Abstract

We extend recently developed algebraic space–time analogies for the dispersive and nonlinear propagation of optical breathers. Geometrical arguments can explain the similarity of evolutionary behavior between spatial and temporal phenomena even when strict algebraic translation of solutions may not be possible. This explanation offers a new set of tools for understanding and predicting the evolutionary structure of self-consistent Gaussian breathers in nonlinear optical fibers.

© 2001 Optical Society of America

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Errata

Shayan Mookherjea and Amnon Yariv, "Algebraic and geometric space-time analogies in nonlinear optical pulse propagation: errata," Opt. Lett. 27, 137-137 (2002)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-27-2-137

References

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  1. S. Akhmanov, A. Chirkin, K. Drabovich, A. Kovrigin, R. Khokhlov, and A. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
    [CrossRef]
  2. B. Kolner and M. Nazarathy, Opt. Lett. 14, 632 (1989).
    [CrossRef]
  3. A. Lohmann and D. Mendlovic, Appl. Opt. 31, 6212 (1992).
    [CrossRef] [PubMed]
  4. S. Mookherjea and A. Yariv, Phys. Rev. E 64, 016611 (2001).
    [CrossRef]
  5. A. Yariv, J. Nonlinear Opt. Phys. Mater. 8, 165 (1999).
    [CrossRef]
  6. A. Yariv, Optical Electronics in Modern Communications (Oxford University, New York, 1997).
  7. M. LaGasse, K. Anderson, C. Wang, H. Haus, and J. Fujimoto, Appl. Phys. Lett. 56, 417 (1990).
    [CrossRef]
  8. M. Nakahara, Geometry, Topology and Physics (Institute of Physics, London, 1990).
    [CrossRef]

2001

S. Mookherjea and A. Yariv, Phys. Rev. E 64, 016611 (2001).
[CrossRef]

1999

A. Yariv, J. Nonlinear Opt. Phys. Mater. 8, 165 (1999).
[CrossRef]

1992

1990

M. LaGasse, K. Anderson, C. Wang, H. Haus, and J. Fujimoto, Appl. Phys. Lett. 56, 417 (1990).
[CrossRef]

1989

B. Kolner and M. Nazarathy, Opt. Lett. 14, 632 (1989).
[CrossRef]

1968

S. Akhmanov, A. Chirkin, K. Drabovich, A. Kovrigin, R. Khokhlov, and A. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[CrossRef]

Akhmanov, S.

S. Akhmanov, A. Chirkin, K. Drabovich, A. Kovrigin, R. Khokhlov, and A. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[CrossRef]

Anderson, K.

M. LaGasse, K. Anderson, C. Wang, H. Haus, and J. Fujimoto, Appl. Phys. Lett. 56, 417 (1990).
[CrossRef]

Chirkin, A.

S. Akhmanov, A. Chirkin, K. Drabovich, A. Kovrigin, R. Khokhlov, and A. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[CrossRef]

Drabovich, K.

S. Akhmanov, A. Chirkin, K. Drabovich, A. Kovrigin, R. Khokhlov, and A. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[CrossRef]

Fujimoto, J.

M. LaGasse, K. Anderson, C. Wang, H. Haus, and J. Fujimoto, Appl. Phys. Lett. 56, 417 (1990).
[CrossRef]

Haus, H.

M. LaGasse, K. Anderson, C. Wang, H. Haus, and J. Fujimoto, Appl. Phys. Lett. 56, 417 (1990).
[CrossRef]

Khokhlov, R.

S. Akhmanov, A. Chirkin, K. Drabovich, A. Kovrigin, R. Khokhlov, and A. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[CrossRef]

Kolner, B.

B. Kolner and M. Nazarathy, Opt. Lett. 14, 632 (1989).
[CrossRef]

Kovrigin, A.

S. Akhmanov, A. Chirkin, K. Drabovich, A. Kovrigin, R. Khokhlov, and A. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[CrossRef]

LaGasse, M.

M. LaGasse, K. Anderson, C. Wang, H. Haus, and J. Fujimoto, Appl. Phys. Lett. 56, 417 (1990).
[CrossRef]

Lohmann, A.

Mendlovic, D.

Mookherjea, S.

S. Mookherjea and A. Yariv, Phys. Rev. E 64, 016611 (2001).
[CrossRef]

Nakahara, M.

M. Nakahara, Geometry, Topology and Physics (Institute of Physics, London, 1990).
[CrossRef]

Nazarathy, M.

B. Kolner and M. Nazarathy, Opt. Lett. 14, 632 (1989).
[CrossRef]

Sukhorukov, A.

S. Akhmanov, A. Chirkin, K. Drabovich, A. Kovrigin, R. Khokhlov, and A. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[CrossRef]

Wang, C.

M. LaGasse, K. Anderson, C. Wang, H. Haus, and J. Fujimoto, Appl. Phys. Lett. 56, 417 (1990).
[CrossRef]

Yariv, A.

S. Mookherjea and A. Yariv, Phys. Rev. E 64, 016611 (2001).
[CrossRef]

A. Yariv, J. Nonlinear Opt. Phys. Mater. 8, 165 (1999).
[CrossRef]

A. Yariv, Optical Electronics in Modern Communications (Oxford University, New York, 1997).

Appl. Opt.

Appl. Phys. Lett.

M. LaGasse, K. Anderson, C. Wang, H. Haus, and J. Fujimoto, Appl. Phys. Lett. 56, 417 (1990).
[CrossRef]

IEEE J. Quantum Electron.

S. Akhmanov, A. Chirkin, K. Drabovich, A. Kovrigin, R. Khokhlov, and A. Sukhorukov, IEEE J. Quantum Electron. QE-4, 598 (1968).
[CrossRef]

J. Nonlinear Opt. Phys. Mater.

A. Yariv, J. Nonlinear Opt. Phys. Mater. 8, 165 (1999).
[CrossRef]

Opt. Lett.

B. Kolner and M. Nazarathy, Opt. Lett. 14, 632 (1989).
[CrossRef]

Phys. Rev. E

S. Mookherjea and A. Yariv, Phys. Rev. E 64, 016611 (2001).
[CrossRef]

Other

A. Yariv, Optical Electronics in Modern Communications (Oxford University, New York, 1997).

M. Nakahara, Geometry, Topology and Physics (Institute of Physics, London, 1990).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Temporal evolution of a Gaussian breather pulse (a) in a hypothetical medium described by Eq.  (7) and exactly analogous to Gaussian beam propagation in a RSQ-GRIN fiber and (b) in a realistic fiber with the Kerr effect, as described by Eq.  (10).

Fig. 2
Fig. 2

Temporal evolution of a Gaussian breather in the (hypothetical) temporal RSQ-GRIN medium: phase-plane analysis of Eq.  (13).

Fig. 3
Fig. 3

Temporal evolution of a Gaussian breather in the presence of the Kerr effect: phase-plane analysis of Eq.  (14).

Equations (16)

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

2A-2ikAz-kk2r2A=0,
Ar,z=expiPz+k2qzr2,
1qz1Rz-i2 λkw2z
qz=Azq0+BzCzq0+Dz,
Az=cosk2/kz,  Bz=k/k2sink2/kz,Cz=-k2/ksink2/kz,  Dz=cosk2/kz.
zz, rT, 2T2,k-1/β, k24γ,
-iAz+β22AT2+b22T2A=0,
-iAz+β22AT2-γΔnn2A=0,
Δnz,T=n2exp-2T2τ2zn21-2T2τ2z,
-iAz+β22AT2-γ1-2T2τ2zA=0,
Az,T=expiPz+T22βqz,
1qz1Rz+i2βτ2zrzcosθz+isinθz,
dr/dz=r2cosθ+2γcosθ,dθ/dz=1rr2sinθ-2γsinθ,r0r0,θ0θ0=π/2,
dr/dz=r2cosθ+2γcosθrsinθ,dθ/dz=1rr2sinθ-2γsinθrsinθ,r0r0,θ0θ0=π/2.
τi={Sir0|a<r0<b},a,b0,
π1X1π1X2π1S1Z.

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