Abstract

Squeezing with solitons has been analyzed thoroughly both numerically and analytically. Here we extend the analysis of soliton squeezing to account for the continuum and address the issue of squeezing detection when using nonoptimal pulses.

© 1998 Optical Society of America

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References

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  1. H. P. Yuen and J. Shapiro, “Generation and detection of two-photon coherent states in degenerate four-wave mixing,” Opt. Lett. 4, 334–336 (1979).
    [CrossRef] [PubMed]
  2. P. D. Drummond, M. D. Reid, S. J. Carter, and R. M. Shelby, “Squeezing of quantum solitons,” Phys. Rev. Lett. 58, 1841–1944 (1987).
    [CrossRef] [PubMed]
  3. P. D. Drummond and S. J. Carter, “Quantum-field theory of squeezing in soliton,” J. Opt. Soc. Am. B 4, 1565–1573 (1987).
    [CrossRef]
  4. Y. Lai and H. A. Haus, “Quantum theory of solitons in optical fiber. I and II,” Phys. Rev. A 16, 848–866 (1989).
  5. M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett. 66, 153–156 (1991).
    [CrossRef] [PubMed]
  6. M. Shirasaki and H. A. Haus, “Squeezing of pulses in a nonlinear interferometer,” J. Opt. Soc. Am. B 7, 30–34 (1990).
    [CrossRef]
  7. H. A. Haus and Y. Lai, “Quantum theory of soliton squeezing: a linearized approach,” J. Opt. Soc. Am. B 7, 386–392 (1990).
    [CrossRef]
  8. Y. Lai, “Quantum theory of soliton propagation: a unified approach based on the linearization approximation,” J. Opt. Soc. Am. B 10, 475–484 (1993).
    [CrossRef]
  9. M. Shirasaki, C. R. Doerr, and F. I. Khatri, “Simulation of pulsed squeezing in optical fiber with chromatic dispersion,” J. Opt. Soc. Am. B 11, 143–149 (1994).
    [CrossRef]
  10. M. D. Levenson, R. M. Shelby, and P. W. Bayer, “Guided acoustic wave Brillouin scattering,” Phys. Rev. B 31, 5244–5252 (1985).
    [CrossRef]
  11. S. J. Carter and P. D. Drummond, “Squeezed quantum solitons and Raman noise,” Phys. Rev. Lett. 67, 3757–3760 (1991).
    [CrossRef] [PubMed]
  12. J. P. Gordon, “Dispersive perturbations of the nonlinear Schrödinger equations,” J. Opt. Soc. Am. B 9, 91–97 (1992).
    [CrossRef]
  13. W. S. Wong, H. A. Haus, and F. I. Khatri, “Continuum generation by perturbation of solitons,” J. Opt. Soc. Am. B 14, 304–313 (1997).
    [CrossRef]
  14. F. X. Kärtner and L. Boivin, “Quantum noise of the fundamental soliton,” Phys. Rev. A 53, 454–466 (1996).
    [CrossRef]
  15. Y. Demin, “Quantum fluctuations of optical solitons in fibers,” Phys. Rev. A 52, 4871–4881 (1995).
    [CrossRef]

1997 (1)

1996 (1)

F. X. Kärtner and L. Boivin, “Quantum noise of the fundamental soliton,” Phys. Rev. A 53, 454–466 (1996).
[CrossRef]

1995 (1)

Y. Demin, “Quantum fluctuations of optical solitons in fibers,” Phys. Rev. A 52, 4871–4881 (1995).
[CrossRef]

1994 (1)

1993 (1)

1992 (1)

1991 (2)

M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett. 66, 153–156 (1991).
[CrossRef] [PubMed]

S. J. Carter and P. D. Drummond, “Squeezed quantum solitons and Raman noise,” Phys. Rev. Lett. 67, 3757–3760 (1991).
[CrossRef] [PubMed]

1990 (2)

1989 (1)

Y. Lai and H. A. Haus, “Quantum theory of solitons in optical fiber. I and II,” Phys. Rev. A 16, 848–866 (1989).

1987 (2)

P. D. Drummond and S. J. Carter, “Quantum-field theory of squeezing in soliton,” J. Opt. Soc. Am. B 4, 1565–1573 (1987).
[CrossRef]

P. D. Drummond, M. D. Reid, S. J. Carter, and R. M. Shelby, “Squeezing of quantum solitons,” Phys. Rev. Lett. 58, 1841–1944 (1987).
[CrossRef] [PubMed]

1985 (1)

M. D. Levenson, R. M. Shelby, and P. W. Bayer, “Guided acoustic wave Brillouin scattering,” Phys. Rev. B 31, 5244–5252 (1985).
[CrossRef]

1979 (1)

Bayer, P. W.

M. D. Levenson, R. M. Shelby, and P. W. Bayer, “Guided acoustic wave Brillouin scattering,” Phys. Rev. B 31, 5244–5252 (1985).
[CrossRef]

Boivin, L.

F. X. Kärtner and L. Boivin, “Quantum noise of the fundamental soliton,” Phys. Rev. A 53, 454–466 (1996).
[CrossRef]

Carter, S. J.

S. J. Carter and P. D. Drummond, “Squeezed quantum solitons and Raman noise,” Phys. Rev. Lett. 67, 3757–3760 (1991).
[CrossRef] [PubMed]

P. D. Drummond and S. J. Carter, “Quantum-field theory of squeezing in soliton,” J. Opt. Soc. Am. B 4, 1565–1573 (1987).
[CrossRef]

P. D. Drummond, M. D. Reid, S. J. Carter, and R. M. Shelby, “Squeezing of quantum solitons,” Phys. Rev. Lett. 58, 1841–1944 (1987).
[CrossRef] [PubMed]

Demin, Y.

Y. Demin, “Quantum fluctuations of optical solitons in fibers,” Phys. Rev. A 52, 4871–4881 (1995).
[CrossRef]

Doerr, C. R.

Drummond, P. D.

S. J. Carter and P. D. Drummond, “Squeezed quantum solitons and Raman noise,” Phys. Rev. Lett. 67, 3757–3760 (1991).
[CrossRef] [PubMed]

P. D. Drummond and S. J. Carter, “Quantum-field theory of squeezing in soliton,” J. Opt. Soc. Am. B 4, 1565–1573 (1987).
[CrossRef]

P. D. Drummond, M. D. Reid, S. J. Carter, and R. M. Shelby, “Squeezing of quantum solitons,” Phys. Rev. Lett. 58, 1841–1944 (1987).
[CrossRef] [PubMed]

Gordon, J. P.

Haus, H. A.

Kärtner, F. X.

F. X. Kärtner and L. Boivin, “Quantum noise of the fundamental soliton,” Phys. Rev. A 53, 454–466 (1996).
[CrossRef]

Khatri, F. I.

Lai, Y.

Levenson, M. D.

M. D. Levenson, R. M. Shelby, and P. W. Bayer, “Guided acoustic wave Brillouin scattering,” Phys. Rev. B 31, 5244–5252 (1985).
[CrossRef]

Reid, M. D.

P. D. Drummond, M. D. Reid, S. J. Carter, and R. M. Shelby, “Squeezing of quantum solitons,” Phys. Rev. Lett. 58, 1841–1944 (1987).
[CrossRef] [PubMed]

Rosenbluh, M.

M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett. 66, 153–156 (1991).
[CrossRef] [PubMed]

Shapiro, J.

Shelby, R. M.

M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett. 66, 153–156 (1991).
[CrossRef] [PubMed]

P. D. Drummond, M. D. Reid, S. J. Carter, and R. M. Shelby, “Squeezing of quantum solitons,” Phys. Rev. Lett. 58, 1841–1944 (1987).
[CrossRef] [PubMed]

M. D. Levenson, R. M. Shelby, and P. W. Bayer, “Guided acoustic wave Brillouin scattering,” Phys. Rev. B 31, 5244–5252 (1985).
[CrossRef]

Shirasaki, M.

Wong, W. S.

Yuen, H. P.

J. Opt. Soc. Am. B (7)

Opt. Lett. (1)

Phys. Rev. A (3)

Y. Lai and H. A. Haus, “Quantum theory of solitons in optical fiber. I and II,” Phys. Rev. A 16, 848–866 (1989).

F. X. Kärtner and L. Boivin, “Quantum noise of the fundamental soliton,” Phys. Rev. A 53, 454–466 (1996).
[CrossRef]

Y. Demin, “Quantum fluctuations of optical solitons in fibers,” Phys. Rev. A 52, 4871–4881 (1995).
[CrossRef]

Phys. Rev. B (1)

M. D. Levenson, R. M. Shelby, and P. W. Bayer, “Guided acoustic wave Brillouin scattering,” Phys. Rev. B 31, 5244–5252 (1985).
[CrossRef]

Phys. Rev. Lett. (3)

S. J. Carter and P. D. Drummond, “Squeezed quantum solitons and Raman noise,” Phys. Rev. Lett. 67, 3757–3760 (1991).
[CrossRef] [PubMed]

P. D. Drummond, M. D. Reid, S. J. Carter, and R. M. Shelby, “Squeezing of quantum solitons,” Phys. Rev. Lett. 58, 1841–1944 (1987).
[CrossRef] [PubMed]

M. Rosenbluh and R. M. Shelby, “Squeezed optical solitons,” Phys. Rev. Lett. 66, 153–156 (1991).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Squeezing as a function of ΦNL for I, quasi-cw and II, hyperbolic secant local-oscillators (without accounting for the continuum).

Fig. 2
Fig. 2

Optimal phase of the local oscillator for maximum squeezing detection. I, quasi-cw and II, hyperbolic secant local oscillators (without accounting for the continuum).

Fig. 3
Fig. 3

Noise reduction as a function of local-oscillator phase. I, quasi-cw and II, hyperbolic secant local oscillator (without the continuum).

Fig. 4
Fig. 4

Squeezing as a function of ΦNL with a hyperbolic secant local oscillator. I, without the continuum projection and II, with the continuum projection.

Fig. 5
Fig. 5

Noise reduction as a function of local-oscillator phase. I, without the continuum projection and II, with the continuum projection.

Equations (38)

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τ uˆ=i2 2x2 uˆ+icu^uˆuˆ,
H^K=k2 dxu^u^uˆuˆ
ckvg|β|.
uˆ=u0+Δuˆ,
[Δuˆ, Δu^]=δ(x-x).
u0=expiz2-p022 z+p02x+θ0×sech(x-x0-p0z).
Δuˆ(x, z)=[Δwˆ(z)fw(x)+Δθˆ(z)fθ(x)+Δpˆ(z)fp(x)+Δtˆ(z)ft(x)]exp(iz/2)+Δu^c(x, z).
f̲n(x)=[1-x tanh(x)]u0(z=0, x),
f̲θ(x)=-iu0(z=0, x),
f̲x(x)=tanh(x)u0(z=0, x),
f̲p(x)=-ixu0(z=0, x).
½dx[f̲i(x)fj*(x)+c.c.]=δij
f̲n(x)=u0(z=0, x),
f̲θ(x)=i[1-x tanh(x)]u0(z=0, x),
f̲x(x)=xu0(z=0, x),
f̲p(x)=i tanh(x)u0(z=0, x).
Δn^0=½dx(aˆf̲n*+a^f̲n),
Δθ^0=½dx(aˆf̲θ*+a^f̲θ),
Δnˆ(z)=Δn^0,
Δθˆ(z)=Δθ^0+z2 Δn^0,
fc(x, Ω, z)=C[Ω2-iΩ tanh(x)+tanh2(x)]exp-i(Ωx+Ω22 z)+C*u0(x, z)expi(Ωx+Ω22 z+z),
V^c,s(Ω)=½dx[aˆff̲c,s*(x, Ω, z=0)+a^f̲c,s(x, Ω, z=0)],
v^c,s(x, Ω, z)=V^c,s(Ω)fc,s(x, Ω, z).
sˆ(x)=dΩ[v^c(x, Ω, L)+v^s(x, Ω, L)]+Δnˆfn(x)+Δθˆfθ(x),
Iˆ=dx[sˆ(x)sech(x)exp(iΨ)+sˆ(x) sech(x)exp(-iΨ)].
dx[fs(x, Ω, z)sech(x)cos(Ψ)]=0.
Iˆ=dΩ[V^c(Ω)Ic(Ω)]+ΔnˆIn+ΔθˆIθ,
Ic=12 dx[fs(x, Ω, L)sech(x)exp(-iΨ)+c.c.],
Ic(Ω, Ψ, L)=πΩ2+1 sechπ2 Ωcos12 Ω2Lsin(Ψ),
In=½dx[fn(x)sech(x)exp(-iΨ)+c.c.]=cos(Ψ),
Iθ=½dx[fθ(x)sech(x)exp(iΨ)+c.c.]=2 sin(Ψ),
IˆI^+I^Iˆ=Δn^02[cos2(Ψ)+4ΦNL2 sin2(Ψ)+2ΦNL sin(2Ψ)]+Δθ^024 sin2(Ψ)+dΩIc2(Ω, Ψ)V^c2(Ω)+dΩ[2 sin(Ψ)Ic(Ω, Ψ)ΔθˆV^c(Ω)].
ΔθˆV^c(Ω)=½dx(f̲θ*f̲c+f̲θf̲c*)=π21/2 1-2Ω2Ω2+1 sechπ2 Ω+πΩΩ2+1 tanhπ2 Ωsechπ2 Ω.
Δn^2=½dt(|f̲n|2)=1,
Δθ^2=½dt(|f̲θ|2)=0.607,
V^c,s2(Ω)=½dt(|f̲c,s|2)=1/2,
PLO(x)=cos(Ψ)f̲n(x)+sin(Ψ)f̲n(x),
IˆI^+I^Iˆ=Δn^02[cos2(Ψ)+ΦNL2 sin2(Ψ)+ΦNL sin(2Ψ)]+Δθ^02sin2(Ψ).

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