Abstract

We study the quantum-noise properties of spectrally filtered solitons in optical fibers. Perturbation theory, including a quantum description of the continuum, is used to derive a complete analytical expression for the second-order correlator of the amplitude quadrature. This correlator is subsequently used to optimize the frequency response of the filter numerically in order to achieve the minimum photon-number noise. For propagation distances up to three soliton periods, the length at which the best noise reduction occurs, a square filter is found to be approximately optimum. For longer distances, more-complicated filter shapes are predicted for the best noise reduction.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996)S. Spälter, M. Burk, U. Strössner, M. Böhm, A. Sizmann, and G. Leuchs, Europhys. Lett. 38, 335 (1997)S. Spälter, M. Burk, U. Strössner, A. Sizmann, and G. Leuchs, Opt. Express 2, 77 (1998).
    [CrossRef] [PubMed]
  2. M. J. Werner and S. R. Friberg, Phys. Rev. Lett. 79, 4143 (1997).
    [CrossRef]
  3. A. Mecozzi and P. Kumar, Opt. Lett. 22, 1232 (1997).
    [CrossRef] [PubMed]
  4. D. Levandovsky, M. Vasilyev, and P. Kumar, in International Quantum Electronics Conference, Vol. 7 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 131.
  5. S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
    [CrossRef]
  6. D. J. Kaup, Phys. Rev. A 42, 5689 (1990)H. A. Haus and Y. Lai, J. Opt. Soc. Am. B 7, 386 (1990)H. A. Haus, W. S. Wong, and F. I. Khatri, J. Opt. Soc. Am. B 14, 304 (1997).
    [CrossRef] [PubMed]

1998 (1)

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

1997 (2)

M. J. Werner and S. R. Friberg, Phys. Rev. Lett. 79, 4143 (1997).
[CrossRef]

A. Mecozzi and P. Kumar, Opt. Lett. 22, 1232 (1997).
[CrossRef] [PubMed]

1996 (1)

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996)S. Spälter, M. Burk, U. Strössner, M. Böhm, A. Sizmann, and G. Leuchs, Europhys. Lett. 38, 335 (1997)S. Spälter, M. Burk, U. Strössner, A. Sizmann, and G. Leuchs, Opt. Express 2, 77 (1998).
[CrossRef] [PubMed]

1990 (1)

D. J. Kaup, Phys. Rev. A 42, 5689 (1990)H. A. Haus and Y. Lai, J. Opt. Soc. Am. B 7, 386 (1990)H. A. Haus, W. S. Wong, and F. I. Khatri, J. Opt. Soc. Am. B 14, 304 (1997).
[CrossRef] [PubMed]

Friberg, S. R.

M. J. Werner and S. R. Friberg, Phys. Rev. Lett. 79, 4143 (1997).
[CrossRef]

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996)S. Spälter, M. Burk, U. Strössner, M. Böhm, A. Sizmann, and G. Leuchs, Europhys. Lett. 38, 335 (1997)S. Spälter, M. Burk, U. Strössner, A. Sizmann, and G. Leuchs, Opt. Express 2, 77 (1998).
[CrossRef] [PubMed]

Kaup, D. J.

D. J. Kaup, Phys. Rev. A 42, 5689 (1990)H. A. Haus and Y. Lai, J. Opt. Soc. Am. B 7, 386 (1990)H. A. Haus, W. S. Wong, and F. I. Khatri, J. Opt. Soc. Am. B 14, 304 (1997).
[CrossRef] [PubMed]

König, F.

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Korolkova, N.

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Kumar, P.

A. Mecozzi and P. Kumar, Opt. Lett. 22, 1232 (1997).
[CrossRef] [PubMed]

D. Levandovsky, M. Vasilyev, and P. Kumar, in International Quantum Electronics Conference, Vol. 7 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 131.

Leuchs, G.

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Levandovsky, D.

D. Levandovsky, M. Vasilyev, and P. Kumar, in International Quantum Electronics Conference, Vol. 7 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 131.

Levanon, A.

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996)S. Spälter, M. Burk, U. Strössner, M. Böhm, A. Sizmann, and G. Leuchs, Europhys. Lett. 38, 335 (1997)S. Spälter, M. Burk, U. Strössner, A. Sizmann, and G. Leuchs, Opt. Express 2, 77 (1998).
[CrossRef] [PubMed]

Machida, S.

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996)S. Spälter, M. Burk, U. Strössner, M. Böhm, A. Sizmann, and G. Leuchs, Europhys. Lett. 38, 335 (1997)S. Spälter, M. Burk, U. Strössner, A. Sizmann, and G. Leuchs, Opt. Express 2, 77 (1998).
[CrossRef] [PubMed]

Mecozzi, A.

Mukai, T.

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996)S. Spälter, M. Burk, U. Strössner, M. Böhm, A. Sizmann, and G. Leuchs, Europhys. Lett. 38, 335 (1997)S. Spälter, M. Burk, U. Strössner, A. Sizmann, and G. Leuchs, Opt. Express 2, 77 (1998).
[CrossRef] [PubMed]

Sizmann, A.

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Spälter, S.

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

Vasilyev, M.

D. Levandovsky, M. Vasilyev, and P. Kumar, in International Quantum Electronics Conference, Vol. 7 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 131.

Werner, M. J.

M. J. Werner and S. R. Friberg, Phys. Rev. Lett. 79, 4143 (1997).
[CrossRef]

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996)S. Spälter, M. Burk, U. Strössner, M. Böhm, A. Sizmann, and G. Leuchs, Europhys. Lett. 38, 335 (1997)S. Spälter, M. Burk, U. Strössner, A. Sizmann, and G. Leuchs, Opt. Express 2, 77 (1998).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. A (1)

D. J. Kaup, Phys. Rev. A 42, 5689 (1990)H. A. Haus and Y. Lai, J. Opt. Soc. Am. B 7, 386 (1990)H. A. Haus, W. S. Wong, and F. I. Khatri, J. Opt. Soc. Am. B 14, 304 (1997).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

S. Spälter, N. Korolkova, F. König, A. Sizmann, and G. Leuchs, Phys. Rev. Lett. 81, 786 (1998).
[CrossRef]

S. R. Friberg, S. Machida, M. J. Werner, A. Levanon, and T. Mukai, Phys. Rev. Lett. 77, 3775 (1996)S. Spälter, M. Burk, U. Strössner, M. Böhm, A. Sizmann, and G. Leuchs, Europhys. Lett. 38, 335 (1997)S. Spälter, M. Burk, U. Strössner, A. Sizmann, and G. Leuchs, Opt. Express 2, 77 (1998).
[CrossRef] [PubMed]

M. J. Werner and S. R. Friberg, Phys. Rev. Lett. 79, 4143 (1997).
[CrossRef]

Other (1)

D. Levandovsky, M. Vasilyev, and P. Kumar, in International Quantum Electronics Conference, Vol. 7 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 131.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Top, gray-scale visualization of the optimum filter response Hωopt2, where white and black correspond to 0 and 1, respectively. Bottom, Fano factor obtained for a square filter with α=0.18 (dashed curve) and the optimum filter (solid curve); total loss α for the square filter (dotted–dashed line) and the optimum filter (dotted curve). In both plots distance is in soliton periods.

Fig. 2
Fig. 2

Top, normally ordered quadrature-noise correlator GNω,ω,ξ. Bottom, frequency response Hωopt2 of the optimum filter (interpolated circles), amplitude-quadrature variance GNω,ω,ξ (dotted curve), and zero-frequency-to-sideband correlation function GN0,ω,ξ (dashed curve). All functions are shown for z2ξ/π=10.73.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

ξa^τ,ξ=i122τ2+a^τ,ξa^τ,ξa^τ,ξ.
a^τ,ξ=f̲nτexpiξ/2+Δb^τ,ξ[f̲nτ+Δa^τ,ξ]expiξ/2,
Δb^ξ=i22τ2Δb^+2iaτ,ξ2Δb^+iaτ,ξ2Δb^,
Δa^oω,ξ=HωΔa^ω,ξ+1-Hω2v^ω,
FξΔN^oξ2/N^o=1+N^o-1dω2πdω2πf̲nωHω2GNω,ω,ξHω2f̲nω,
Gω,ω,ξ=2πδω-ω+GNω,ω,ξ[Δα^ω,ξ+Δα^ω,ξ] [Δα^ω,ξ+Δα^ω,ξ].
Gτ,τ,ξ=δτ+τ+GNτ,τ,ξ=[Δa^τ,ξ+Δa^-τ,ξ] [Δa^τ,ξ+Δa^-τ,ξ].
Δa^τ,ξ=dΩ2π[V^cΩ,ξfcΩ,τ+V^sΩ,ξfsΩ,τ]+i=n,p,τ,θV^iξfiτ,
fi·f̲j*=Refiτf̲j*τdτ=Refiωf̲j*ωdω2π
Gτ,τ,ξ/4=Δa^cτ,ξΔa^cτ,ξ=dΩ2πdΩ2πV^cΩ,ξV^cΩ,ξfcΩ,τfcΩ,τ+dΩ2πV^nV^cΩ,ξ[fnτfcΩ,τ+fnτfcΩ,τ]+dΩ2πV^pV^cΩ,ξ[fpτfcΩ,τ+fpτfcΩ,τ]+V^n2fnτfnτ+V^p2fpτfpτ;
V^nV^cΩ,ξ=-π/4sechπΩ/2cos[(1+Ω2)ξ/2],V^pV^cΩ,ξ=πΩ/12sechπΩ/2cos[(1+Ω2)ξ/2],V^cΩ,ξV^cΩ,ξ=BΩ,Ωcos[(Ω2-Ω2)ξ/2]-AΩ,Ωcos[(1+(Ω2+Ω2)/2)ξ],AΩ,Ω=Ω+Ω2-6ΩΩ-2(Ω2+1)(Ω2+1)πΩ+Ω/12sinhπΩ+Ω/2,BΩ,Ω=Ω-Ω2+4(Ω2+1)(Ω2+1)πΩ-Ω/12sinhπΩ-Ω/2,+π/2δΩ-Ω,

Metrics