Abstract

The presence of fiber attenuation and chromatic dispersion is one of the major design aspects of fiber-optic communication systems when one addresses high-rate and long-distance digital data transmission. Conventional digital communication systems implement a modulation technique that generates light pulses at the fiber input end and tries to detect them at the fiber output end. Here an advanced modulation transmission system is developed based on knowledge of the exact dispersion parameters of the fiber and the principles of space–time mathematical analogy. The information encodes the phase of the input light beam (a continuous laser beam). This phase is designed such that, when the signal is transmitted through a fiber with a given chromatic dispersion, high peak pulses emerge at the output, which follows a desired bit pattern. Thus the continuous input energy is concentrated into short time intervals in which the information needs to be represented at the output. The proposed method provides a high rate–distance product even for fibers with high dispersion parameters, high power at the output, and also unique protection properties. Theoretical analysis of the proposed method, computer simulations, and some design aspects are given.

© 1999 Optical Society of America

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References

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  1. L. Kazovski, Optical Fiber Communication Systems, S. Benedetto, A. E. Willner, contributors (Artech House, Norwood, Mass., 1996).
  2. G. P. Agrawal, Fiber-Optic Communication System (Wiley, New York, 1992).
  3. S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kourigin, R. V. Khokhlon, A. P. Sukhorukov, “Globality and speed of optical parallel processors,” IEEE J. Quantum Electron. QE-4, 598–605 (1968).
    [CrossRef]
  4. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  5. A. W. Lohman, D. Mendlovic, “Temporal filtering with time lenses,” Appl. Opt. 31, 6212–6219 (1992).
    [CrossRef]
  6. U. Krackhardt, J. N. Mait, N. Streibl, “Upper bound on the diffraction efficiency of phase-only fanout elements,” Appl. Opt. 31, 27–37 (1992).
    [CrossRef] [PubMed]
  7. R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237 (1972).
  8. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [CrossRef] [PubMed]
  9. R. J. Gibby, J. W. Smith, “Some extensions of nyquist’s telegraph transmission theory,” Bell Syst. Tech. J. 44, 1487–1509 (1965).
    [CrossRef]

1992 (2)

1982 (1)

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237 (1972).

1968 (1)

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kourigin, R. V. Khokhlon, A. P. Sukhorukov, “Globality and speed of optical parallel processors,” IEEE J. Quantum Electron. QE-4, 598–605 (1968).
[CrossRef]

1965 (1)

R. J. Gibby, J. W. Smith, “Some extensions of nyquist’s telegraph transmission theory,” Bell Syst. Tech. J. 44, 1487–1509 (1965).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication System (Wiley, New York, 1992).

Akhmanov, S. A.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kourigin, R. V. Khokhlon, A. P. Sukhorukov, “Globality and speed of optical parallel processors,” IEEE J. Quantum Electron. QE-4, 598–605 (1968).
[CrossRef]

Benedetto, S.

L. Kazovski, Optical Fiber Communication Systems, S. Benedetto, A. E. Willner, contributors (Artech House, Norwood, Mass., 1996).

Chirkin, A. S.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kourigin, R. V. Khokhlon, A. P. Sukhorukov, “Globality and speed of optical parallel processors,” IEEE J. Quantum Electron. QE-4, 598–605 (1968).
[CrossRef]

Drabovich, K. N.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kourigin, R. V. Khokhlon, A. P. Sukhorukov, “Globality and speed of optical parallel processors,” IEEE J. Quantum Electron. QE-4, 598–605 (1968).
[CrossRef]

Fienup, J. R.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237 (1972).

Gibby, R. J.

R. J. Gibby, J. W. Smith, “Some extensions of nyquist’s telegraph transmission theory,” Bell Syst. Tech. J. 44, 1487–1509 (1965).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Kazovski, L.

L. Kazovski, Optical Fiber Communication Systems, S. Benedetto, A. E. Willner, contributors (Artech House, Norwood, Mass., 1996).

Khokhlon, R. V.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kourigin, R. V. Khokhlon, A. P. Sukhorukov, “Globality and speed of optical parallel processors,” IEEE J. Quantum Electron. QE-4, 598–605 (1968).
[CrossRef]

Kourigin, A. I.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kourigin, R. V. Khokhlon, A. P. Sukhorukov, “Globality and speed of optical parallel processors,” IEEE J. Quantum Electron. QE-4, 598–605 (1968).
[CrossRef]

Krackhardt, U.

Lohman, A. W.

Mait, J. N.

Mendlovic, D.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237 (1972).

Smith, J. W.

R. J. Gibby, J. W. Smith, “Some extensions of nyquist’s telegraph transmission theory,” Bell Syst. Tech. J. 44, 1487–1509 (1965).
[CrossRef]

Streibl, N.

Sukhorukov, A. P.

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kourigin, R. V. Khokhlon, A. P. Sukhorukov, “Globality and speed of optical parallel processors,” IEEE J. Quantum Electron. QE-4, 598–605 (1968).
[CrossRef]

Willner, A. E.

L. Kazovski, Optical Fiber Communication Systems, S. Benedetto, A. E. Willner, contributors (Artech House, Norwood, Mass., 1996).

Appl. Opt. (3)

Bell Syst. Tech. J. (1)

R. J. Gibby, J. W. Smith, “Some extensions of nyquist’s telegraph transmission theory,” Bell Syst. Tech. J. 44, 1487–1509 (1965).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. A. Akhmanov, A. S. Chirkin, K. N. Drabovich, A. I. Kourigin, R. V. Khokhlon, A. P. Sukhorukov, “Globality and speed of optical parallel processors,” IEEE J. Quantum Electron. QE-4, 598–605 (1968).
[CrossRef]

Optik (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237 (1972).

Other (3)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

L. Kazovski, Optical Fiber Communication Systems, S. Benedetto, A. E. Willner, contributors (Artech House, Norwood, Mass., 1996).

G. P. Agrawal, Fiber-Optic Communication System (Wiley, New York, 1992).

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Figures (10)

Fig. 1
Fig. 1

Basic system.

Fig. 2
Fig. 2

Analogous spatial system.

Fig. 3
Fig. 3

Basic pulse transmission system.

Fig. 4
Fig. 4

Causality.

Fig. 5
Fig. 5

Gerchberg–Saxton algorithm.

Fig. 6
Fig. 6

(a) Input phase and amplitude function and (b) output amplitude produced (solid curve) compared with target amplitude (dashed curve) for a 0111001 binary word.

Fig. 7
Fig. 7

(a) Detector relative output current for 1010110 at 9.92 Gbit/s, (b) for 1010011 at 2.48 Gbit/s. Units are relative to produced current at steady-state, continuous laser radiation.

Fig. 8
Fig. 8

ISI diagram for 9.92 Gbit/s after 1930 km.

Fig. 9
Fig. 9

(a) Generating input signal and (b) detector relative output for 1.2-ns input failure. 1010001; rate, -2.48 Gbit/s.

Fig. 10
Fig. 10

Pulse power propagation along the fiber for 1010010; rate, -2.48 Gbit/s.

Equations (40)

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ut, z=0+=uintlt,
Uμ, z=0+=- UinρLμ-ρdρ.
Uμ, z=Uμ, z=0+exp-i2πβμz,
ut, z=- Uμ, z=0+expi2πμt-βμzdμ.
βμβ0+β1μ+β2μ2/2,
lt=exp-iπt/τ2,
Lμ=τ exp-iπ/4expiπμτ2.
ut, z=-- Uinρexpi2πμt-i2πβ0z-i2πβ1μz-iπβ2μ2zτ exp-iπ/4expiπμτ2-2iπμρτ2+iπρτ2dμdρ.
z=f,  τ2=β2f,
t1=β1f.
ut, z=f=τ exp-iπ/4-i2πβ0f×-- Uinρexpi2πμt-ρτ2-t1×expiπρτ2dμdρ.
δx-x0=- expi2πfx-x0df,
- expi2πμt-ρτ2-t1dμ=δt-ρτ2-t1,
ut, z=f=C - Uinρexpiπρτ2δt-ρτ2-t1dρ,
ut, f=C×Uint-t1τ2expiπt-t1τ2.
t  x,  β2  λ,  μ  ω,  ut, z  ux, z,  Uinμ  Uinω.
qt=q0t*combt.
Qμ=Q0μcombμ=n=- Q0nδμ-n.
Qμn=-NgNg Q0nδμ-n.
Qμ=n=-NgNg a0,n expiθ0,nδμ-n,
qt=n=-NgNg a0,n expiθ0,nexp-i2πtn.
qt=Atexpθt,
gt=1 expθt.
Fgmax=Ng/Twg.
Fl=12πdangleltdt=tτ2.
tmax=Flmaxτ2.
Tl=2tmax=2Flmaxτ2 =2Flmaxβ2f.
1/Twg2Ng+1β2f=2β2fFlmax.
Fgmax=2Ng/2Ng+1Flmax.
Twg×Per=2β2fFlmax.
f=2Ng+1Per4β2Flmax2.
Fout=Twgβ2f.
Fout=2Flmax/Per.
β1f12 2β2fFlmax+122NgTwg β2f,
Flmax+Fgmaxβ1/β2.
dt1/8Flmax.
Fμ=12πdangledt=zβ1+β2μ.
dμ1/8Fμmax,
N=8f/dtβ1+β2Flmax.
BL=Foutf=2Ng+12β2Flmax.

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