Abstract

Nondegenerate four-wave mixing in an optical fiber is shown to attenuate one quadrature of random sideband fluctuations created by external modulators. A theory of the nonlinear interaction that includes nonlinear dispersion fits the results. Analogous experiments on quantum noise inputs should prove successful.

© 1985 Optical Society of America

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References

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  1. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 9, pp. 117–140.
  2. R. A. Baumgartner, R. L. Byer, IEEE J. Quantum Electron. QE-15, 432 (1979), and references therein.
    [CrossRef]
  3. D. F. Walls, Nature 306, 141 (1983), and references therein.
    [CrossRef]
  4. C. H. Caves, B. L. Schumaker, Phys. Rev. A 31, 3068, 3093 (1985).
    [CrossRef] [PubMed]
  5. H. P. Yuen, in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983), pp. 249–268; H. P. Yuen, V. W. S. Chan, Opt. Lett. 8, 177 (1983).
    [CrossRef] [PubMed]
  6. M. D. Levenson, R. M. Shelby, M. Reid, D. F. Walls, A. Aspect, “The generation and detection of squeezed states of light by nondegenerate four wave mixing in an optical fiber,” Phys. Rev. A (to be published).
  7. G. W. Spetz, A. G. Mann, W. O. Hamilton, W. C. Oelfike, Phys. Lett. 104A, 335 (1984).
  8. D. Blair, University of Western Australia, Perth, W.A., Australia (personal communication).
  9. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 26, pp. 505–509.
  10. D. S. Elliot, R. Roy, S. J. Smith, Phys. Rev. A 24, 12 (1982).
    [CrossRef]
  11. W. Lenth, IEEE J. Quantum Electron. QE-20, 1045 (1984).
    [CrossRef]
  12. R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
    [CrossRef]

1985 (2)

C. H. Caves, B. L. Schumaker, Phys. Rev. A 31, 3068, 3093 (1985).
[CrossRef] [PubMed]

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[CrossRef]

1984 (2)

W. Lenth, IEEE J. Quantum Electron. QE-20, 1045 (1984).
[CrossRef]

G. W. Spetz, A. G. Mann, W. O. Hamilton, W. C. Oelfike, Phys. Lett. 104A, 335 (1984).

1983 (1)

D. F. Walls, Nature 306, 141 (1983), and references therein.
[CrossRef]

1982 (1)

D. S. Elliot, R. Roy, S. J. Smith, Phys. Rev. A 24, 12 (1982).
[CrossRef]

1979 (1)

R. A. Baumgartner, R. L. Byer, IEEE J. Quantum Electron. QE-15, 432 (1979), and references therein.
[CrossRef]

Aspect, A.

M. D. Levenson, R. M. Shelby, M. Reid, D. F. Walls, A. Aspect, “The generation and detection of squeezed states of light by nondegenerate four wave mixing in an optical fiber,” Phys. Rev. A (to be published).

Baumgartner, R. A.

R. A. Baumgartner, R. L. Byer, IEEE J. Quantum Electron. QE-15, 432 (1979), and references therein.
[CrossRef]

Bayer, P. W.

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[CrossRef]

Blair, D.

D. Blair, University of Western Australia, Perth, W.A., Australia (personal communication).

Byer, R. L.

R. A. Baumgartner, R. L. Byer, IEEE J. Quantum Electron. QE-15, 432 (1979), and references therein.
[CrossRef]

Caves, C. H.

C. H. Caves, B. L. Schumaker, Phys. Rev. A 31, 3068, 3093 (1985).
[CrossRef] [PubMed]

Elliot, D. S.

D. S. Elliot, R. Roy, S. J. Smith, Phys. Rev. A 24, 12 (1982).
[CrossRef]

Hamilton, W. O.

G. W. Spetz, A. G. Mann, W. O. Hamilton, W. C. Oelfike, Phys. Lett. 104A, 335 (1984).

Lenth, W.

W. Lenth, IEEE J. Quantum Electron. QE-20, 1045 (1984).
[CrossRef]

Levenson, M. D.

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[CrossRef]

M. D. Levenson, R. M. Shelby, M. Reid, D. F. Walls, A. Aspect, “The generation and detection of squeezed states of light by nondegenerate four wave mixing in an optical fiber,” Phys. Rev. A (to be published).

Mann, A. G.

G. W. Spetz, A. G. Mann, W. O. Hamilton, W. C. Oelfike, Phys. Lett. 104A, 335 (1984).

Oelfike, W. C.

G. W. Spetz, A. G. Mann, W. O. Hamilton, W. C. Oelfike, Phys. Lett. 104A, 335 (1984).

Reid, M.

M. D. Levenson, R. M. Shelby, M. Reid, D. F. Walls, A. Aspect, “The generation and detection of squeezed states of light by nondegenerate four wave mixing in an optical fiber,” Phys. Rev. A (to be published).

Roy, R.

D. S. Elliot, R. Roy, S. J. Smith, Phys. Rev. A 24, 12 (1982).
[CrossRef]

Schumaker, B. L.

C. H. Caves, B. L. Schumaker, Phys. Rev. A 31, 3068, 3093 (1985).
[CrossRef] [PubMed]

Shelby, R. M.

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[CrossRef]

M. D. Levenson, R. M. Shelby, M. Reid, D. F. Walls, A. Aspect, “The generation and detection of squeezed states of light by nondegenerate four wave mixing in an optical fiber,” Phys. Rev. A (to be published).

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 26, pp. 505–509.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 9, pp. 117–140.

Smith, S. J.

D. S. Elliot, R. Roy, S. J. Smith, Phys. Rev. A 24, 12 (1982).
[CrossRef]

Spetz, G. W.

G. W. Spetz, A. G. Mann, W. O. Hamilton, W. C. Oelfike, Phys. Lett. 104A, 335 (1984).

Walls, D. F.

D. F. Walls, Nature 306, 141 (1983), and references therein.
[CrossRef]

M. D. Levenson, R. M. Shelby, M. Reid, D. F. Walls, A. Aspect, “The generation and detection of squeezed states of light by nondegenerate four wave mixing in an optical fiber,” Phys. Rev. A (to be published).

Yuen, H. P.

H. P. Yuen, in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983), pp. 249–268; H. P. Yuen, V. W. S. Chan, Opt. Lett. 8, 177 (1983).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (2)

R. A. Baumgartner, R. L. Byer, IEEE J. Quantum Electron. QE-15, 432 (1979), and references therein.
[CrossRef]

W. Lenth, IEEE J. Quantum Electron. QE-20, 1045 (1984).
[CrossRef]

Nature (1)

D. F. Walls, Nature 306, 141 (1983), and references therein.
[CrossRef]

Phys. Lett. (1)

G. W. Spetz, A. G. Mann, W. O. Hamilton, W. C. Oelfike, Phys. Lett. 104A, 335 (1984).

Phys. Rev. A (2)

D. S. Elliot, R. Roy, S. J. Smith, Phys. Rev. A 24, 12 (1982).
[CrossRef]

C. H. Caves, B. L. Schumaker, Phys. Rev. A 31, 3068, 3093 (1985).
[CrossRef] [PubMed]

Phys. Rev. B (1)

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[CrossRef]

Other (5)

H. P. Yuen, in Quantum Optics, Experimental Gravity and Measurement Theory, P. Meystre, M. O. Scully, eds. (Plenum, New York, 1983), pp. 249–268; H. P. Yuen, V. W. S. Chan, Opt. Lett. 8, 177 (1983).
[CrossRef] [PubMed]

M. D. Levenson, R. M. Shelby, M. Reid, D. F. Walls, A. Aspect, “The generation and detection of squeezed states of light by nondegenerate four wave mixing in an optical fiber,” Phys. Rev. A (to be published).

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 9, pp. 117–140.

D. Blair, University of Western Australia, Perth, W.A., Australia (personal communication).

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984), Chap. 26, pp. 505–509.

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Figures (3)

Fig. 1
Fig. 1

Experimental apparatus as described in the text. The amplitude and phase modulators are labeled A and ϕ, respectively. The digital voltmeter, labeled DVM, measures the average current of detector D.

Fig. 2
Fig. 2

Polar plot of the normalized variance function 4V(r, Φ) [see Eq. (9)] as fitted to experimental data for 3-m fiber length and 30 mW of pump (r = 0) and 100-m fiber with 180 mW of transmitted pump radiation (r = 0.5). The deviation of the r = 0 data from the circle is due to a scattered-light contribution to the measured intensity at Φ = 0 and to servo instability near Φ = 90°.

Fig. 3
Fig. 3

Squeeze parameter and noise suppression for 100 m of Hitachi 6315 fiber as function of transmitted pump power. The solid and dashed lines correspond to the measured nonlinearity of Ref. 6 with and without preserved polarization, respectively.

Equations (13)

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E P z = i κ E P E 2 P ,
E I z = i 2 κ E P E 2 I + i κ E P 2 E S * ,
E S * z = - i 2 κ E P E 2 S * - i κ E P * 2 E I ,
E P ( l ) = E P ( 0 ) e i r ,
E I ( l ) = e i r [ ( 1 + i r ) E I ( 0 ) + i r E S * ( 0 ) ] ,
E S * ( l ) = e - i r [ - i r E I ( 0 ) + ( 1 - i r ) E S * ( 0 ) ] ,
P ( δ ω , Φ ) E LO * E I ( l ) + E LO E S * ( l ) + c . c . = T E P ( 0 ) { E I ( l ) exp [ - i ( Φ + r ) ] + E S * ( l ) exp [ i ( Φ + r ) ] + c . c . } = T E P ( 0 ) { [ E I ( 0 ) + E S * ( 0 ) ] × ( cos Φ + 2 r sin Φ ) - i [ E I ( 0 ) - E S * ( 0 ) ] sin Φ + c . c . } .
P 2 ( δ ω , Φ ) V ( r , Φ ) T 2 E P E 2 N 2 ,
V ( r , Φ ) = ¼ [ 1 + 2 r sin 2 Φ + 2 r 2 ( 1 - cos 2 Φ ) ] .
tan 2 Φ min max = - 1 / r ,
V ( r , Φ min max ) = 1 / 4 [ 1 + 2 r 2 2 r ( 1 + r 2 ) 1 / 2 ] .
T ( Δ ) = R [ 1 + ( L / R ) - 2 L / R cos Δ 1 + ( L R ) - 2 L R cos Δ ] 1 / 2 ,
Φ ( Δ ) = arctan [ ( L R - L / R ) sin Δ 1 + L - ( L / R + L R ) cos Δ ] ,

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