Abstract

We describe a simple scheme to allow for the achievement of flat gain over ultrabroad bands with a single-pump fiber-optic parametric amplifier operating in the zero-dispersion wavelength region. The proposed method, based on a multisection dispersion-tailored in-line nonlinear fiber arrangement, is demonstrated by both modulational instability theory and numerical simulations of the nonlinear Schrödinger equation. The results show that the design can be adjusted to generate gain bands that exceed either 100 nm with a ripple of less than 0.2 dB and for a pump power of only 500 mW, or even 200 nm when a pump power of 5 W is used. In addition, the robustness of this gain-flattening technique has been numerically checked against random fluctuations of the zero-dispersion wavelength in each of the fiber sections.

© 2003 Optical Society of America

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  1. F. S. Yang, M. E. Marhic, and L. G. Kazovsky, “CW fiber optical parametric amplifier with net gain and wavelength conversion efficiency >1,” Electron. Lett. 32, 2236–2238 (1996).
    [CrossRef]
  2. J. Hansryd and P. A. Andrekson, “Broad-band continuous-wave-pumped fiber optical parametric amplifier with 49-dB gain and wavelength-conversion efficiency,” IEEE Photon. Technol. Lett. 13, 194–196 (2001).
    [CrossRef]
  3. C. J. S. de Matos, D. A. Chestnut, P. C. Reeves-Hall, and J. R. Taylor, “Continuous-wave-pumped Raman-assisted fiber optical parametric amplifier and wavelength converter in conventional dispersion-shifted fiber,” Opt. Lett. 26, 1583–1585 (2001).
    [CrossRef]
  4. J. L. Blows and S. E. French, “Low-noise-figure optical parametric amplifier with a continuous-wave frequency-modulated pump,” Opt. Lett. 27, 491–493 (2002).
    [CrossRef]
  5. W. Imajuku, A. Takada, and Y. Yamabayashi, “In-line coher-ent optical amplifier with noise figure lower than 3dB quantum limit,” Electron. Lett. 36, 63–65 (2000).
    [CrossRef]
  6. M. N. Islam and Ö. Boyraz, “Fiber parametric amplifiers for wavelength band conversion,” IEEE J. Sel. Top. Quantum Electron. 8, 527–537 (2002).
    [CrossRef]
  7. J. Hansryd, P. A. Andrekson, M. Westlund, J. Lie, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
    [CrossRef]
  8. M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. 21, 573–575 (1996).
    [CrossRef] [PubMed]
  9. M. E. Marhic, Y. Park, F. S. Yang, and L. G. Kazovsky, “Broadband fiber-optical parametric amplifiers and wavelength converters with low-ripple Chebyshev gain spectra,” Opt. Lett. 21, 1354–1356 (1996).
    [CrossRef] [PubMed]
  10. C. J. McKinstrie and S. Radic, “Parametric amplifiers driven by two pump waves with dissimilar frequencies,” Opt. Lett. 27, 1138–1140 (2002).
    [CrossRef]
  11. K. Inoue, “Arrangement of fiber pieces for a wide wavelength conversion range by fiber four-wave mixing,” Opt. Lett. 19, 1189–1191 (1994).
    [CrossRef] [PubMed]
  12. M. E. Marhic, F. S. Yang, M.-C. Ho, and L. G. Kazovsky, “High-nonlinearity fiber optical parametric amplifier with periodic dispersion compensation,” J. Lightwave Technol. 17, 210–215 (1999).
    [CrossRef]
  13. J. Kim, O. Boyraz, J. H. Lim, and M. N. Islam, “Gain enhancement in cascaded fiber parametric amplifier with quasi-phase matching: theory and experiment,” J. Lightwave Technol. 19, 247–251 (2001).
    [CrossRef]
  14. Y. Su, L. Wang, A. Agarwal, and P. Kumar, “All-optical lim-iter using gain flattened fibre optical parametric amplifier,” Electron. Lett. 36, 1103–1105 (2000).
    [CrossRef]
  15. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif., 2001).
  16. A. Hasegawa and W. F. Brinkman, “Tunable coherent IR and FIR sources utilizing modulational instability,” IEEE J. Quantum Electron. QE-16, 694–697 (1980).
    [CrossRef]
  17. R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
    [CrossRef]
  18. D. Gindre, H. Maillotte, J. Monneret, E. Lantz, and C. Froehly, “Coherent picosecond parametric amplification through a Kerr-induced index grating in a single-mode fiber,” Opt. Commun. 112, 75–79 (1994).
    [CrossRef]
  19. M. Eiselt, R. M. Jopson, and R. H. Stolen, “Nondestructive position-resolved measurement of the zero-dipersion wavelength in an optical fiber,” J. Lightwave Technol. 15, 135–143 (1997).
    [CrossRef]
  20. M. Karlsson, “Four-wave mixing in fibers with randomly varying zero-dispersion wavelength,” J. Opt. Soc. Am. B 15, 2269–2275 (1998).
    [CrossRef]
  21. N. Kuwaki and M. Ohashi, “Evaluation of longitudinal chromatic dispersion,” J. Lightwave Technol. 8, 1476–1481 (1990).
    [CrossRef]
  22. S. E. French and J. L. Blows, “Continuous wave optical parametric amplifier with flattened gain,” in Optical Amplifiers and Their Applications, N. E. Jolley, J. D. Minelly, and Y. Nakano, eds., Vol. 60 of OSA Trends in Optics and Photonics (Optical Society of America, Washington D.C., 2001), Postdeadline paper PD7.

2002

J. L. Blows and S. E. French, “Low-noise-figure optical parametric amplifier with a continuous-wave frequency-modulated pump,” Opt. Lett. 27, 491–493 (2002).
[CrossRef]

M. N. Islam and Ö. Boyraz, “Fiber parametric amplifiers for wavelength band conversion,” IEEE J. Sel. Top. Quantum Electron. 8, 527–537 (2002).
[CrossRef]

J. Hansryd, P. A. Andrekson, M. Westlund, J. Lie, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

C. J. McKinstrie and S. Radic, “Parametric amplifiers driven by two pump waves with dissimilar frequencies,” Opt. Lett. 27, 1138–1140 (2002).
[CrossRef]

2001

2000

W. Imajuku, A. Takada, and Y. Yamabayashi, “In-line coher-ent optical amplifier with noise figure lower than 3dB quantum limit,” Electron. Lett. 36, 63–65 (2000).
[CrossRef]

Y. Su, L. Wang, A. Agarwal, and P. Kumar, “All-optical lim-iter using gain flattened fibre optical parametric amplifier,” Electron. Lett. 36, 1103–1105 (2000).
[CrossRef]

1999

1998

1997

M. Eiselt, R. M. Jopson, and R. H. Stolen, “Nondestructive position-resolved measurement of the zero-dipersion wavelength in an optical fiber,” J. Lightwave Technol. 15, 135–143 (1997).
[CrossRef]

1996

1994

K. Inoue, “Arrangement of fiber pieces for a wide wavelength conversion range by fiber four-wave mixing,” Opt. Lett. 19, 1189–1191 (1994).
[CrossRef] [PubMed]

D. Gindre, H. Maillotte, J. Monneret, E. Lantz, and C. Froehly, “Coherent picosecond parametric amplification through a Kerr-induced index grating in a single-mode fiber,” Opt. Commun. 112, 75–79 (1994).
[CrossRef]

1990

N. Kuwaki and M. Ohashi, “Evaluation of longitudinal chromatic dispersion,” J. Lightwave Technol. 8, 1476–1481 (1990).
[CrossRef]

1982

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
[CrossRef]

1980

A. Hasegawa and W. F. Brinkman, “Tunable coherent IR and FIR sources utilizing modulational instability,” IEEE J. Quantum Electron. QE-16, 694–697 (1980).
[CrossRef]

Agarwal, A.

Y. Su, L. Wang, A. Agarwal, and P. Kumar, “All-optical lim-iter using gain flattened fibre optical parametric amplifier,” Electron. Lett. 36, 1103–1105 (2000).
[CrossRef]

Andrekson, P. A.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Lie, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

J. Hansryd and P. A. Andrekson, “Broad-band continuous-wave-pumped fiber optical parametric amplifier with 49-dB gain and wavelength-conversion efficiency,” IEEE Photon. Technol. Lett. 13, 194–196 (2001).
[CrossRef]

Bjorkholm, J. E.

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
[CrossRef]

Blows, J. L.

Boyraz, O.

Boyraz, Ö.

M. N. Islam and Ö. Boyraz, “Fiber parametric amplifiers for wavelength band conversion,” IEEE J. Sel. Top. Quantum Electron. 8, 527–537 (2002).
[CrossRef]

Brinkman, W. F.

A. Hasegawa and W. F. Brinkman, “Tunable coherent IR and FIR sources utilizing modulational instability,” IEEE J. Quantum Electron. QE-16, 694–697 (1980).
[CrossRef]

Chestnut, D. A.

Chiang, T.-K.

de Matos, C. J. S.

Eiselt, M.

M. Eiselt, R. M. Jopson, and R. H. Stolen, “Nondestructive position-resolved measurement of the zero-dipersion wavelength in an optical fiber,” J. Lightwave Technol. 15, 135–143 (1997).
[CrossRef]

French, S. E.

Froehly, C.

D. Gindre, H. Maillotte, J. Monneret, E. Lantz, and C. Froehly, “Coherent picosecond parametric amplification through a Kerr-induced index grating in a single-mode fiber,” Opt. Commun. 112, 75–79 (1994).
[CrossRef]

Gindre, D.

D. Gindre, H. Maillotte, J. Monneret, E. Lantz, and C. Froehly, “Coherent picosecond parametric amplification through a Kerr-induced index grating in a single-mode fiber,” Opt. Commun. 112, 75–79 (1994).
[CrossRef]

Hansryd, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Lie, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

J. Hansryd and P. A. Andrekson, “Broad-band continuous-wave-pumped fiber optical parametric amplifier with 49-dB gain and wavelength-conversion efficiency,” IEEE Photon. Technol. Lett. 13, 194–196 (2001).
[CrossRef]

Hasegawa, A.

A. Hasegawa and W. F. Brinkman, “Tunable coherent IR and FIR sources utilizing modulational instability,” IEEE J. Quantum Electron. QE-16, 694–697 (1980).
[CrossRef]

Hedekvist, P.-O.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Lie, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

Ho, M.-C.

Imajuku, W.

W. Imajuku, A. Takada, and Y. Yamabayashi, “In-line coher-ent optical amplifier with noise figure lower than 3dB quantum limit,” Electron. Lett. 36, 63–65 (2000).
[CrossRef]

Inoue, K.

Islam, M. N.

M. N. Islam and Ö. Boyraz, “Fiber parametric amplifiers for wavelength band conversion,” IEEE J. Sel. Top. Quantum Electron. 8, 527–537 (2002).
[CrossRef]

J. Kim, O. Boyraz, J. H. Lim, and M. N. Islam, “Gain enhancement in cascaded fiber parametric amplifier with quasi-phase matching: theory and experiment,” J. Lightwave Technol. 19, 247–251 (2001).
[CrossRef]

Jopson, R. M.

M. Eiselt, R. M. Jopson, and R. H. Stolen, “Nondestructive position-resolved measurement of the zero-dipersion wavelength in an optical fiber,” J. Lightwave Technol. 15, 135–143 (1997).
[CrossRef]

Kagi, N.

Karlsson, M.

Kazovsky, L. G.

Kim, J.

Kumar, P.

Y. Su, L. Wang, A. Agarwal, and P. Kumar, “All-optical lim-iter using gain flattened fibre optical parametric amplifier,” Electron. Lett. 36, 1103–1105 (2000).
[CrossRef]

Kuwaki, N.

N. Kuwaki and M. Ohashi, “Evaluation of longitudinal chromatic dispersion,” J. Lightwave Technol. 8, 1476–1481 (1990).
[CrossRef]

Lantz, E.

D. Gindre, H. Maillotte, J. Monneret, E. Lantz, and C. Froehly, “Coherent picosecond parametric amplification through a Kerr-induced index grating in a single-mode fiber,” Opt. Commun. 112, 75–79 (1994).
[CrossRef]

Lie, J.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Lie, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

Lim, J. H.

Maillotte, H.

D. Gindre, H. Maillotte, J. Monneret, E. Lantz, and C. Froehly, “Coherent picosecond parametric amplification through a Kerr-induced index grating in a single-mode fiber,” Opt. Commun. 112, 75–79 (1994).
[CrossRef]

Marhic, M. E.

McKinstrie, C. J.

Monneret, J.

D. Gindre, H. Maillotte, J. Monneret, E. Lantz, and C. Froehly, “Coherent picosecond parametric amplification through a Kerr-induced index grating in a single-mode fiber,” Opt. Commun. 112, 75–79 (1994).
[CrossRef]

Ohashi, M.

N. Kuwaki and M. Ohashi, “Evaluation of longitudinal chromatic dispersion,” J. Lightwave Technol. 8, 1476–1481 (1990).
[CrossRef]

Park, Y.

Radic, S.

Reeves-Hall, P. C.

Stolen, R. H.

M. Eiselt, R. M. Jopson, and R. H. Stolen, “Nondestructive position-resolved measurement of the zero-dipersion wavelength in an optical fiber,” J. Lightwave Technol. 15, 135–143 (1997).
[CrossRef]

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
[CrossRef]

Su, Y.

Y. Su, L. Wang, A. Agarwal, and P. Kumar, “All-optical lim-iter using gain flattened fibre optical parametric amplifier,” Electron. Lett. 36, 1103–1105 (2000).
[CrossRef]

Takada, A.

W. Imajuku, A. Takada, and Y. Yamabayashi, “In-line coher-ent optical amplifier with noise figure lower than 3dB quantum limit,” Electron. Lett. 36, 63–65 (2000).
[CrossRef]

Taylor, J. R.

Wang, L.

Y. Su, L. Wang, A. Agarwal, and P. Kumar, “All-optical lim-iter using gain flattened fibre optical parametric amplifier,” Electron. Lett. 36, 1103–1105 (2000).
[CrossRef]

Westlund, M.

J. Hansryd, P. A. Andrekson, M. Westlund, J. Lie, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

Yamabayashi, Y.

W. Imajuku, A. Takada, and Y. Yamabayashi, “In-line coher-ent optical amplifier with noise figure lower than 3dB quantum limit,” Electron. Lett. 36, 63–65 (2000).
[CrossRef]

Yang, F. S.

Electron. Lett.

F. S. Yang, M. E. Marhic, and L. G. Kazovsky, “CW fiber optical parametric amplifier with net gain and wavelength conversion efficiency >1,” Electron. Lett. 32, 2236–2238 (1996).
[CrossRef]

W. Imajuku, A. Takada, and Y. Yamabayashi, “In-line coher-ent optical amplifier with noise figure lower than 3dB quantum limit,” Electron. Lett. 36, 63–65 (2000).
[CrossRef]

Y. Su, L. Wang, A. Agarwal, and P. Kumar, “All-optical lim-iter using gain flattened fibre optical parametric amplifier,” Electron. Lett. 36, 1103–1105 (2000).
[CrossRef]

IEEE J. Quantum Electron.

A. Hasegawa and W. F. Brinkman, “Tunable coherent IR and FIR sources utilizing modulational instability,” IEEE J. Quantum Electron. QE-16, 694–697 (1980).
[CrossRef]

R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18, 1062–1072 (1982).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. N. Islam and Ö. Boyraz, “Fiber parametric amplifiers for wavelength band conversion,” IEEE J. Sel. Top. Quantum Electron. 8, 527–537 (2002).
[CrossRef]

J. Hansryd, P. A. Andrekson, M. Westlund, J. Lie, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. 8, 506–520 (2002).
[CrossRef]

IEEE Photon. Technol. Lett.

J. Hansryd and P. A. Andrekson, “Broad-band continuous-wave-pumped fiber optical parametric amplifier with 49-dB gain and wavelength-conversion efficiency,” IEEE Photon. Technol. Lett. 13, 194–196 (2001).
[CrossRef]

J. Lightwave Technol.

M. Eiselt, R. M. Jopson, and R. H. Stolen, “Nondestructive position-resolved measurement of the zero-dipersion wavelength in an optical fiber,” J. Lightwave Technol. 15, 135–143 (1997).
[CrossRef]

M. E. Marhic, F. S. Yang, M.-C. Ho, and L. G. Kazovsky, “High-nonlinearity fiber optical parametric amplifier with periodic dispersion compensation,” J. Lightwave Technol. 17, 210–215 (1999).
[CrossRef]

J. Kim, O. Boyraz, J. H. Lim, and M. N. Islam, “Gain enhancement in cascaded fiber parametric amplifier with quasi-phase matching: theory and experiment,” J. Lightwave Technol. 19, 247–251 (2001).
[CrossRef]

N. Kuwaki and M. Ohashi, “Evaluation of longitudinal chromatic dispersion,” J. Lightwave Technol. 8, 1476–1481 (1990).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

D. Gindre, H. Maillotte, J. Monneret, E. Lantz, and C. Froehly, “Coherent picosecond parametric amplification through a Kerr-induced index grating in a single-mode fiber,” Opt. Commun. 112, 75–79 (1994).
[CrossRef]

Opt. Lett.

Other

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, San Diego, Calif., 2001).

S. E. French and J. L. Blows, “Continuous wave optical parametric amplifier with flattened gain,” in Optical Amplifiers and Their Applications, N. E. Jolley, J. D. Minelly, and Y. Nakano, eds., Vol. 60 of OSA Trends in Optics and Photonics (Optical Society of America, Washington D.C., 2001), Postdeadline paper PD7.

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Figures (5)

Fig. 1
Fig. 1

Schematic of the proposed multisection optical parametric amplifier architecture.

Fig. 2
Fig. 2

Small-signal gain versus wavelength at the amplifier output for pump power P0=500 mW and wavelength λP=1550 nm (bold solid curve): (a) successive output gain bands Gk after each fiber segment and (b) differential gains Gk-Gk-1 (k=2,, 4) in one fiber segment.

Fig. 3
Fig. 3

Small-signal gain band versus propagation in a four-section FOPA for pump power P0=500 mW. Same parameters as in Fig. 2.

Fig. 4
Fig. 4

(a) ZDW map versus amplifier length for the multisection FOPA, without longitudinal fluctuations (dashed curve) and with longitudinal fluctuations (solid curve). (b) Small-signal gain versus wavelength at the amplifier output in the presence of random fluctuations of the ZDW, with the same parameters as in Fig. 2. The solid and dashed curves correspond, respectively, to the cases with and without ZDW fluctuations.

Fig. 5
Fig. 5

(a) ZDW map versus amplifier length for the multisection FOPA, without longitudinal fluctuations (dashed curve) and with longitudinal fluctuations (solid curve) but with the average λ0 values adjusted to the nominal ones determined by the gain-flattening procedure. (b) Small-signal gain versus wavelength at the amplifier output in the presence of random fluctuations of the ZDW, with the same parameters as in Fig. 2. The solid and dashed curves correspond, respectively, to the cases with and without ZDW fluctuations.

Equations (15)

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Az+i β222At2-β363At3-i β4244At4=iγ|A|2A,
A(z, t)=[P0+u(z, t)]exp(iγP0z),
uz+i β222ut2-β363ut3-i β4244ut4=iγP0(u+u*),
u(z, t)=usexp[i(Ωt-Kz)]+uiexp[-(iΩt-Kz)],
[M][Y]=K[Y],
[Y(z, Ω)]T=[us(z, Ω), ui*(z, Ω)].
[M]=ΔβL+2γP0-β36 Ω3γP0-γP0-ΔβL-2γP0-β36 Ω3,
K±=-β36 Ω3±ΔβLΔβL4+γP01/2,
Y(z, Ω)=us(z, Ω)ui*(z, Ω)=a11ηexp(iK+z)+a2η-11exp(iK-z),
g=(γP0)2-κ221/2,
Ψ(z)=11-η2egz-η2 e-gzη(e-gz-egz)η(egz-e-gz)e-gz-η2 egz.
YN(zN, Ω)=k=1NΨ(zk)×Y(0, Ω).
Gk=10 log[|usk(Ln, Ω)|2].
β2(z)=β2LS(z)+β2SS(z),
β2LS(z)=A1×n=1msin(κ1,nz+ψ1,n)+A2×n=1msin(κ2,nz+ψ2,n),

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