Abstract

We observed a periodic intensity-noise variation in the output of a Mach–Zehnder interferometer as we changed the arm-length difference in the range of several millimeters. We found that the period of the variation coincided with that expected for the longitudinal-mode separation of the semiconductor laser. The origin of the huge excess noise of a bright fringe (approximately 30  dB above the shot-noise level) was the longitudinal-mode-partition noise that was due to the selective destructive interference of side modes.

© 1997 Optical Society of America

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References

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  1. D. Rugar, H. J. Mamin, R. Erlandsson, J. E. Stern, and B. D. Terris, Rev. Sci. Instrum. 59, 2337 (1988).
    [Crossref]
  2. D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, and A. Rüdinger, Phys. Rev. D 38, 423 (1988).
    [Crossref]
  3. J. A. Armstrong, J. Opt. Soc. Am. 56, 1024 (1966).
  4. Y. Yamamoto, T. Mukai, and S. Saito, Electron. Lett. 17, 31 (1981).
    [Crossref]
  5. S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 46, 2757 (1992).
    [Crossref] [PubMed]
  6. F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J.-Ph. Poizat, J.-F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
    [Crossref] [PubMed]
  7. S. Inoue, G. Björk, and Y. Yamamoto, Proc. SPIE 2378, 99 (1995).
    [Crossref]
  8. S. Inoue, Y. Yamamoto, and G. Björk, in International Quantum Electronics Conference, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 210.
  9. S. Inoue, S. Machida, Y. Yamamoto, and H. Ohzu, Phys. Rev. A 48, 2230 (1993).
    [Crossref] [PubMed]
  10. H. Wang, M. J. Freeman, and D. G. Steel, Phys. Rev. Lett. 71, 3951 (1993).
    [Crossref] [PubMed]
  11. M. J. Freeman, H. Wang, D. G. Steel, R. Cragi, and D. R. Scifres, Opt. Lett. 18, 2141 (1993).
    [Crossref]

1995 (2)

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J.-Ph. Poizat, J.-F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[Crossref] [PubMed]

S. Inoue, G. Björk, and Y. Yamamoto, Proc. SPIE 2378, 99 (1995).
[Crossref]

1993 (3)

S. Inoue, S. Machida, Y. Yamamoto, and H. Ohzu, Phys. Rev. A 48, 2230 (1993).
[Crossref] [PubMed]

H. Wang, M. J. Freeman, and D. G. Steel, Phys. Rev. Lett. 71, 3951 (1993).
[Crossref] [PubMed]

M. J. Freeman, H. Wang, D. G. Steel, R. Cragi, and D. R. Scifres, Opt. Lett. 18, 2141 (1993).
[Crossref]

1992 (1)

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 46, 2757 (1992).
[Crossref] [PubMed]

1988 (2)

D. Rugar, H. J. Mamin, R. Erlandsson, J. E. Stern, and B. D. Terris, Rev. Sci. Instrum. 59, 2337 (1988).
[Crossref]

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, and A. Rüdinger, Phys. Rev. D 38, 423 (1988).
[Crossref]

1981 (1)

Y. Yamamoto, T. Mukai, and S. Saito, Electron. Lett. 17, 31 (1981).
[Crossref]

1966 (1)

Armstrong, J. A.

Björk, G.

S. Inoue, G. Björk, and Y. Yamamoto, Proc. SPIE 2378, 99 (1995).
[Crossref]

S. Inoue, Y. Yamamoto, and G. Björk, in International Quantum Electronics Conference, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 210.

Bramati, A.

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J.-Ph. Poizat, J.-F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[Crossref] [PubMed]

Cragi, R.

Erlandsson, R.

D. Rugar, H. J. Mamin, R. Erlandsson, J. E. Stern, and B. D. Terris, Rev. Sci. Instrum. 59, 2337 (1988).
[Crossref]

Freeman, M. J.

Giacobino, E.

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J.-Ph. Poizat, J.-F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[Crossref] [PubMed]

Grangier, P.

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J.-Ph. Poizat, J.-F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[Crossref] [PubMed]

Inoue, S.

S. Inoue, G. Björk, and Y. Yamamoto, Proc. SPIE 2378, 99 (1995).
[Crossref]

S. Inoue, S. Machida, Y. Yamamoto, and H. Ohzu, Phys. Rev. A 48, 2230 (1993).
[Crossref] [PubMed]

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 46, 2757 (1992).
[Crossref] [PubMed]

S. Inoue, Y. Yamamoto, and G. Björk, in International Quantum Electronics Conference, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 210.

Machida, S.

S. Inoue, S. Machida, Y. Yamamoto, and H. Ohzu, Phys. Rev. A 48, 2230 (1993).
[Crossref] [PubMed]

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 46, 2757 (1992).
[Crossref] [PubMed]

Maischberger, K.

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, and A. Rüdinger, Phys. Rev. D 38, 423 (1988).
[Crossref]

Mamin, H. J.

D. Rugar, H. J. Mamin, R. Erlandsson, J. E. Stern, and B. D. Terris, Rev. Sci. Instrum. 59, 2337 (1988).
[Crossref]

Marin, F.

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J.-Ph. Poizat, J.-F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[Crossref] [PubMed]

Mukai, T.

Y. Yamamoto, T. Mukai, and S. Saito, Electron. Lett. 17, 31 (1981).
[Crossref]

Ohzu, H.

S. Inoue, S. Machida, Y. Yamamoto, and H. Ohzu, Phys. Rev. A 48, 2230 (1993).
[Crossref] [PubMed]

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 46, 2757 (1992).
[Crossref] [PubMed]

Poizat, J.-Ph.

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J.-Ph. Poizat, J.-F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[Crossref] [PubMed]

Roch, J.-F.

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J.-Ph. Poizat, J.-F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[Crossref] [PubMed]

Rüdinger, A.

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, and A. Rüdinger, Phys. Rev. D 38, 423 (1988).
[Crossref]

Rugar, D.

D. Rugar, H. J. Mamin, R. Erlandsson, J. E. Stern, and B. D. Terris, Rev. Sci. Instrum. 59, 2337 (1988).
[Crossref]

Saito, S.

Y. Yamamoto, T. Mukai, and S. Saito, Electron. Lett. 17, 31 (1981).
[Crossref]

Schilling, R.

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, and A. Rüdinger, Phys. Rev. D 38, 423 (1988).
[Crossref]

Schnupp, L.

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, and A. Rüdinger, Phys. Rev. D 38, 423 (1988).
[Crossref]

Scifres, D. R.

Shoemaker, D.

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, and A. Rüdinger, Phys. Rev. D 38, 423 (1988).
[Crossref]

Steel, D. G.

Stern, J. E.

D. Rugar, H. J. Mamin, R. Erlandsson, J. E. Stern, and B. D. Terris, Rev. Sci. Instrum. 59, 2337 (1988).
[Crossref]

Terris, B. D.

D. Rugar, H. J. Mamin, R. Erlandsson, J. E. Stern, and B. D. Terris, Rev. Sci. Instrum. 59, 2337 (1988).
[Crossref]

Wang, H.

Winkler, W.

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, and A. Rüdinger, Phys. Rev. D 38, 423 (1988).
[Crossref]

Yamamoto, Y.

S. Inoue, G. Björk, and Y. Yamamoto, Proc. SPIE 2378, 99 (1995).
[Crossref]

S. Inoue, S. Machida, Y. Yamamoto, and H. Ohzu, Phys. Rev. A 48, 2230 (1993).
[Crossref] [PubMed]

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 46, 2757 (1992).
[Crossref] [PubMed]

Y. Yamamoto, T. Mukai, and S. Saito, Electron. Lett. 17, 31 (1981).
[Crossref]

S. Inoue, Y. Yamamoto, and G. Björk, in International Quantum Electronics Conference, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 210.

Zhang, T.-C.

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J.-Ph. Poizat, J.-F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[Crossref] [PubMed]

Electron. Lett. (1)

Y. Yamamoto, T. Mukai, and S. Saito, Electron. Lett. 17, 31 (1981).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

Phys. Rev. A (2)

S. Inoue, H. Ohzu, S. Machida, and Y. Yamamoto, Phys. Rev. A 46, 2757 (1992).
[Crossref] [PubMed]

S. Inoue, S. Machida, Y. Yamamoto, and H. Ohzu, Phys. Rev. A 48, 2230 (1993).
[Crossref] [PubMed]

Phys. Rev. D (1)

D. Shoemaker, R. Schilling, L. Schnupp, W. Winkler, K. Maischberger, and A. Rüdinger, Phys. Rev. D 38, 423 (1988).
[Crossref]

Phys. Rev. Lett. (2)

H. Wang, M. J. Freeman, and D. G. Steel, Phys. Rev. Lett. 71, 3951 (1993).
[Crossref] [PubMed]

F. Marin, A. Bramati, E. Giacobino, T.-C. Zhang, J.-Ph. Poizat, J.-F. Roch, and P. Grangier, Phys. Rev. Lett. 75, 4606 (1995).
[Crossref] [PubMed]

Proc. SPIE (1)

S. Inoue, G. Björk, and Y. Yamamoto, Proc. SPIE 2378, 99 (1995).
[Crossref]

Rev. Sci. Instrum. (1)

D. Rugar, H. J. Mamin, R. Erlandsson, J. E. Stern, and B. D. Terris, Rev. Sci. Instrum. 59, 2337 (1988).
[Crossref]

Other (1)

S. Inoue, Y. Yamamoto, and G. Björk, in International Quantum Electronics Conference, OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 210.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup for measuring the intensity noise of the interferometer output while changing the arm-length difference. BS’s, beam splitters; PBS, polarizing beam splitter; PZT, piezoelectric transducer.

Fig. 2
Fig. 2

(a) Intensity-noise variation in the output of the interferometer for an initial arm-length difference of 2.44  mm as one arm-length is changed by roughly one wavelength. The measurement frequency was 28  MHz. (b), (c) Schematic spectra of a bright fringe and a dark fringe for the arm-length differences (b) Δl=nc/Δf and (c) n+1/2c/Δf.

Fig. 3
Fig. 3

Intensity-noise variation of a bright fringe as a function of the arm-length difference. The measurement frequency was 28  MHz. The horizontal line shows the shot-noise-level line corresponding to the photocurrent of a bright fringe.

Fig. 4
Fig. 4

Intensity-noise variation in the output of the interferometer for arm-length differences Δl=0 and Δl=6  mm as one arm-length is changed by roughly one wavelength. The measurement frequency was 28  MHz.

Equations (2)

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ω0-ω1Δlc=2nπ,
ω0-ω1Δlc=2n+1π.

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