Abstract

We report the initial results for femtosecond electromagnetic soliton propagation and collision obtained from first principles, i.e., by a direct time integration of Maxwell’s equations. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit the modeling of two- and three-dimensional optical soliton propagation, scattering, and switching from the full-vector Maxwell’s equations.

© 1992 Optical Society of America

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References

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  1. R. M. Joseph, S. C. Hagness, A. Taflove, Opt. Lett. 16, 1412 (1991).
    [CrossRef] [PubMed]
  2. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).
  3. G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989).
  4. K. J. Blow, D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
    [CrossRef]
  5. T. E. Bell, IEEE Spectrum 27(8), 56 (1990).
    [CrossRef]
  6. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991).

1991 (1)

1990 (1)

T. E. Bell, IEEE Spectrum 27(8), 56 (1990).
[CrossRef]

1989 (1)

K. J. Blow, D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989).

Bell, T. E.

T. E. Bell, IEEE Spectrum 27(8), 56 (1990).
[CrossRef]

Blow, K. J.

K. J. Blow, D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
[CrossRef]

Hagness, S. C.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).

Joseph, R. M.

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991).

Taflove, A.

Wood, D.

K. J. Blow, D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. J. Blow, D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
[CrossRef]

IEEE Spectrum (1)

T. E. Bell, IEEE Spectrum 27(8), 56 (1990).
[CrossRef]

Opt. Lett. (1)

Other (3)

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989).

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991).

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Figures (4)

Fig. 1
Fig. 1

Finite-difference time-domain results for the optical carrier pulse (linear case) after it has propagated 55 μm and 126 μm in the Lorentz medium.

Fig. 2
Fig. 2

Finite-difference time-domain results for the optical soliton carrier pulse that correspond to the observation locations of Fig. 1.

Fig. 3
Fig. 3

Red shift of the Fourier spectrum of the main propagating soliton of Fig. 2.

Fig. 4
Fig. 4

Phase lag of the rightward-moving daughter soliton as a result of collisions with counterpropagating solitons.

Equations (12)

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H y t = 1 μ 0 E z x ,
D z t = H y x ,
E z = D z ( P z L + P z NL ) 0 .
P z L ( x , t ) = 0 χ ( 1 ) ( t t ) E z ( x , t ) d t ,
P z NL ( x , t ) = 0 χ ( 3 ) ( t t 1 , t t 2 , t t 3 ) × E z ( x , t 1 ) E z ( x , t 2 ) E z ( x , t 3 ) d t 1 d t 2 d t 3 .
χ ( 1 ) ( t ) = ω p 2 υ 0 e δ t / 2 sin υ 0 t = F 1 [ χ ( 1 ) ( ω ) ] ( ω ) = + ω 0 2 ( s ) ω 0 2 j δ ω ω 2 ,
P z NL ( x , t ) = 0 χ ( 3 ) E z ( x , t ) × [ α δ ( t t ) + ( 1 α ) g R ( t t ) ] E z 2 ( x , t ) d t .
F ( t ) = 0 0 t χ ( 1 ) ( t t ) E z ( x , t ) d t ,
G ( t ) = 0 0 t g R ( t t ) E z 2 ( x , t ) d t .
1 ω 0 2 d 2 F d t 2 + δ ω 0 2 d F d t + [ 1 + s + α χ ( 3 ) E 2 ] F + ( s ) ( 1 α ) χ ( 3 ) E G + α χ ( 3 ) E 2 = ( s ) D + α χ ( 3 ) E 2 ,
1 ω ¯ 0 2 d 2 G d t 2 + δ ¯ ω ¯ 0 2 dG d t + [ 1 + ( 1 α ) χ ( 3 ) E 2 + α χ ( 3 ) E 2 ] G + E F + α χ ( 3 ) E 2 = D E + α χ ( 3 ) E 2 ,
E = D F ( 1 α ) χ ( 3 ) E G 0 ( + α χ ( 3 ) E 2 ) .

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