 24, 1902–1904 (1985).
    [CrossRef] [PubMed]
  2. Y. Wu et al., “Coherent Optical Fiber System with Zeeman Lasers,” Electron. Lett. 23, 49–50 (1987).
    [CrossRef]
  3. Y. Wu et al., “Experiment on 1500nm Stabilized Zeeman Laser,” Electron. Lett. 23, 318–319 (1987).
  4. T. Kimura, “Coherent Optical Fiber Transmission,” IEEE/OSA J. Lightwave Technol. LT-5, 414–428 (1987).
    [CrossRef]
  5. G. W. Hopkins, Ed., Interferometry, Proc. Soc. Photo-Opt. Instrum. Eng.192 (1979), p. 17.
  6. M. Sargent, W. E. Lamb, “Theory of a Zeeman Laser II,” Phys. Rev. 164, 450–465 (1967).
    [CrossRef]
  7. W. J. Tomplinson, R. L. Fork, “Properties of Gaseous Optical Maser,” Phys. Rev. 164, 466–483 (1967).
    [CrossRef]
  8. M. A. Bouchiat, L. Pottier, “A High-Purity Circular Polarization Modulator: Application to Birefringence and Circular Dichroism Measurements on Multidielectric Mirrors,” Opt. Commun. 37, 229–233 (1981).
    [CrossRef]
  9. J. A. Kong, Theory of Electromagnetic Waves (Wiley, New York, 1975), Chap. 3.3c.

1987 (3)

Y. Wu et al., “Coherent Optical Fiber System with Zeeman Lasers,” Electron. Lett. 23, 49–50 (1987).
[CrossRef]

Y. Wu et al., “Experiment on 1500nm Stabilized Zeeman Laser,” Electron. Lett. 23, 318–319 (1987).

T. Kimura, “Coherent Optical Fiber Transmission,” IEEE/OSA J. Lightwave Technol. LT-5, 414–428 (1987).
[CrossRef]

1985 (1)

1981 (1)

M. A. Bouchiat, L. Pottier, “A High-Purity Circular Polarization Modulator: Application to Birefringence and Circular Dichroism Measurements on Multidielectric Mirrors,” Opt. Commun. 37, 229–233 (1981).
[CrossRef]

1967 (2)

M. Sargent, W. E. Lamb, “Theory of a Zeeman Laser II,” Phys. Rev. 164, 450–465 (1967).
[CrossRef]

W. J. Tomplinson, R. L. Fork, “Properties of Gaseous Optical Maser,” Phys. Rev. 164, 466–483 (1967).
[CrossRef]

Bouchiat, M. A.

M. A. Bouchiat, L. Pottier, “A High-Purity Circular Polarization Modulator: Application to Birefringence and Circular Dichroism Measurements on Multidielectric Mirrors,” Opt. Commun. 37, 229–233 (1981).
[CrossRef]

Fork, R. L.

W. J. Tomplinson, R. L. Fork, “Properties of Gaseous Optical Maser,” Phys. Rev. 164, 466–483 (1967).
[CrossRef]

Kimura, T.

T. Kimura, “Coherent Optical Fiber Transmission,” IEEE/OSA J. Lightwave Technol. LT-5, 414–428 (1987).
[CrossRef]

Kong, J. A.

J. A. Kong, Theory of Electromagnetic Waves (Wiley, New York, 1975), Chap. 3.3c.

Lamb, W. E.

M. Sargent, W. E. Lamb, “Theory of a Zeeman Laser II,” Phys. Rev. 164, 450–465 (1967).
[CrossRef]

Pottier, L.

M. A. Bouchiat, L. Pottier, “A High-Purity Circular Polarization Modulator: Application to Birefringence and Circular Dichroism Measurements on Multidielectric Mirrors,” Opt. Commun. 37, 229–233 (1981).
[CrossRef]

Sargent, M.

M. Sargent, W. E. Lamb, “Theory of a Zeeman Laser II,” Phys. Rev. 164, 450–465 (1967).
[CrossRef]

Tomplinson, W. J.

W. J. Tomplinson, R. L. Fork, “Properties of Gaseous Optical Maser,” Phys. Rev. 164, 466–483 (1967).
[CrossRef]

Wu, Y.

Y. Wu et al., “Coherent Optical Fiber System with Zeeman Lasers,” Electron. Lett. 23, 49–50 (1987).
[CrossRef]

Y. Wu et al., “Experiment on 1500nm Stabilized Zeeman Laser,” Electron. Lett. 23, 318–319 (1987).

Zumberge, M. A.

Appl. Opt. (1)

Electron. Lett. (2)

Y. Wu et al., “Coherent Optical Fiber System with Zeeman Lasers,” Electron. Lett. 23, 49–50 (1987).
[CrossRef]

Y. Wu et al., “Experiment on 1500nm Stabilized Zeeman Laser,” Electron. Lett. 23, 318–319 (1987).

IEEE/OSA J. Lightwave Technol. (1)

T. Kimura, “Coherent Optical Fiber Transmission,” IEEE/OSA J. Lightwave Technol. LT-5, 414–428 (1987).
[CrossRef]

Opt. Commun. (1)

M. A. Bouchiat, L. Pottier, “A High-Purity Circular Polarization Modulator: Application to Birefringence and Circular Dichroism Measurements on Multidielectric Mirrors,” Opt. Commun. 37, 229–233 (1981).
[CrossRef]

Phys. Rev. (2)

M. Sargent, W. E. Lamb, “Theory of a Zeeman Laser II,” Phys. Rev. 164, 450–465 (1967).
[CrossRef]

W. J. Tomplinson, R. L. Fork, “Properties of Gaseous Optical Maser,” Phys. Rev. 164, 466–483 (1967).
[CrossRef]

Other (2)

J. A. Kong, Theory of Electromagnetic Waves (Wiley, New York, 1975), Chap. 3.3c.

G. W. Hopkins, Ed., Interferometry, Proc. Soc. Photo-Opt. Instrum. Eng.192 (1979), p. 17.

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Figures (4)

Fig. 1
Fig. 1

Block diagram of the theoretical model.

Fig. 2
Fig. 2

Theoretical curves of the orthogonal errors.

Fig. 3
Fig. 3

Experimental setup for the measurement of orthogonal errors.

Fig. 4
Fig. 4

Curve of the spectrum halfwidth of the system as a function of orthogonal errors.

Tables (1)

Tables Icon

Table I Summary of the Measurements of Three Laser Tubes (Degree)

Equations (19)

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T 0 = [ exp ( i k d ) 0 0 exp ( i k d ) ] [ a 1 exp ( i b 1 ) 0 0 a 2 exp ( i b 2 ) ] × [ exp ( i k d ) 0 0 exp ( i k d ) ] [ a 3 exp ( i b 3 ) 0 0 a 4 exp ( i b 4 ) ] ,
T 1 = ( T 0 ) q = A [ 1 0 0 B exp ( i α ) ] ,
[ E i x E i y ] ± = 1 / 2 E i [ 1 ± i ] exp ( i ω ± t ) ,
[ E i x E i y ] laser ± = 1 / 2 A E i [ 1 ± i B exp ( i α ) ] exp ( i ω ± t ) .
T 2 = [ 0 0 0 i ] .
T 3 = [ cos ϑ sin ϑ sin ϑ cos ϑ ] [ 1 0 0 0 ] [ cos ϑ sin ϑ sin ϑ cos ϑ ] .
[ E o x E o y ] system ± = A E i / 2 exp ( i ω ± t ) × [ cos 2 ϑ ± B sin ϑ cos ϑ exp ( i α ) sin ϑ cos ϑ ± B sin 2 ϑ exp ( i α ) ] .
I ± = 1 / 2 ( a 1 a 2 ) 2 q exp ( 2 G ± q d ) I i × ( cos 2 ϑ + B 2 sin 2 ϑ ± B sin 2 ϑ cos α ) .
ϑ m = | ϑ m + | + | ϑ m | = tan 1 | 2 B cos α / ( 1 B 2 ) | .
E ( t ) = E + ( t ) + E ( t ) = E 0 + exp ( i ω + t ) + E 0 exp ( i ω t ) = ( E 0 + E 0 ) + 2 E 0 cos [ ( ω + ω ) t / 2 ] exp ( i ω + t ) .
W ( ω ) = ( π A / σ ) exp [ ( ω ω + ) 2 / 4 σ 2 ] + ( π B / σ ) exp [ ( ω ω + + ω + ω 2 2 σ ) 2 ] + ( π A / σ ) exp [ ( ω ω + ω + ω 2 2 σ ) 2 ] .
W 12 ( ω ) = ( π A / σ ) exp [ ( ω ω + ) 2 / 4 σ 2 ] + ( π B / σ ) exp [ ( ω ω + + ω + ω 2 2 σ ) 2 ] ,
W 12 ( x , x 0 ) = ( π A / σ ) exp ( x 2 ) { 1 + ( B / A ) exp [ ( x x 0 ) x 0 ] } ,
W 12 ( x , x 0 ) = ( π A / σ ) exp ( 1 ) .
x 0 2 x x 0 + I n { ( A / B ) [ exp ( x 2 1 ) 1 ] } = 0 .
x 0 = x x 2 I n { ( A / B ) [ exp ( x 2 1 ) 1 ] } .
x 2 I n { ( A / B ) [ exp ( x 2 1 ) 1 ] } .
Δ ω = ω + ω 2 σ I n { 1 / [ exp ( 1 ) B / A ] } .
Δ ω m = 2 σ I n { 1 / [ exp ( 1 ) B / A ] } ,

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