Abstract

We investigate theoretically the conditions under which optical phase conjugation via difference-frequency generation compensates for the effects of dispersion and self-phase modulation in the propagation of ultrashort pulses through fibers. We find that it is desirable to operate in the regime of large fiber dispersion and that nearly perfect pulse reconstruction can occur even with appreciable depletion of the pump wave in the nonlinear crystal.

© 2000 Optical Society of America

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References

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  1. A. Yariv, D. Fekete, and D. M. Pepper, “Compensation for channel dispersion by nonlinear optical phase conjugation,” Opt. Lett. 4, 52–54 (1979).
    [CrossRef] [PubMed]
  2. J. H. Marburger, “Optical pulse integration and chirp reversal in degenerate four-wave mixing,” Appl. Phys. Lett. 32, 372–374 (1978).
    [CrossRef]
  3. R. A. Fisher, B. R. Suydam, and D. Yevick, “Optical phase conjugation for time-domain undoing of dispersive self-phase-modulation effects,” Opt. Lett. 8, 611–613 (1983).
    [CrossRef] [PubMed]
  4. S. Watanabe, T. Naito, and T. Chikama, “Compensation of chromatic dispersion in a single-mode fiber by optical phase conjugation,” IEEE Photonics Technol. Lett. 5, 92–95 (1993); A. H. Gnauck, R. M. Jopson, and R. M. Derosier, “10-Gb/s 360-km transmission over dispersive fiber using midsystem spectral inversion,” IEEE Photonics Technol. Lett. 5, 663–666 (1993); S. Watanabe, T. Chikama, G. Ishikawa, T. Terahara, and H. Kuwahara, “Compensation of pulse shape distortion due to chromatic dispersion and Kerr effect by optical phase conjugation,” IEEE Photonics Technol. Lett. IPTLEL 5, 1241–1243 (1993); R. I. Laming, D. J. Richardson, D. Taverner, and D. N. Payne, “Transmission of 6 ps linear pulses over 50 km of standard fiber using midpoint spectral inversion to eliminate dispersion,” IEEE J. Quantum Electron. IEJQA7 3, 2114–2119 (1994).
    [CrossRef]
  5. K. Kikuchi and C. Lorattanasane, “Transmission of 6 ps linear pulses over 50 km of standard fiber using midpoint spectral inversion to eliminate dispersion,” IEEE Photonics Technol. Lett. 6, 104–105 (1994); W. Forysiak and N. J. Doran, “Conjugate solitons in amplified optical fibre transmission systems,” Electron. Lett. 30, 154–155 (1994); N. J. Doran and W. Forysiak, “Phase conjugation for jitter and soliton–soliton compensation in soliton communications,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 Tech. Dig. Ser.-Opt. Soc. Am. (Optical Society of America, Washington, D.C., 1994), pp. 367–368; S. Chi and S. Wen, “Recovery of the soliton self-frequency shift by optical phase conjugation,” Opt. Lett. OPLEDP 19, 1705–1707 (1994); M. Yu, G. P. Agrawal, and C. J. McKinstrie, “Effect of residual dispersion in the phase-conjugation fiber on dispersion compensation in optical communication systems,” IEEE Photonics Technol. Lett. IPTLEL 7, 932–934 (1995).
    [CrossRef] [PubMed]
  6. S. Murata, A. Tomita, J. Shimizu, and A. Suzuki, “THz optical-frequency conversion of 1-Gb/s signals using highly nondegenerate four-wave mixing in an InGaAsP semiconductor laser,” IEEE Photonics Technol. Lett. 3, 1021–1023 (1991).
    [CrossRef]
  7. M. C. Tatham, G. Sherlock, and L. D. Westbrook, “Compensation of fibre chromatic dispersion by optical phase conjugation in a semiconductor laser amplifier,” Electron. Lett. 29, 1851–1852 (1995).
    [CrossRef]
  8. P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
    [CrossRef]
  9. L. Lefort and A. Barthelemy, “Revisiting optical phase conjugation by difference-frequency generation,” Opt. Lett. 21, 848–850 (1996).
    [CrossRef] [PubMed]
  10. M. L. Bortz, M. A. Arbore, and M. M. Fejer, “Quasi-phase-matched optical parametric amplification and oscillation in periodically poled LiNbO3 waveguides,” Opt. Lett. 20, 49–51 (1995).
    [CrossRef] [PubMed]
  11. See, for example, G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995), pp. 41–46.
  12. See, for example, M. J. Potasek, G. P. Agrawal, and S. C. Pinault, “Analytic and numerical study of pulse broadening in nonlinear dispersive optical fibers,” J. Opt. Soc. Am. B 3, 205–211 (1986).
    [CrossRef]
  13. See, for example, R. W. Boyd, Nonlinear Optics (Academic, Boston, 1992), pp. 241–252.

1996

1995

M. C. Tatham, G. Sherlock, and L. D. Westbrook, “Compensation of fibre chromatic dispersion by optical phase conjugation in a semiconductor laser amplifier,” Electron. Lett. 29, 1851–1852 (1995).
[CrossRef]

M. L. Bortz, M. A. Arbore, and M. M. Fejer, “Quasi-phase-matched optical parametric amplification and oscillation in periodically poled LiNbO3 waveguides,” Opt. Lett. 20, 49–51 (1995).
[CrossRef] [PubMed]

1991

S. Murata, A. Tomita, J. Shimizu, and A. Suzuki, “THz optical-frequency conversion of 1-Gb/s signals using highly nondegenerate four-wave mixing in an InGaAsP semiconductor laser,” IEEE Photonics Technol. Lett. 3, 1021–1023 (1991).
[CrossRef]

1986

1983

1979

1978

J. H. Marburger, “Optical pulse integration and chirp reversal in degenerate four-wave mixing,” Appl. Phys. Lett. 32, 372–374 (1978).
[CrossRef]

1977

P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
[CrossRef]

Agrawal, G. P.

Arbore, M. A.

Avizonis, P. V.

P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
[CrossRef]

Barthelemy, A.

Bomberger, W. D.

P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
[CrossRef]

Bortz, M. L.

Fejer, M. M.

Fekete, D.

Fisher, R. A.

Hopf, F. A.

P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
[CrossRef]

Jacobs, S. F.

P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
[CrossRef]

Lefort, L.

Marburger, J. H.

J. H. Marburger, “Optical pulse integration and chirp reversal in degenerate four-wave mixing,” Appl. Phys. Lett. 32, 372–374 (1978).
[CrossRef]

Murata, S.

S. Murata, A. Tomita, J. Shimizu, and A. Suzuki, “THz optical-frequency conversion of 1-Gb/s signals using highly nondegenerate four-wave mixing in an InGaAsP semiconductor laser,” IEEE Photonics Technol. Lett. 3, 1021–1023 (1991).
[CrossRef]

Pepper, D. M.

Pinault, S. C.

Potasek, M. J.

Sherlock, G.

M. C. Tatham, G. Sherlock, and L. D. Westbrook, “Compensation of fibre chromatic dispersion by optical phase conjugation in a semiconductor laser amplifier,” Electron. Lett. 29, 1851–1852 (1995).
[CrossRef]

Shimizu, J.

S. Murata, A. Tomita, J. Shimizu, and A. Suzuki, “THz optical-frequency conversion of 1-Gb/s signals using highly nondegenerate four-wave mixing in an InGaAsP semiconductor laser,” IEEE Photonics Technol. Lett. 3, 1021–1023 (1991).
[CrossRef]

Suydam, B. R.

Suzuki, A.

S. Murata, A. Tomita, J. Shimizu, and A. Suzuki, “THz optical-frequency conversion of 1-Gb/s signals using highly nondegenerate four-wave mixing in an InGaAsP semiconductor laser,” IEEE Photonics Technol. Lett. 3, 1021–1023 (1991).
[CrossRef]

Tatham, M. C.

M. C. Tatham, G. Sherlock, and L. D. Westbrook, “Compensation of fibre chromatic dispersion by optical phase conjugation in a semiconductor laser amplifier,” Electron. Lett. 29, 1851–1852 (1995).
[CrossRef]

Tomita, A.

S. Murata, A. Tomita, J. Shimizu, and A. Suzuki, “THz optical-frequency conversion of 1-Gb/s signals using highly nondegenerate four-wave mixing in an InGaAsP semiconductor laser,” IEEE Photonics Technol. Lett. 3, 1021–1023 (1991).
[CrossRef]

P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
[CrossRef]

Westbrook, L. D.

M. C. Tatham, G. Sherlock, and L. D. Westbrook, “Compensation of fibre chromatic dispersion by optical phase conjugation in a semiconductor laser amplifier,” Electron. Lett. 29, 1851–1852 (1995).
[CrossRef]

Womack, K. H.

P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
[CrossRef]

Yariv, A.

Yevick, D.

Appl. Phys. Lett.

P. V. Avizonis, F. A. Hopf, W. D. Bomberger, S. F. Jacobs, A. Tomita, and K. H. Womack, “Optical phase conjugation in a lithium formate crystal,” Appl. Phys. Lett. 31, 435–437 (1977).
[CrossRef]

J. H. Marburger, “Optical pulse integration and chirp reversal in degenerate four-wave mixing,” Appl. Phys. Lett. 32, 372–374 (1978).
[CrossRef]

Electron. Lett.

M. C. Tatham, G. Sherlock, and L. D. Westbrook, “Compensation of fibre chromatic dispersion by optical phase conjugation in a semiconductor laser amplifier,” Electron. Lett. 29, 1851–1852 (1995).
[CrossRef]

IEEE Photonics Technol. Lett.

S. Murata, A. Tomita, J. Shimizu, and A. Suzuki, “THz optical-frequency conversion of 1-Gb/s signals using highly nondegenerate four-wave mixing in an InGaAsP semiconductor laser,” IEEE Photonics Technol. Lett. 3, 1021–1023 (1991).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Other

S. Watanabe, T. Naito, and T. Chikama, “Compensation of chromatic dispersion in a single-mode fiber by optical phase conjugation,” IEEE Photonics Technol. Lett. 5, 92–95 (1993); A. H. Gnauck, R. M. Jopson, and R. M. Derosier, “10-Gb/s 360-km transmission over dispersive fiber using midsystem spectral inversion,” IEEE Photonics Technol. Lett. 5, 663–666 (1993); S. Watanabe, T. Chikama, G. Ishikawa, T. Terahara, and H. Kuwahara, “Compensation of pulse shape distortion due to chromatic dispersion and Kerr effect by optical phase conjugation,” IEEE Photonics Technol. Lett. IPTLEL 5, 1241–1243 (1993); R. I. Laming, D. J. Richardson, D. Taverner, and D. N. Payne, “Transmission of 6 ps linear pulses over 50 km of standard fiber using midpoint spectral inversion to eliminate dispersion,” IEEE J. Quantum Electron. IEJQA7 3, 2114–2119 (1994).
[CrossRef]

K. Kikuchi and C. Lorattanasane, “Transmission of 6 ps linear pulses over 50 km of standard fiber using midpoint spectral inversion to eliminate dispersion,” IEEE Photonics Technol. Lett. 6, 104–105 (1994); W. Forysiak and N. J. Doran, “Conjugate solitons in amplified optical fibre transmission systems,” Electron. Lett. 30, 154–155 (1994); N. J. Doran and W. Forysiak, “Phase conjugation for jitter and soliton–soliton compensation in soliton communications,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 Tech. Dig. Ser.-Opt. Soc. Am. (Optical Society of America, Washington, D.C., 1994), pp. 367–368; S. Chi and S. Wen, “Recovery of the soliton self-frequency shift by optical phase conjugation,” Opt. Lett. OPLEDP 19, 1705–1707 (1994); M. Yu, G. P. Agrawal, and C. J. McKinstrie, “Effect of residual dispersion in the phase-conjugation fiber on dispersion compensation in optical communication systems,” IEEE Photonics Technol. Lett. IPTLEL 7, 932–934 (1995).
[CrossRef] [PubMed]

See, for example, G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1995), pp. 41–46.

See, for example, R. W. Boyd, Nonlinear Optics (Academic, Boston, 1992), pp. 241–252.

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Figures (3)

Fig. 1
Fig. 1

Effects of fiber TOD at low and high powers. Dashed curve, the perfectly reconstructed pulse in the absence of TOD; solid and dotted curves, the output pulses for a high-power input signal (i.e., LSPM=3×10-4LTOD) and for a low-power input signal (i.e., LSPM=0.02 LTOD), respectively. In all cases, the fiber length is Lf=50 LGVD=0.4 LTOD.

Fig. 2
Fig. 2

Effect of GVM in a 10.8-mm BBO crystal. Fiber length Lf=50LGVD. Dashed curve, the perfectly reconstructed pulse in the absence of GVM; solid curve, the output pulse from the second fiber when LSPM=0.6LGVD in the fiber; and dotted curve, the output pulse shape in the absence of SPM.

Fig. 3
Fig. 3

Demonstration of effective phase conjugation, even under conditions of severe pump depletion in the DFG crystal. Crystal dispersion and fiber TOD are neglected. Dashed curve, the perfectly reconstructed pulse; and solid curve, the output pulse under conditions of complete pump depletion.

Equations (7)

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Aiz=8πidωinic Ap As*,
As*z=[β1(i)-β1(s)] As*τ-8πidωsnsc Ap*Ai,
Apz=[β1(i)-β1(p)] Apτ+8πidωpnpc As Ai,
Az=-i β222τ2+β363τ3A+i n0 n2ωs2π |A|2A,
Aiz=8πidωinic Ap As*,
As*z=β1(i)-β1(s)+i β2(s)22τ2+β3(s)63τ3As*τ-8πidωsnsc Ap*Ai,
Apz=β1(i)-β1(p)-i β2(p)22τ2+β3(p)63τ3Apτ+8πidωpnpc As Ai,

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