Abstract

A perturbation approach is used to study the quantum noise of optical solitons in an asymmetric fiber Sagnac interferometer (a highly transmissive nonlinear optical loop mirror). Analytical expressions for the three second-order quadrature correlators are derived and used to predict the amount of detectable amplitude squeezing along with the optimum power-splitting ratio of the Sagnac interferometer. We find that it is the number-phase correlation owing to the Kerr nonlinearity that is primarily responsible for the observable noise reduction. The group-velocity dispersion affecting the field in the nonsoliton arm of the fiber interferometer is shown to limit the minimum achievable Fano factor.

© 1999 Optical Society of America

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  1. M. J. Werner, presented at the OSA Annual Meeting, October 11–17, Long Beach, California, 1997M. J. Werner and S. R. Friberg, in International Quantum Electronics Conference, Vol. 7 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 130.
  2. S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
    [CrossRef] [PubMed]
  3. S. Schmitt, J. Ficker, M. Wolff, F. Köenig, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
    [CrossRef]
  4. D. Krylov and K. Bergman, Opt. Lett. 23, 1390 (1998).
    [CrossRef]
  5. H. A. Haus and Y. Lai, J. Opt. Soc. Am. B 9, 386 (1990)H. A. Haus, W. S. Wong, and F. I. Khatri, J. Opt. Soc. Am. B 14, 304 (1997).
    [CrossRef]
  6. D. Levandovsky, M. Vasilyev, and P. Kumar, Opt. Lett. 24, 43 (1999).
    [CrossRef]
  7. M. Kitagawa and Y. Yamamoto, Phys. Rev. A 34, 3974 (1986).
    [CrossRef] [PubMed]
  8. M. Margalit, E. P. Ippen, and H. A. Haus, in International Quantum Electronics Conference, Vol. 7 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 170.

1999 (1)

1998 (2)

S. Schmitt, J. Ficker, M. Wolff, F. Köenig, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

D. Krylov and K. Bergman, Opt. Lett. 23, 1390 (1998).
[CrossRef]

1990 (1)

H. A. Haus and Y. Lai, J. Opt. Soc. Am. B 9, 386 (1990)H. A. Haus, W. S. Wong, and F. I. Khatri, J. Opt. Soc. Am. B 14, 304 (1997).
[CrossRef]

1987 (1)

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

1986 (1)

M. Kitagawa and Y. Yamamoto, Phys. Rev. A 34, 3974 (1986).
[CrossRef] [PubMed]

Bergman, K.

Carter, S. J.

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

Drummond, P. D.

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

Ficker, J.

S. Schmitt, J. Ficker, M. Wolff, F. Köenig, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

Haus, H. A.

H. A. Haus and Y. Lai, J. Opt. Soc. Am. B 9, 386 (1990)H. A. Haus, W. S. Wong, and F. I. Khatri, J. Opt. Soc. Am. B 14, 304 (1997).
[CrossRef]

M. Margalit, E. P. Ippen, and H. A. Haus, in International Quantum Electronics Conference, Vol. 7 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 170.

Ippen, E. P.

M. Margalit, E. P. Ippen, and H. A. Haus, in International Quantum Electronics Conference, Vol. 7 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 170.

Kitagawa, M.

M. Kitagawa and Y. Yamamoto, Phys. Rev. A 34, 3974 (1986).
[CrossRef] [PubMed]

Köenig, F.

S. Schmitt, J. Ficker, M. Wolff, F. Köenig, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

Krylov, D.

Kumar, P.

Lai, Y.

H. A. Haus and Y. Lai, J. Opt. Soc. Am. B 9, 386 (1990)H. A. Haus, W. S. Wong, and F. I. Khatri, J. Opt. Soc. Am. B 14, 304 (1997).
[CrossRef]

Leuchs, G.

S. Schmitt, J. Ficker, M. Wolff, F. Köenig, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

Levandovsky, D.

Margalit, M.

M. Margalit, E. P. Ippen, and H. A. Haus, in International Quantum Electronics Conference, Vol. 7 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 170.

Reid, M. D.

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

Schmitt, S.

S. Schmitt, J. Ficker, M. Wolff, F. Köenig, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

Shelby, R. M.

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

Sizmann, A.

S. Schmitt, J. Ficker, M. Wolff, F. Köenig, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

Vasilyev, M.

Werner, M. J.

M. J. Werner, presented at the OSA Annual Meeting, October 11–17, Long Beach, California, 1997M. J. Werner and S. R. Friberg, in International Quantum Electronics Conference, Vol. 7 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 130.

Wolff, M.

S. Schmitt, J. Ficker, M. Wolff, F. Köenig, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

Yamamoto, Y.

M. Kitagawa and Y. Yamamoto, Phys. Rev. A 34, 3974 (1986).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (1)

H. A. Haus and Y. Lai, J. Opt. Soc. Am. B 9, 386 (1990)H. A. Haus, W. S. Wong, and F. I. Khatri, J. Opt. Soc. Am. B 14, 304 (1997).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

M. Kitagawa and Y. Yamamoto, Phys. Rev. A 34, 3974 (1986).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett. 58, 1841 (1987).
[CrossRef] [PubMed]

S. Schmitt, J. Ficker, M. Wolff, F. Köenig, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 2446 (1998).
[CrossRef]

Other (2)

M. J. Werner, presented at the OSA Annual Meeting, October 11–17, Long Beach, California, 1997M. J. Werner and S. R. Friberg, in International Quantum Electronics Conference, Vol. 7 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 130.

M. Margalit, E. P. Ippen, and H. A. Haus, in International Quantum Electronics Conference, Vol. 7 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 170.

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Figures (1)

Fig. 1
Fig. 1

Top: contour plot showing the Fano factor, including dispersion, versus T (solid curves, F=-10 dB; dashed curves, F=-5 dB; thick solid curves, F=0 dB; dotted-dashed curves, F=5 dB; dotted curves, F=10 dB; thick gray curves, F=15 dB). Middle: Fano factor minimized by the proper choice of T with (solid curves) and without (dashed curves) dispersion taken into account; the Fano factor limit imposed by the loss 1-T in each case (dotted curves) is also shown. Bottom: optimum T corresponding to the minimum Fano factor in the middle figure, with (solid curves) and without (dashed curves) dispersion. The distance is in soliton periods in all three plots.

Equations (20)

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a^outaout+Δa^out=Ta^solξ+i1-Ta^gvdξ,
aout=Ta0expiξ/21-1-TTexp-iψ+ξ/2,
Δa^out=TΔa^solξexpiξ/2-1-TΔa^gvdξ.
Fξ=1+Taout2dω/2π-1aout aout×i,j=c,sΦiGNijω,ω,ξΦjdωdω/4π2,
GNccω,ω,ξ4:Δa^solcΔa^solc:ξ,
GNssω,ω,ξ4:Δa^solsΔa^sols:ξ,
GNcsω,ω,ξ4:Δa^solcΔa^sols:ξ=-GNcs*ω,ω,ξ=GNscω,ω,ξ.
[Δa^solτ,ξ+Δa^sol-τ,ξ]/2=i=n,p,cΔX^i,
[Δa^solτ,ξ-Δa^sol-τ,ξ]/2=i=θ,τ,sΔX^i,
Gccτ,τ,ξ=4i,j=n,p,cΔX^iτΔX^jτξ,
Gssτ,τ,ξ=4i,j=θ,τ,sΔX^iτΔX^jτ)ξ,
Gcsτ,τ,ξ=4i=n,p,c;j=θ,τ,sΔX^iτΔX^jτξ.
V^n2ξ=1/2, V^θ2ξ=(π2+12)/72+ξ2/2,
V^p2ξ=1/6, V^τ2ξ=(π2+4ξ2)/24,
[V^nV^θξV^pV^τξ]=i4[-11]-ξ[1/21/6],
[V^nV^cΩξV^nV^sΩξV^pV^cΩξV^pV^sΩξ]=a0Ω4[-cosαsinαΩ/3cosα-Ω/3sinα]
[V^θV^cΩξV^τV^cΩξV^θV^sΩξV^τV^sΩξ]=[sinα-ξcosαcosαξsinα]×[V^θV^sΩ0V^τV^sΩ0V^nV^cΩ0V^pV^cΩ0]
[V^cΩV^cΩξV^sΩV^sΩξV^cΩV^sΩξ]=[1cosβ-cosγ1cosβcosγisinβsinγ]×π2[δΩ-ΩΩ-Ω2+46(Ω2+1) (Ω2+1)Ω-ΩsinhπΩ-Ω/2Ω+Ω2-6ΩΩ-26(Ω2+1) (Ω2+1)Ω+ΩsinhπΩ+Ω/2]
V^θV^sΩ0=-a0Ω42/3Ω2+1+πΩ6tanhπΩ2
V^τV^sΩ0=a0Ω2ΩΩ2+1-π4tanhπΩ2

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