Abstract

Nonlinear processes that rely on phase matching in optical fibers can be highly sensitive to the dispersive properties of the fibers. As an example of this sensitivity and of the resulting complex behavior that may occur, we show that multiple frequencies can be generated from a single pump frequency owing to stimulated four-photon mixing on single-mode fibers. We compare the nature of this multiple-frequency generation in two fibers with widely different dispersion characteristics.

© 1989 Optical Society of America

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References

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  1. H. G. Winful, “Nonlinear optical phenomena in single mode fibers,” in Optical Fiber Transmission, E. E. Basch, ed. (Sams, Indianapolis, Ind., 1987), pp. 179–240.
  2. R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. QE-18, 1062–1072 (1982).
    [CrossRef]
  3. C. Lin, W. A. Reed, A. D. Pearson, and H.-T. Shang, “Phase matching in the minimum chromatic dispersion region of single-mode fibers for stimulated four-photon mixing,” Opt. Lett. 6, 493–495 (1981).
    [CrossRef] [PubMed]
  4. S. J. Garth and C. Pask, “Four-photon mixing and dispersion in single-mode fibers,” Opt. Lett. 11, 380–382 (1986).
    [CrossRef] [PubMed]
  5. C. Lin, V. T. Nguyen, and W. G. French, “Wideband near-IR continuum (0.7–2.1 μm) generated in low-loss optical fibers,” Electron. Lett. 14, 822–823 (1978).
    [CrossRef]
  6. S. J. Garth, “Phase-matching the stimulated four photon mixing process on single-mode fibers operating in the 1.55-μm region,” Opt. Lett. 13, 1117–1119 (1988).
    [CrossRef] [PubMed]
  7. J. W. Fleming, “Material dispersion in lightguide glasses,” Electron. Lett. 14, 326–328 (1978).
    [CrossRef]
  8. A. Vatarescu, “Light conversion in nonlinear monomode optical fibers,” IEEE J. Lightwave Technol. LT-5, 1652–1659 (1987).
    [CrossRef]
  9. K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “Cw three-wave mixing in single mode optical fibers,” J. Appl. Phys. 49, 5098–5106 (1978).
    [CrossRef]
  10. N. Shibata, R. P. Braun, and R. G. Waarts, “Crosstalk due to three-wave mixing process in a coherent single-mode transmission line,” Electron. Lett. 22, 675–677 (1986).
    [CrossRef]
  11. V. V. Grigor’yants, V. I. Smirnov, and Yu. K. Chamorovskii, “Generation of wide-band optical continuum in fiber waveguides,” Sov. J. Quantum Electron. 12, 841–847 (1982).
    [CrossRef]
  12. M. Monerie, “Propagation in doubly clad single mode fibers,” IEEE J. Quantum Electron. QE-18, 535–542 (1982).
    [CrossRef]

1988 (1)

1987 (1)

A. Vatarescu, “Light conversion in nonlinear monomode optical fibers,” IEEE J. Lightwave Technol. LT-5, 1652–1659 (1987).
[CrossRef]

1986 (2)

S. J. Garth and C. Pask, “Four-photon mixing and dispersion in single-mode fibers,” Opt. Lett. 11, 380–382 (1986).
[CrossRef] [PubMed]

N. Shibata, R. P. Braun, and R. G. Waarts, “Crosstalk due to three-wave mixing process in a coherent single-mode transmission line,” Electron. Lett. 22, 675–677 (1986).
[CrossRef]

1982 (3)

V. V. Grigor’yants, V. I. Smirnov, and Yu. K. Chamorovskii, “Generation of wide-band optical continuum in fiber waveguides,” Sov. J. Quantum Electron. 12, 841–847 (1982).
[CrossRef]

M. Monerie, “Propagation in doubly clad single mode fibers,” IEEE J. Quantum Electron. QE-18, 535–542 (1982).
[CrossRef]

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

1981 (1)

1978 (3)

C. Lin, V. T. Nguyen, and W. G. French, “Wideband near-IR continuum (0.7–2.1 μm) generated in low-loss optical fibers,” Electron. Lett. 14, 822–823 (1978).
[CrossRef]

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “Cw three-wave mixing in single mode optical fibers,” J. Appl. Phys. 49, 5098–5106 (1978).
[CrossRef]

J. W. Fleming, “Material dispersion in lightguide glasses,” Electron. Lett. 14, 326–328 (1978).
[CrossRef]

Bjorkholm, J. E.

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

Braun, R. P.

N. Shibata, R. P. Braun, and R. G. Waarts, “Crosstalk due to three-wave mixing process in a coherent single-mode transmission line,” Electron. Lett. 22, 675–677 (1986).
[CrossRef]

Chamorovskii, Yu. K.

V. V. Grigor’yants, V. I. Smirnov, and Yu. K. Chamorovskii, “Generation of wide-band optical continuum in fiber waveguides,” Sov. J. Quantum Electron. 12, 841–847 (1982).
[CrossRef]

Fleming, J. W.

J. W. Fleming, “Material dispersion in lightguide glasses,” Electron. Lett. 14, 326–328 (1978).
[CrossRef]

French, W. G.

C. Lin, V. T. Nguyen, and W. G. French, “Wideband near-IR continuum (0.7–2.1 μm) generated in low-loss optical fibers,” Electron. Lett. 14, 822–823 (1978).
[CrossRef]

Garth, S. J.

Grigor’yants, V. V.

V. V. Grigor’yants, V. I. Smirnov, and Yu. K. Chamorovskii, “Generation of wide-band optical continuum in fiber waveguides,” Sov. J. Quantum Electron. 12, 841–847 (1982).
[CrossRef]

Hill, K. O.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “Cw three-wave mixing in single mode optical fibers,” J. Appl. Phys. 49, 5098–5106 (1978).
[CrossRef]

Johnson, D. C.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “Cw three-wave mixing in single mode optical fibers,” J. Appl. Phys. 49, 5098–5106 (1978).
[CrossRef]

Kawasaki, B. S.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “Cw three-wave mixing in single mode optical fibers,” J. Appl. Phys. 49, 5098–5106 (1978).
[CrossRef]

Lin, C.

C. Lin, W. A. Reed, A. D. Pearson, and H.-T. Shang, “Phase matching in the minimum chromatic dispersion region of single-mode fibers for stimulated four-photon mixing,” Opt. Lett. 6, 493–495 (1981).
[CrossRef] [PubMed]

C. Lin, V. T. Nguyen, and W. G. French, “Wideband near-IR continuum (0.7–2.1 μm) generated in low-loss optical fibers,” Electron. Lett. 14, 822–823 (1978).
[CrossRef]

MacDonald, R. I.

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “Cw three-wave mixing in single mode optical fibers,” J. Appl. Phys. 49, 5098–5106 (1978).
[CrossRef]

Monerie, M.

M. Monerie, “Propagation in doubly clad single mode fibers,” IEEE J. Quantum Electron. QE-18, 535–542 (1982).
[CrossRef]

Nguyen, V. T.

C. Lin, V. T. Nguyen, and W. G. French, “Wideband near-IR continuum (0.7–2.1 μm) generated in low-loss optical fibers,” Electron. Lett. 14, 822–823 (1978).
[CrossRef]

Pask, C.

Pearson, A. D.

Reed, W. A.

Shang, H.-T.

Shibata, N.

N. Shibata, R. P. Braun, and R. G. Waarts, “Crosstalk due to three-wave mixing process in a coherent single-mode transmission line,” Electron. Lett. 22, 675–677 (1986).
[CrossRef]

Smirnov, V. I.

V. V. Grigor’yants, V. I. Smirnov, and Yu. K. Chamorovskii, “Generation of wide-band optical continuum in fiber waveguides,” Sov. J. Quantum Electron. 12, 841–847 (1982).
[CrossRef]

Stolen, R. H.

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

Vatarescu, A.

A. Vatarescu, “Light conversion in nonlinear monomode optical fibers,” IEEE J. Lightwave Technol. LT-5, 1652–1659 (1987).
[CrossRef]

Waarts, R. G.

N. Shibata, R. P. Braun, and R. G. Waarts, “Crosstalk due to three-wave mixing process in a coherent single-mode transmission line,” Electron. Lett. 22, 675–677 (1986).
[CrossRef]

Winful, H. G.

H. G. Winful, “Nonlinear optical phenomena in single mode fibers,” in Optical Fiber Transmission, E. E. Basch, ed. (Sams, Indianapolis, Ind., 1987), pp. 179–240.

Electron. Lett. (3)

C. Lin, V. T. Nguyen, and W. G. French, “Wideband near-IR continuum (0.7–2.1 μm) generated in low-loss optical fibers,” Electron. Lett. 14, 822–823 (1978).
[CrossRef]

J. W. Fleming, “Material dispersion in lightguide glasses,” Electron. Lett. 14, 326–328 (1978).
[CrossRef]

N. Shibata, R. P. Braun, and R. G. Waarts, “Crosstalk due to three-wave mixing process in a coherent single-mode transmission line,” Electron. Lett. 22, 675–677 (1986).
[CrossRef]

IEEE J. Lightwave Technol. (1)

A. Vatarescu, “Light conversion in nonlinear monomode optical fibers,” IEEE J. Lightwave Technol. LT-5, 1652–1659 (1987).
[CrossRef]

IEEE J. Quantum Electron. (2)

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

M. Monerie, “Propagation in doubly clad single mode fibers,” IEEE J. Quantum Electron. QE-18, 535–542 (1982).
[CrossRef]

J. Appl. Phys. (1)

K. O. Hill, D. C. Johnson, B. S. Kawasaki, and R. I. MacDonald, “Cw three-wave mixing in single mode optical fibers,” J. Appl. Phys. 49, 5098–5106 (1978).
[CrossRef]

Opt. Lett. (3)

Sov. J. Quantum Electron. (1)

V. V. Grigor’yants, V. I. Smirnov, and Yu. K. Chamorovskii, “Generation of wide-band optical continuum in fiber waveguides,” Sov. J. Quantum Electron. 12, 841–847 (1982).
[CrossRef]

Other (1)

H. G. Winful, “Nonlinear optical phenomena in single mode fibers,” in Optical Fiber Transmission, E. E. Basch, ed. (Sams, Indianapolis, Ind., 1987), pp. 179–240.

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Figures (6)

Fig. 1
Fig. 1

Pump and output wavelengths for a step-index fiber with core radius 4.5 μm and refractive-index differences 0.004. Also shown is the chromatic dipersion in the vicinity of the zero-dispersion wavelength.

Fig. 2
Fig. 2

Pump and output wavelengths showing the second- and third-order generated waves. The dashed curves correspond to the Stokes and anti-Stokes waves generated from the first anti-Stokes wave, and the dotted curves to the Stokes and anti-Stokes waves generated from the second anti-Stokes wave. Fiber parameters are as for Fig. 1.

Fig. 3
Fig. 3

Typical output spectrum corresponding to a pump wavelength of λp = 1.3105 μm in Fig. 2. Fiber parameters are as for Fig. 1.

Fig. 4
Fig. 4

Pump and output wavelengths for a W fiber. Fiber parameters are taken from Ref. 5. Also shown is the chromatic dipersion curve indicating the presence of three distinct zero-dispersion wavelengths.

Fig. 5
Fig. 5

Pump and output wavelengths showing the second-order generated waves (dashed curves). Fiber parameters are as for Fig. 4.

Fig. 6
Fig. 6

Typical output spectrum corresponding to a pump wavelength of λp = 1.5 μm in Fig. 5. Fiber parameters are as for Fig. 4.

Equations (4)

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2 ω p = ω a + ω s .
Δ β p = 2 β ( ω p ) β ( ω a ) β ( ω s ) = 0 .
2 ω a = ω aa + ω as
Δ β a = 2 β ( ω a ) β ( ω aa ) β ( ω as ) = 0 ,

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