Abstract

A new method of using a Mach-Zehnder interferometer formed by single-mode optical fibers to stabilize the frequency of a helium–neon laser has been studied. Preliminary experimental result of 5000-Hz linewidth within the time scale of 1 s is presented.

© 1989 Optical Society of America

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References

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  1. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munely, H. Ward, “Laser Phase and frequency Stabilization Using an Optical Resonator,” Appl. Phys. B 31, 97–105 (1983).
    [CrossRef]
  2. L. D. Landau, E. M. Lifshitz, Statistical Physics, 3rd Edition, Part 1, (Pergamon, New York, 1980), part. 1.
  3. T. Baer, F. V. Kowalski, J. L. Hall, “Frequency Stabilization of a 0.633-μm He–Ne Longitudinal Zeeman Laser,” Appl. Opt. 19, 3173–3177 (1980).
    [CrossRef] [PubMed]
  4. M. A. Zumberge, “Frequency Stability of a Zeeman-Stabilized Laser,” Appl. Opt. 24, 1902–1904 (1985).
    [CrossRef] [PubMed]
  5. J. Hough, D. Hils, M. D. Rayman, L-S. Ma, L. Hollberg, J. L. Hall, “Dye-Laser Frequency Stabilization Using Optical Resonators,” Appl. Phys. B 33, 179–185 (1984).
    [CrossRef]
  6. J. Kauppinen, “A Simple Method for Single-Frequency Operation and Stabilization of a He–Ne Laser,” Appl. Phys. B 26, 193–195 (1981).
    [CrossRef]

1985 (1)

1984 (1)

J. Hough, D. Hils, M. D. Rayman, L-S. Ma, L. Hollberg, J. L. Hall, “Dye-Laser Frequency Stabilization Using Optical Resonators,” Appl. Phys. B 33, 179–185 (1984).
[CrossRef]

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munely, H. Ward, “Laser Phase and frequency Stabilization Using an Optical Resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

1981 (1)

J. Kauppinen, “A Simple Method for Single-Frequency Operation and Stabilization of a He–Ne Laser,” Appl. Phys. B 26, 193–195 (1981).
[CrossRef]

1980 (1)

Baer, T.

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munely, H. Ward, “Laser Phase and frequency Stabilization Using an Optical Resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munely, H. Ward, “Laser Phase and frequency Stabilization Using an Optical Resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Hall, J. L.

J. Hough, D. Hils, M. D. Rayman, L-S. Ma, L. Hollberg, J. L. Hall, “Dye-Laser Frequency Stabilization Using Optical Resonators,” Appl. Phys. B 33, 179–185 (1984).
[CrossRef]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munely, H. Ward, “Laser Phase and frequency Stabilization Using an Optical Resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

T. Baer, F. V. Kowalski, J. L. Hall, “Frequency Stabilization of a 0.633-μm He–Ne Longitudinal Zeeman Laser,” Appl. Opt. 19, 3173–3177 (1980).
[CrossRef] [PubMed]

Hils, D.

J. Hough, D. Hils, M. D. Rayman, L-S. Ma, L. Hollberg, J. L. Hall, “Dye-Laser Frequency Stabilization Using Optical Resonators,” Appl. Phys. B 33, 179–185 (1984).
[CrossRef]

Hollberg, L.

J. Hough, D. Hils, M. D. Rayman, L-S. Ma, L. Hollberg, J. L. Hall, “Dye-Laser Frequency Stabilization Using Optical Resonators,” Appl. Phys. B 33, 179–185 (1984).
[CrossRef]

Hough, J.

J. Hough, D. Hils, M. D. Rayman, L-S. Ma, L. Hollberg, J. L. Hall, “Dye-Laser Frequency Stabilization Using Optical Resonators,” Appl. Phys. B 33, 179–185 (1984).
[CrossRef]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munely, H. Ward, “Laser Phase and frequency Stabilization Using an Optical Resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Kauppinen, J.

J. Kauppinen, “A Simple Method for Single-Frequency Operation and Stabilization of a He–Ne Laser,” Appl. Phys. B 26, 193–195 (1981).
[CrossRef]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munely, H. Ward, “Laser Phase and frequency Stabilization Using an Optical Resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

T. Baer, F. V. Kowalski, J. L. Hall, “Frequency Stabilization of a 0.633-μm He–Ne Longitudinal Zeeman Laser,” Appl. Opt. 19, 3173–3177 (1980).
[CrossRef] [PubMed]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Statistical Physics, 3rd Edition, Part 1, (Pergamon, New York, 1980), part. 1.

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Statistical Physics, 3rd Edition, Part 1, (Pergamon, New York, 1980), part. 1.

Ma, L-S.

J. Hough, D. Hils, M. D. Rayman, L-S. Ma, L. Hollberg, J. L. Hall, “Dye-Laser Frequency Stabilization Using Optical Resonators,” Appl. Phys. B 33, 179–185 (1984).
[CrossRef]

Munely, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munely, H. Ward, “Laser Phase and frequency Stabilization Using an Optical Resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Rayman, M. D.

J. Hough, D. Hils, M. D. Rayman, L-S. Ma, L. Hollberg, J. L. Hall, “Dye-Laser Frequency Stabilization Using Optical Resonators,” Appl. Phys. B 33, 179–185 (1984).
[CrossRef]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munely, H. Ward, “Laser Phase and frequency Stabilization Using an Optical Resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Zumberge, M. A.

Appl. Opt. (2)

Appl. Phys. B (3)

J. Hough, D. Hils, M. D. Rayman, L-S. Ma, L. Hollberg, J. L. Hall, “Dye-Laser Frequency Stabilization Using Optical Resonators,” Appl. Phys. B 33, 179–185 (1984).
[CrossRef]

J. Kauppinen, “A Simple Method for Single-Frequency Operation and Stabilization of a He–Ne Laser,” Appl. Phys. B 26, 193–195 (1981).
[CrossRef]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munely, H. Ward, “Laser Phase and frequency Stabilization Using an Optical Resonator,” Appl. Phys. B 31, 97–105 (1983).
[CrossRef]

Other (1)

L. D. Landau, E. M. Lifshitz, Statistical Physics, 3rd Edition, Part 1, (Pergamon, New York, 1980), part. 1.

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Figures (5)

Fig. 1
Fig. 1

Scheme of the optical fiber used as optical delay line to stabilize the frequency of laser. In the drawing, R.S. means reference signal; P.S. means phase sensitive detector; B.S. means beam splitter.

Fig. 2
Fig. 2

The experimental setup of the fiber optics stabilizer. All the parts of the optical frequency-phase convertor are housed in a temperature controlled cylinder which is sealed in a vacuum tank. In the drawing, PBS means polarized beam splitter; H.V. AMP means high voltage amplifier.

Fig. 3
Fig. 3

Schematic illustration of the mechanical setup of optical fiber stabilizer.

Fig. 4
Fig. 4

The control diagram of the testing fiber interferometer.

Fig. 5
Fig. 5

Power spectrum of the fluctuation of laser output taken when the fiber stabilizer is working and the output of the testing fiber interferometer is locked on the dark fringe. The high peak in the photo is the calibration signal.

Equations (26)

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E 1 = E 0 sin ( Ω t + Ω t 0 ) ,
E 2 = E 0 sin ( Ω t + Γ sin ω t ) ,
t 0 = ( L 1 L 2 ) / c ,
E = E 1 + E 2 .
I = | E | 2 = E 0 2 { 2 + Γ / 2 Γ / 2 cos 2 ω t + 2 cos [ ( Ω Ω ) t Ω t 0 ] + Γ cos [ ( Ω Ω ) t + ω t Ω t 0 ] Γ cos [ ( Ω Ω ) t ω t Ω t 0 ] } .
P = E 0 2 Γ sin [ ( Ω Ω ) t 2 π L 1 L 2 λ ] ,
sin [ ( Ω Ω ) t 2 π L 1 L 2 λ ] = 0 .
( Ω Ω ) t 2 π L 1 L 2 λ = n π ,
Ω Ω = 0 ,
2 L 1 L 2 λ = n π .
L 1 L 2 = L 1 o L 2 o + ( L 1 o L 2 o ) B i sin ( m i t ) ,
( Ω Ω ) t λ = 2 π ( L 1 o L 2 o ) B sin ( m t ) ,
2 L 1 L 2 λ = n π .
δ f / f = B δ ( L 1 L 2 ) L 1 L 2 .
d L = n l T d T + l n T d T .
δ f / f = B = 1 n 1 l 1 n 2 l 2 ( l 1 n 1 T l 2 n 2 T + n 1 l 1 T n 2 l 2 T ) d T ,
1 l l T 5 × 10 7 K 1 , n T 10 5 K 1 .
δ f / f 1 n n T d T .
( δ f / f ) ω = 1 L 1 L 2 ћ c λ π η p ,
( δ ρ ¯ 2 ) = ρ 2 γ k T l A ,
γ = 1 V ( V p ) T
( δ ρ ) ω 2 = 2 ρ 2 β γ k T l A 1 ω 2 + β 2 ,
( δ f / f ) ω = 2 l k T γ υ A ( ω 2 + υ 2 / l 2 ) .
( δ f / f ) ω = 5 × 10 14 / Hz .
δ f / f = d L a / L a ,
ϕ = 2 π d L b λ ( 1 d L a × L b d L b × L a ) .

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