Abstract

Based on a newly developed general quantum theory of nonlinear optical pulse propagation, the influences of the self-Raman effect and third-order dispersion on the achievable squeezing ratio in squeezing experiments with optical fibers at both the 1.3- and 1.55-μm wavelengths are studied. In the presence of these effects, squeezing still survives, but the achievable squeezing will reach a limit as the propagation distance increases. Temperature dependence of the squeezing ratio is also examined.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Bergman and H. A. Haus, "Squeezing in fibers with optical pulses," Opt. Lett. 16, 663 (1991).
    [CrossRef] [PubMed]
  2. K. Bergman, C. R. Doerr, H. A. Haus, and M. Shirasaki, "Sub-shot-noise measurement with fiber-squeezed optical pulses," Opt. Lett. 18, 643 (1993).
    [CrossRef] [PubMed]
  3. K. Bergman, H. A. Haus, E. P. Ippen, and M. Shirasaki, "Squeezing in a fiber interferometer with a gigahertz pump," Opt. Lett. 19, 290 (1994).
    [CrossRef] [PubMed]
  4. M. Rosenbluh and R. M. Shelby, "Squeezed optical solitons," Phys. Rev. Lett. 66, 153 (1991).
    [CrossRef] [PubMed]
  5. M. Shirasaki and H. A. Haus, "Squeezing of pulses in a nonlinear interferometer," J. Opt. Soc. Am. B 7, 30 (1990).
    [CrossRef]
  6. K. Bergman, H. A. Haus, and Y. Lai, "Fiber gyros using squeezed pulses," J. Opt. Soc. Am. B 8, 1952 (1991).
  7. K. J. Blow, R. Loudon, and S. J. D. Phoenix, "Quantum theory of nonlinear loop mirrors," Phys. Rev. A 45, 8064 (1992).
    [CrossRef] [PubMed]
  8. F. X. Kärtner, L. G. Jonechis, and H. A. Haus, "Classical and quantum dynamics of a pulse in a dispersionless nonlinear fiber," Quantum Opt. 4, 379 (1992).
    [CrossRef]
  9. L. G. Jonechis and J. H. Shapiro, "Quantum propagation in a Kerr medium: lossless, dispersionless fiber," J. Opt. Soc. Am. B 10, 1102 (1993).
    [CrossRef]
  10. P. D. Drummond and S. J. Carter, "Quantum field theory of squeezing in solitons," J. Opt. Soc. Am. B 4, 1565 (1987).
    [CrossRef]
  11. P. D. Drummond, S. J. Carter, and R. M. Shelby, "Time dependence of quantum fluctuations in solitons," Opt. Lett. 14, 373 (1989).
    [CrossRef] [PubMed]
  12. H. A. Haus and Y. Lai, "Quantum theory of soliton squeezing—a linearized approach," J. Opt. Soc. Am. B 7, 386 (1990).
    [CrossRef]
  13. Y. Lai, "Quantum theory of soliton propagation—a unified approach," J. Opt. Soc. Am. B 10, 475 (1993).
    [CrossRef]
  14. F. Singer, M. J. Potasek, J. M. Fang, and M. C. Teich, "Femtosecond solitons in nonlinear optical fibers: classical and quantum effects," Phys. Rev. A 46, 4192 (1992).
    [CrossRef] [PubMed]
  15. S. J. Carter and P. D. Drummond, "Squeezed quantum solitons and Raman noise," Phys. Rev. Lett. 67, 3757 (1991).
    [CrossRef] [PubMed]
  16. F. X. Kärtner, D. J. Dougherty, H. A. Haus, and E. P. Ippen, "Raman noise and soliton squeezing," J. Opt. Soc. Am. B 11, 1267 (1994).
    [CrossRef]
  17. P. D. Drummond and A. D. Hardman, "Simulation of quantum effects in Raman-active waveguides," Europhys. Lett. 21, 279 (1993).
    [CrossRef]
  18. Y. Lai and S.-S. Yu, "General quantum theory of nonlinear optical pulse propagation," Phys. Rev. A 51, 817 (1995).
    [CrossRef] [PubMed]
  19. J. P. Gordon, "Theory of the soliton self-frequency shift," Opt. Lett. 11, 662 (1986).
    [CrossRef] [PubMed]
  20. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, "Raman response function of silica-core fibers," J. Opt. Soc. Am. B 6, 1159 (1989).
    [CrossRef]
  21. D. Dougherty, F. X. Kärtner, I. P. Ippen, and H. A. Haus, "Low-frequency Raman gain measurements," Opt. Lett. 20, 31 (1995).
    [CrossRef] [PubMed]
  22. R. M. Shelby, M. D. Levenson, and P. W. Bayer, "Guided acoustic-wave Brillouin scattering," Phys. Rev. B 31, 5244 (1985).
    [CrossRef]
  23. R. M. Shelby, P. D. Drummond, and S. J. Carter, "Phase-noise scaling in quantum soliton propagation," Phys. Rev. A 42, 2966 (1990).
    [CrossRef] [PubMed]
  24. R. H. Stolen and C. Lin, "Self-phase-modulation in silica optical fibers," Phys. Rev. A 17, 1448 (1978).
    [CrossRef]

1995 (2)

Y. Lai and S.-S. Yu, "General quantum theory of nonlinear optical pulse propagation," Phys. Rev. A 51, 817 (1995).
[CrossRef] [PubMed]

D. Dougherty, F. X. Kärtner, I. P. Ippen, and H. A. Haus, "Low-frequency Raman gain measurements," Opt. Lett. 20, 31 (1995).
[CrossRef] [PubMed]

1994 (2)

1993 (4)

1992 (3)

F. Singer, M. J. Potasek, J. M. Fang, and M. C. Teich, "Femtosecond solitons in nonlinear optical fibers: classical and quantum effects," Phys. Rev. A 46, 4192 (1992).
[CrossRef] [PubMed]

K. J. Blow, R. Loudon, and S. J. D. Phoenix, "Quantum theory of nonlinear loop mirrors," Phys. Rev. A 45, 8064 (1992).
[CrossRef] [PubMed]

F. X. Kärtner, L. G. Jonechis, and H. A. Haus, "Classical and quantum dynamics of a pulse in a dispersionless nonlinear fiber," Quantum Opt. 4, 379 (1992).
[CrossRef]

1991 (4)

K. Bergman and H. A. Haus, "Squeezing in fibers with optical pulses," Opt. Lett. 16, 663 (1991).
[CrossRef] [PubMed]

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

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

K. Bergman, H. A. Haus, and Y. Lai, "Fiber gyros using squeezed pulses," J. Opt. Soc. Am. B 8, 1952 (1991).

1990 (3)

1989 (2)

1987 (1)

1986 (1)

1985 (1)

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

1978 (1)

R. H. Stolen and C. Lin, "Self-phase-modulation in silica optical fibers," Phys. Rev. A 17, 1448 (1978).
[CrossRef]

Bayer, P. W.

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

Bergman, K.

Blow, K. J.

K. J. Blow, R. Loudon, and S. J. D. Phoenix, "Quantum theory of nonlinear loop mirrors," Phys. Rev. A 45, 8064 (1992).
[CrossRef] [PubMed]

Carter, S. J.

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

R. M. Shelby, P. D. Drummond, and S. J. Carter, "Phase-noise scaling in quantum soliton propagation," Phys. Rev. A 42, 2966 (1990).
[CrossRef] [PubMed]

P. D. Drummond, S. J. Carter, and R. M. Shelby, "Time dependence of quantum fluctuations in solitons," Opt. Lett. 14, 373 (1989).
[CrossRef] [PubMed]

P. D. Drummond and S. J. Carter, "Quantum field theory of squeezing in solitons," J. Opt. Soc. Am. B 4, 1565 (1987).
[CrossRef]

Doerr, C. R.

Dougherty, D.

Dougherty, D. J.

Drummond, P. D.

P. D. Drummond and A. D. Hardman, "Simulation of quantum effects in Raman-active waveguides," Europhys. Lett. 21, 279 (1993).
[CrossRef]

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

R. M. Shelby, P. D. Drummond, and S. J. Carter, "Phase-noise scaling in quantum soliton propagation," Phys. Rev. A 42, 2966 (1990).
[CrossRef] [PubMed]

P. D. Drummond, S. J. Carter, and R. M. Shelby, "Time dependence of quantum fluctuations in solitons," Opt. Lett. 14, 373 (1989).
[CrossRef] [PubMed]

P. D. Drummond and S. J. Carter, "Quantum field theory of squeezing in solitons," J. Opt. Soc. Am. B 4, 1565 (1987).
[CrossRef]

Fang, J. M.

F. Singer, M. J. Potasek, J. M. Fang, and M. C. Teich, "Femtosecond solitons in nonlinear optical fibers: classical and quantum effects," Phys. Rev. A 46, 4192 (1992).
[CrossRef] [PubMed]

Gordon, J. P.

Hardman, A. D.

P. D. Drummond and A. D. Hardman, "Simulation of quantum effects in Raman-active waveguides," Europhys. Lett. 21, 279 (1993).
[CrossRef]

Haus, H. A.

Ippen, E. P.

Ippen, I. P.

Jonechis, L. G.

L. G. Jonechis and J. H. Shapiro, "Quantum propagation in a Kerr medium: lossless, dispersionless fiber," J. Opt. Soc. Am. B 10, 1102 (1993).
[CrossRef]

F. X. Kärtner, L. G. Jonechis, and H. A. Haus, "Classical and quantum dynamics of a pulse in a dispersionless nonlinear fiber," Quantum Opt. 4, 379 (1992).
[CrossRef]

Kärtner, F. X.

Lai, Y.

Levenson, M. D.

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

Lin, C.

R. H. Stolen and C. Lin, "Self-phase-modulation in silica optical fibers," Phys. Rev. A 17, 1448 (1978).
[CrossRef]

Loudon, R.

K. J. Blow, R. Loudon, and S. J. D. Phoenix, "Quantum theory of nonlinear loop mirrors," Phys. Rev. A 45, 8064 (1992).
[CrossRef] [PubMed]

Phoenix, S. J. D.

K. J. Blow, R. Loudon, and S. J. D. Phoenix, "Quantum theory of nonlinear loop mirrors," Phys. Rev. A 45, 8064 (1992).
[CrossRef] [PubMed]

Potasek, M. J.

F. Singer, M. J. Potasek, J. M. Fang, and M. C. Teich, "Femtosecond solitons in nonlinear optical fibers: classical and quantum effects," Phys. Rev. A 46, 4192 (1992).
[CrossRef] [PubMed]

Rosenbluh, M.

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

Shapiro, J. H.

Shelby, R. M.

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

R. M. Shelby, P. D. Drummond, and S. J. Carter, "Phase-noise scaling in quantum soliton propagation," Phys. Rev. A 42, 2966 (1990).
[CrossRef] [PubMed]

P. D. Drummond, S. J. Carter, and R. M. Shelby, "Time dependence of quantum fluctuations in solitons," Opt. Lett. 14, 373 (1989).
[CrossRef] [PubMed]

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

Shirasaki, M.

Singer, F.

F. Singer, M. J. Potasek, J. M. Fang, and M. C. Teich, "Femtosecond solitons in nonlinear optical fibers: classical and quantum effects," Phys. Rev. A 46, 4192 (1992).
[CrossRef] [PubMed]

Stolen, R. H.

Teich, M. C.

F. Singer, M. J. Potasek, J. M. Fang, and M. C. Teich, "Femtosecond solitons in nonlinear optical fibers: classical and quantum effects," Phys. Rev. A 46, 4192 (1992).
[CrossRef] [PubMed]

Tomlinson, W. J.

Yu, S.-S.

Y. Lai and S.-S. Yu, "General quantum theory of nonlinear optical pulse propagation," Phys. Rev. A 51, 817 (1995).
[CrossRef] [PubMed]

Europhys. Lett. (1)

P. D. Drummond and A. D. Hardman, "Simulation of quantum effects in Raman-active waveguides," Europhys. Lett. 21, 279 (1993).
[CrossRef]

J. Opt. Soc. Am. B (8)

Opt. Lett. (6)

Phys. Rev. A (5)

Y. Lai and S.-S. Yu, "General quantum theory of nonlinear optical pulse propagation," Phys. Rev. A 51, 817 (1995).
[CrossRef] [PubMed]

F. Singer, M. J. Potasek, J. M. Fang, and M. C. Teich, "Femtosecond solitons in nonlinear optical fibers: classical and quantum effects," Phys. Rev. A 46, 4192 (1992).
[CrossRef] [PubMed]

K. J. Blow, R. Loudon, and S. J. D. Phoenix, "Quantum theory of nonlinear loop mirrors," Phys. Rev. A 45, 8064 (1992).
[CrossRef] [PubMed]

R. M. Shelby, P. D. Drummond, and S. J. Carter, "Phase-noise scaling in quantum soliton propagation," Phys. Rev. A 42, 2966 (1990).
[CrossRef] [PubMed]

R. H. Stolen and C. Lin, "Self-phase-modulation in silica optical fibers," Phys. Rev. A 17, 1448 (1978).
[CrossRef]

Phys. Rev. B (1)

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

Phys. Rev. Lett. (2)

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

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

Quantum Opt. (1)

F. X. Kärtner, L. G. Jonechis, and H. A. Haus, "Classical and quantum dynamics of a pulse in a dispersionless nonlinear fiber," Quantum Opt. 4, 379 (1992).
[CrossRef]

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 (6)

Fig. 1
Fig. 1

Squeezing ratio versus normalized propagation distance for 20-ps (FWHM) sech pulses at five temperatures at the 1.3-μm wavelength. The curves at 273 and 298 K are too close to be resolved. Without the Raman effect and third-order dispersion, one normalized propagation distance unit = 1.0 rad nonlinear phase shift.

Fig. 2
Fig. 2

Squeezing ratio versus normalized propagation distance for 20-ps (FWHM) square pulses at five temperatures at the 1.3-μm wavelength. Without the Raman effect and third-order dispersion, one normalized propagation distance unit = 1.0 rad nonlinear phase shift.

Fig. 3
Fig. 3

Squeezing ratio versus normalized propagation distance for 2-ps (FWHM) square pulses at 77 K at the 1.3-μm wavelength. KR, Raman only; D3, third-order dispersion only; KR + D3, both; dotted curve, neither. The dotted curve and the curve labeled KR are too close to be resolved. Without the Raman effect and third-order dispersion, one normalized propagation distance unit = 1.0 rad nonlinear phase shift.

Fig. 4
Fig. 4

Squeezing ratio versus normalized propagation distance for 50-fs (FWHM) pulses at 77 K at the 1.55-μm wavelength. KR, Raman only; D3, third-order dispersion only; KR + D3, both; dotted curve, neither. Without the Raman effect and third-order dispersion, one normalized propagation distance unit = 0.5 rad nonlinear phase shift.

Fig. 5
Fig. 5

Squeezing ratio versus normalized propagation distance for 100-fs (FWHM) pulses at 77 K at the 1.55-μm wavelength. KR, Raman only; D3, third-order dispersion only; KR + D3, both; dotted curve, neither. Without the Raman effect and third-order dispersion, one normalized propagation distance unit = 0.5 rad nonlinear phase shift.

Fig. 6
Fig. 6

Squeezing ratio versus normalized propagation distance for 100-fs (FWHM) pulses at five temperatures at the 1.55-μm wavelength. Without the Raman effect and third-order dispersion, one normalized propagation distance unit = 0.5 rad nonlinear phase shift.

Equations (16)

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

z U ( z , t ) = i d 2 2 t 2 U ( z , t ) + d 3 3 t 3 U ( z , t ) + i k i U ( z , t ) 2 U ( z , t ) + i [ - t h ( t - τ ) U ( z , τ ) 2 d τ ] U ( z , t ) .
A R ( Ω ) 2 Im [ h ( t ) exp ( i Ω t ) d t ] .
h ( t ) = 1 π 0 A R ( Ω ) sin ( Ω t ) d Ω if t 0 , = 0 if t < 0.
A R ( Ω ) = k R [ γ γ 2 + ( Ω - Ω 0 ) 2 - γ γ 2 + ( Ω + Ω 0 ) 2 ] ,
h ( t ) = k R Im { exp [ ( - γ + i Ω 0 ) t ] } if t 0 , = 0 if t < 0.
k i + 0 h ( t ) d t = k i + k R Ω 0 γ 2 + Ω 0 2 .
k i = 0.82 ( ω 0 k 0 n 2 ) / A eff ,
k R Ω 0 / ( γ 2 + Ω 0 2 ) = 0.18 ( ω 0 k 0 n 2 ) / A eff .
z u ^ ( z , t ) = i d i 2 t 2 u ^ ( z , t ) + d 3 3 t 3 u ^ ( z , t ) + 2 i k i U 0 ( z , t ) 2 u ^ ( z , t ) + i k i U 0 2 ( z , t ) u ^ ( z , t ) + i - t h ( t - τ ) U 0 ( z , τ ) 2 d τ u ^ ( z , t ) + i U 0 ( z , t ) - t h ( t - t ) U 0 * ( z , τ ) u ^ ( z , τ ) d τ + i U 0 ( z , t ) - t h ( t - τ ) U 0 ( z , τ ) u ^ ( z , τ ) d τ + i Γ ^ ( z , t ) U 0 ( z , t ) .
Γ ^ ( z , t 1 ) Γ ^ ( z , t 2 ) = N n ( t 1 - t 2 ) δ ( z - z ) ,
N n ( t ) = 1 2 π 0 A R ( Ω ) { [ n Ω ( T ) + 1 ] exp ( - i Ω t ) + n Ω ( T ) exp ( i Ω t ) } d Ω .
Var [ f ( t ) u ^ ( L , t ) ] = Var [ u A ( 0 , t ) u ^ ( 0 , t ) ] + 0 L Q ( t 1 , t 2 , z ) N n ( t 1 - t 2 ) × d t 1 d t 2 d z .
Q ( t 1 , t 2 , z ) = ½ Re [ u A ( z , t 1 ) u A * ( z , t 2 ) U 0 * ( z , t 1 ) U 0 ( z , t 2 ) - u A * ( z , t 1 ) u A * ( z , t 2 ) U 0 ( z , t 1 ) U 0 ( z , t 2 ) ] .
z u A ( z , t ) = i d i 2 t 2 u A ( z , t ) + d 3 3 t 3 u A ( z , t ) + 2 i k i U 0 ( z , t ) 2 u A ( z , t ) - i k i U 0 2 ( z , t ) u A * ( z , t ) + i - t h ( t - τ ) U 0 ( z , τ ) 2 d τ u A ( z , t ) + i U 0 ( z , t ) t h ( τ - t ) U 0 * ( z , τ ) u A ( z , τ ) d τ - i U 0 ( z , t ) t h ( τ - t ) U 0 ( z , τ ) u A * ( z , τ ) d τ .
R ( L ) min [ Θ ] Var [ f L ( t ) u ^ ( L , t ) ] / Var [ f L ( t ) u ^ ( 0 , t ) ] .
f L ( t ) = U 0 ( L , t ) exp ( i Θ ) .

Metrics