Abstract

It is pointed out that the ratio between the cross-phase modulation and the self-phase modulation strengths deviates from 2, since stimulated Raman scattering influences these effects with different weight.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1990).
  2. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, H. A. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
    [Crossref]
  3. K. J. Blow, D. Wood, IEEE J. Quantum Electron. 25, 2665 (1989).
    [Crossref]
  4. P. L. François, J. Opt. Soc. Am. B 8, 276 (1991).
    [Crossref]
  5. P. Butcher, D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990).
    [Crossref]
  6. J. P. Gordon, Opt. Lett. 11, 662 (1986).
    [Crossref] [PubMed]
  7. R. H. Stolen, W. J. Tomlinson, in Digest of Conference on Nonlinear Guided-Wave Phenomena (Optical Society of America, Washington, D.C., 1991), p. 32.

1991 (1)

1989 (2)

1986 (1)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1990).

Blow, K. J.

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

Butcher, P.

P. Butcher, D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990).
[Crossref]

Cotter, D.

P. Butcher, D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990).
[Crossref]

François, P. L.

Gordon, J. P.

Haus, H. A.

Stolen, R. H.

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, H. A. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
[Crossref]

R. H. Stolen, W. J. Tomlinson, in Digest of Conference on Nonlinear Guided-Wave Phenomena (Optical Society of America, Washington, D.C., 1991), p. 32.

Tomlinson, W. J.

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, H. A. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
[Crossref]

R. H. Stolen, W. J. Tomlinson, in Digest of Conference on Nonlinear Guided-Wave Phenomena (Optical Society of America, Washington, D.C., 1991), p. 32.

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]

J. Opt. Soc. Am. B (2)

Opt. Lett. (1)

Other (3)

R. H. Stolen, W. J. Tomlinson, in Digest of Conference on Nonlinear Guided-Wave Phenomena (Optical Society of America, Washington, D.C., 1991), p. 32.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1990).

P. Butcher, D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, Cambridge, 1990).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Equations (24)

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

2 E x ( r , t ) μ 0 0 2 E x ( r , t ) t 2 μ 0 2 P x ( 1 ) ( r , t ) t 2 = μ 0 2 P x ( 3 ) ( r , t ) t 2 ,
β 2 ( ω ) β 0 2 + 2 ( ω ω 0 ) β 0 β 0 + ( ω ω 0 ) 2 × [ ( β 0 ) 2 + β 0 β 0 ] ,
E x ( r , t ) = T ( x , y ) 2 { A p exp [ i ( β p z ω p t ) ] + A p * exp [ i ( β p z ω p t ) ] + A s exp [ i ( β s z ω s t ) ] + A s * exp [ i ( β s z ω s t ) ] } ,
T ( x , y ) 2 { 2 i β p [ A p ( z , t ) z + β p A p ( z , t ) t ] β p β p 2 A p ( z , t ) t 2 } exp [ i ( β p z ω p t ) ] + T ( x , y ) 2 × { 2 i β s [ A s ( z , t ) z + β s A s ( z , t ) t ] β s β s 2 A s ( z , t ) t 2 } × exp [ i ( β s z ω s t ) ] + c . c .
P x ( 3 ) ( r , t ) = 0 + + + R x x x x ( 3 ) ( t t 1 , t t 2 , t t 3 ) × E x ( r , t 1 ) E x ( r , t 2 ) E x ( r , t 3 ) d t 1 d t 2 d t 3 .
P x ( 3 ) , R ( r , t ) = 0 E x ( r , t ) + E x 2 ( r , t 1 ) R ( 3 ) , R ( t t 1 ) d t 1 .
R x x x x ( 3 ) ( t t 1 , t t 2 , t t 3 ) = δ ( t t 3 ) δ ( t 1 t 2 ) R ( 3 ) , R ( t t 1 ) + δ ( t t 1 ) δ ( t t 2 ) δ ( t t 3 ) R ( 3 ) , K ,
P x ( 3 ) ( r , t ) = + P ˜ x ( 3 ) , R ( r , ω ) exp ( i ω t ) d ω + P x ( 3 ) , K ( r , t ) ,
P ˜ x ( 3 ) , R ( r , ω ) = 0 + + χ ( 3 ) , R ( ω 1 ω 2 ) E ˜ x ( r , ω 1 ) × E ˜ x * ( r , ω 2 ) E ˜ x ( r , ω ω 1 + ω 2 ) × d ω 1 d ω 2 ,
P x ( 3 ) , K ( r , t ) = 0 χ Kerr ( 3 ) E x 3 ( r , t ) .
E ˜ x ( r , ω ) = T ( x , y ) 2 [ A p exp ( i β p z ) δ ( ω ω p ) + A p * exp ( i β p z ) δ ( ω + ω p ) + A s exp ( i β s z ) δ ( ω ω s ) + A s * exp ( i β p z ) δ ( ω + ω s ) ] .
P ˜ x ( 3 ) , R ( r , ω ) = 0 T 3 ( x , y ) 8 ( exp ( i β p z ) × { [ 2 χ ( 3 ) , R ( 0 ) + χ ( 3 ) , R ( 2 ω p ) ] | A p | 2 A p + [ 2 χ ( 3 ) , R ( Δ ω ) + 2 χ ( 3 ) , R ( 0 ) + 2 χ ( 3 ) , R ( ω p + ω s ) ] | A s | 2 A p } δ ( ω ω p ) + exp ( i β s z ) { [ 2 χ ( 3 ) , R ( 0 ) + χ ( 3 ) , R ( 2 ω s ) ] × | A s | 2 A s + [ 2 χ ( 3 ) , R ( Δ ω ) + 2 χ ( 3 ) , R ( 0 ) + 2 χ ( 3 ) , R ( ω p + ω s ) ] | A p | 2 A s } δ ( ω ω s ) ) + c . c . ,
χ ( 3 ) , R ( 2 ω p ) = χ ( 3 ) , R ( 2 ω s ) = χ ( 3 ) , R ( ω p + ω s ) = 0 ,
χ ( 3 ) , R ( 0 ) = χ Ram , max ( 3 ) [ χ Ram , max ( 3 ) real and positive ] ;
χ ( 3 ) , R ( Δ ω ) = χ Ram , max ( 3 ) ( α + i β ) ,
χ ( 3 ) , R ( Δ ω ) = χ Ram , max ( 3 ) ( α i β )
P x ( 3 ) , R ( r , t ) = 0 χ Ram , max ( 3 ) T 3 ( x , y ) 4 × { [ | A p ( z , t ) | 2 A p ( z , t ) + ( 1 + α + i β ) × | A s ( z , t ) | 2 A p ( z , t ) ] exp [ i ( β p z ω p t ) ] + [ | A s ( z , t ) | 2 A s ( z , t ) + ( 1 + α i β ) × | A p ( z , t ) | 2 A s ( z , t ) ] exp [ i ( β s z ω s t ) ] } + c . c .
P x ( 3 ) , K ( r , t ) = 3 0 χ Kerr ( 3 ) T 3 ( x , y ) 8 { [ | A p ( z , t ) | 2 A p ( z , t ) + 2 | A s ( z , t ) | 2 A p ( z , t ) ] exp [ i ( β p z ω p t ) ] + [ | A s ( z , t ) | 2 A s ( z , t ) + 2 | A p ( z , t ) | 2 A s ( z , t ) ] × exp [ i ( β s z ω s t ) ] } + c . c .
i ( A p z + β p A p t ) β p 2 2 A p t 2 + 3 ω p 2 T 2 χ Kerr ( 3 ) 8 c 0 2 β p × ( | A p | 2 A p + 2 | A s | 2 A p ) + ω p 2 T 2 χ Ram , max ( 3 ) 4 c 0 2 β p × [ | A p | 2 A p + ( 1 + α + i β ) | A s | 2 A p ] = 0 ,
i ( A s z + β s A p t ) β s 2 2 A s t 2 + 3 ω s 2 T 2 χ Kerr ( 3 ) 8 c 0 2 β s × ( | A s | 2 A s + 2 | A p | 2 A s ) + ω s 2 T 2 χ Ram , max ( 3 ) 4 c 0 2 β s × [ | A s | 2 A s + ( 1 + α + i β ) | A p | 2 A s ] = 0 ,
A p , s ( z , t ) = u p , s ( z , t ) 2 η [ T 2 ( x , y ) d x d y ] 1 / 2 ,
i ( u p z + β p u p t ) β p 2 2 u p t 2 + K p { ( 1 + 2 μ 3 ) | u p | 2 u p + [ 2 + 2 μ 3 ( 1 + α i β ) ] | u s | 2 u p } = 0 ,
i ( u s z + β s u s t ) β s 2 2 u s t 2 + K s { ( 1 + 2 μ 3 ) | u s | 2 u s + [ 2 + 2 μ 3 ( 1 + α i β ) ] | u p | 2 u s } = 0 ,
K p , s = ω p , s 2 c 0 2 3 η 4 β p , s χ Kerr ( 3 ) A eff , A eff = [ T 2 ( x , y ) d x d y ] 2 T 4 ( x , y ) d x d y .

Metrics