Abstract

We show that optical solitons in a broad spectral range can be excited by propagating an off-axis Gaussian beam in nonlinear graded-index (GRIN) waveguides. Owing to periodical variation of both the beam size and dispersion coefficient in GRIN waveguides, the solitons belong to a newly discovered class called guiding-center solitons. In planar GRIN waveguides, solitons may be arranged to interact in both the temporal and spatial domains, thus the waveguide may serve as a novel platform for soliton interactions.

© 1993 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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  8. Numerical estimations are based on the data of GRIN lens W-2.0 provided by NSG America, Inc., Somerset, N.J. 08873.
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1992 (2)

1990 (1)

1989 (1)

1984 (1)

1983 (1)

1980 (1)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

1973 (2)

Y. Suematsu, K. Furuya, T. Kambayashi, Appl. Phys. Lett. 23, 78 (1973).
[CrossRef]

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

1964 (1)

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964 );R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett., erratum, 14, 1056 (1965).
[CrossRef]

Acioli, L. H.

Apostol, T. M.

T. M. Apostol, Calculus, 2nd ed. (McGraw-Hill, New York, 1967), Vol. 1, p. 331.

Chang, R.

Chiao, R. Y.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964 );R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett., erratum, 14, 1056 (1965).
[CrossRef]

Fork, R. L.

Fujimoto, J. G.

Furuya, K.

Y. Suematsu, K. Furuya, T. Kambayashi, Appl. Phys. Lett. 23, 78 (1973).
[CrossRef]

Garmire, E.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964 );R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett., erratum, 14, 1056 (1965).
[CrossRef]

Gordon, J. P.

Hasegawa, A.

Haus, H. A.

Huang, D.

Islam, M. N.

Kambayashi, T.

Y. Suematsu, K. Furuya, T. Kambayashi, Appl. Phys. Lett. 23, 78 (1973).
[CrossRef]

Kodama, Y.

Martinez, O. E.

Merzbacher, E.

E. Merzbacher, Quantum Mechanics, 2nd ed. (Wiley, New York, 1970). The solution can be obtained with the Green’s function given on p. 164.

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

Suematsu, Y.

Y. Suematsu, K. Furuya, T. Kambayashi, Appl. Phys. Lett. 23, 78 (1973).
[CrossRef]

Tappert, F.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Tien, A. C.

Townes, C. H.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964 );R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett., erratum, 14, 1056 (1965).
[CrossRef]

Ulman, M.

Wang, J.

Appl. Phys. Lett. (2)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Y. Suematsu, K. Furuya, T. Kambayashi, Appl. Phys. Lett. 23, 78 (1973).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. Lett. (2)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[CrossRef]

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964 );R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett., erratum, 14, 1056 (1965).
[CrossRef]

Other (3)

E. Merzbacher, Quantum Mechanics, 2nd ed. (Wiley, New York, 1970). The solution can be obtained with the Green’s function given on p. 164.

T. M. Apostol, Calculus, 2nd ed. (McGraw-Hill, New York, 1967), Vol. 1, p. 331.

Numerical estimations are based on the data of GRIN lens W-2.0 provided by NSG America, Inc., Somerset, N.J. 08873.

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Figures (1)

Fig. 1
Fig. 1

(a) Prism pairs for producing negative GVD. (b) A device similar to that shown in (a), with prisms replaced by lenses, (c) A GRIN lens, which can be considered as a continuum of that shown in (b).

Equations (13)

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2 E ( x , y , z , t ) 1 c 2 2 t 2 D ( x , y , z , t ) = 4 π c 2 2 t 2 P NL ,
( x , y ) = n 0 2 ( 1 A r 2 ) ,
E ( x , y , z , t ) = F ( x , y , z , t ) exp ( i k 0 z i ω 0 t ) ,
[ 2 i k 0 z F k 0 2 A r 2 F + ( x 2 + y 2 ) F ] + { z 2 F + i [ ω ( K 2 ) ] t F 1 2 [ ω 2 ( K 2 ) ] t 2 F 1 3 i [ ω 3 ( K 2 ) ] t 3 F + 2 k 0 2 n 0 n 2 | F | 2 F } = 0 ,
ϕ ( x , y , z ) = X ( x , z ) Y ( y , z ) ,
X ( x , z ) = ( exp { i tan 1 [ η x tan ( A z + θ x ) ] / 2 } w [ η x 1 cos 2 ( A z + θ x ) + η x sin 2 ( A z + θ x ) ] 1 / 2 ) × exp { [ x a x cos ( A z + θ x ) ] 2 w 2 [ η x 1 cos 2 ( A z + θ x ) + η x sin 2 ( A z + θ x ) ] } exp ( [ i k 0 A cos 2 ( A z + θ x ) + η x 2 sin 2 ( A z + θ x ) ] × { 1 4 sin [ 2 ( A z + θ x ) ] [ ( 1 η x 2 ) x 2 η x 2 a x 2 ] + η x 2 a x x sin ( A z + θ x ) } ) ,
F ( x , y , z , t ) = ϕ ( x , y , z ) f ( z , t ) ,
2 i k 0 ϕ z f + ( z 2 ϕ ) f + 2 ( z ϕ ) z f + ϕ z 2 f + i [ ω ( K 2 ) ] ϕ t f 1 2 [ ω 2 ( K 2 ) ] ϕ t 2 f i 3 ! [ ω 3 ( K 2 ) ] ϕ t 3 f + 2 k 0 2 n 0 n 2 | ϕ | 2 ϕ | f | 2 f = 0 ,
[ z + 1 υ g ( 1 2 α 2 g 2 ) t ] × f i α 2 g f i 1 2 β t 2 f 2 k 0 2 n 2 i n 0 g J ( z ) | f | 2 f l 1 cos ( 2 A z ) t f i l 2 cos ( 2 A z ) t 2 f = 0 ,
K c 2 ω 2 c 2 n 0 ( ω ) 2 [ 1 A ( ω ) ( a x 2 cos 2 A z + a y 2 sin 2 A z ) ] , α 1 2 i k 0 ( a x 2 + a y 2 ) A , g 2 k 0 2 i α , β ω 2 ( k c 2 ) ¯ g + 2 g υ g 2 8 α 2 g 3 υ g 2 , 1 υ g [ ω ( K c 2 ) ¯ g ] , J ( z ) [ η x η y / w 4 ( cos 2 A z + η x 2 sin 2 A z ) ( sin 2 A z + η y 2 cos 2 A z ) ] 1 / 2 J ¯ + J 0 ( z ) .
l 1 = ω ( k 2 A ) 2 g ( a x 2 a y 2 ) , l 2 = [ ω ( k 2 A ) g 2 υ g + ω 2 ( k 2 A ) 4 g ] ( a x 2 a y 2 ) .
u = 2 k 0 2 n 2 J ¯ n 0 g f exp ( i α 2 g z ) , Z = z , T = t 1 υ g ( 1 2 α 2 g 2 ) z l 1 1 2 A sin ( 2 A z ) ,
i Z u + 1 2 β T 2 u + | u | 2 u + l 2 cos ( 2 A Z ) T 2 u + J 0 ( Z ) J ¯ | u | 2 u = 0 .

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