Abstract

The focusing effects of induced phase modulation generated by a strong pump on the propagation of a probe Gaussian pulse in a χ(3) medium are computed. The probe diameter, the radius of curvature, and the phase are expressed as function of the primary pulse (pump) characteristics. It is proved that waveguiding of the probe by the pump is possible.

© 1989 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Shimizu, Phys. Rev. Lett. 19, 1097 (1967); L. A. Ostrovskii, JETP Lett. 6, 260 (1967); F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967); T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, P. L. Kelley, Phys. Rev. 177, 306 (1969); R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 592 (1970).
    [CrossRef]
  2. J. T. Manassah, M. A. Mustafa, R. R. Alfano, P. P. Ho, Phys. Lett. A 113, 242 (1985).
    [CrossRef]
  3. R. R. Alfano, Q. X. Li, T. Jimbo, J. T. Manassah, P. P. Ho, Opt. Lett. 11, 626 (1986).
    [CrossRef] [PubMed]
  4. J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
    [CrossRef]
  5. P. L. Kelley, Phys. Rev. Lett. 15, 1085 (1965).
    [CrossRef]
  6. V. A. Petrischev, V. I. Talanov, Sov. J. Quantum Electron. 6, 35 (1971).
  7. J. T. Manassah, P. L. Baldeck, R. R. Alfano, Opt. Lett. 13, 1090 (1988).
    [CrossRef] [PubMed]
  8. H. Kogelinik, T. Li, Proc. IEEE 54, 1312 (1966); H. Kogelinik, Appl. Opt. 4, 1562 (1965).
    [CrossRef]
  9. P. K. Tien, J. P. Gordon, J. R. Whinnery, Proc. IEEE 53, 129 (1965).
    [CrossRef]

1988

1986

1985

J. T. Manassah, M. A. Mustafa, R. R. Alfano, P. P. Ho, Phys. Lett. A 113, 242 (1985).
[CrossRef]

1975

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

1971

V. A. Petrischev, V. I. Talanov, Sov. J. Quantum Electron. 6, 35 (1971).

1967

F. Shimizu, Phys. Rev. Lett. 19, 1097 (1967); L. A. Ostrovskii, JETP Lett. 6, 260 (1967); F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967); T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, P. L. Kelley, Phys. Rev. 177, 306 (1969); R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 592 (1970).
[CrossRef]

1966

H. Kogelinik, T. Li, Proc. IEEE 54, 1312 (1966); H. Kogelinik, Appl. Opt. 4, 1562 (1965).
[CrossRef]

1965

P. K. Tien, J. P. Gordon, J. R. Whinnery, Proc. IEEE 53, 129 (1965).
[CrossRef]

P. L. Kelley, Phys. Rev. Lett. 15, 1085 (1965).
[CrossRef]

Alfano, R. R.

Baldeck, P. L.

Gordon, J. P.

P. K. Tien, J. P. Gordon, J. R. Whinnery, Proc. IEEE 53, 129 (1965).
[CrossRef]

Ho, P. P.

R. R. Alfano, Q. X. Li, T. Jimbo, J. T. Manassah, P. P. Ho, Opt. Lett. 11, 626 (1986).
[CrossRef] [PubMed]

J. T. Manassah, M. A. Mustafa, R. R. Alfano, P. P. Ho, Phys. Lett. A 113, 242 (1985).
[CrossRef]

Jimbo, T.

Kelley, P. L.

P. L. Kelley, Phys. Rev. Lett. 15, 1085 (1965).
[CrossRef]

Kogelinik, H.

H. Kogelinik, T. Li, Proc. IEEE 54, 1312 (1966); H. Kogelinik, Appl. Opt. 4, 1562 (1965).
[CrossRef]

Li, Q. X.

Li, T.

H. Kogelinik, T. Li, Proc. IEEE 54, 1312 (1966); H. Kogelinik, Appl. Opt. 4, 1562 (1965).
[CrossRef]

Manassah, J. T.

Marburger, J. H.

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Mustafa, M. A.

J. T. Manassah, M. A. Mustafa, R. R. Alfano, P. P. Ho, Phys. Lett. A 113, 242 (1985).
[CrossRef]

Petrischev, V. A.

V. A. Petrischev, V. I. Talanov, Sov. J. Quantum Electron. 6, 35 (1971).

Shimizu, F.

F. Shimizu, Phys. Rev. Lett. 19, 1097 (1967); L. A. Ostrovskii, JETP Lett. 6, 260 (1967); F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967); T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, P. L. Kelley, Phys. Rev. 177, 306 (1969); R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 592 (1970).
[CrossRef]

Talanov, V. I.

V. A. Petrischev, V. I. Talanov, Sov. J. Quantum Electron. 6, 35 (1971).

Tien, P. K.

P. K. Tien, J. P. Gordon, J. R. Whinnery, Proc. IEEE 53, 129 (1965).
[CrossRef]

Whinnery, J. R.

P. K. Tien, J. P. Gordon, J. R. Whinnery, Proc. IEEE 53, 129 (1965).
[CrossRef]

Opt. Lett.

Phys. Lett. A

J. T. Manassah, M. A. Mustafa, R. R. Alfano, P. P. Ho, Phys. Lett. A 113, 242 (1985).
[CrossRef]

Phys. Rev. Lett.

P. L. Kelley, Phys. Rev. Lett. 15, 1085 (1965).
[CrossRef]

F. Shimizu, Phys. Rev. Lett. 19, 1097 (1967); L. A. Ostrovskii, JETP Lett. 6, 260 (1967); F. De Martini, C. H. Townes, T. K. Gustafson, P. L. Kelley, Phys. Rev. 164, 312 (1967); T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, P. L. Kelley, Phys. Rev. 177, 306 (1969); R. R. Alfano, S. L. Shapiro, Phys. Rev. Lett. 24, 592 (1970).
[CrossRef]

Proc. IEEE

H. Kogelinik, T. Li, Proc. IEEE 54, 1312 (1966); H. Kogelinik, Appl. Opt. 4, 1562 (1965).
[CrossRef]

P. K. Tien, J. P. Gordon, J. R. Whinnery, Proc. IEEE 53, 129 (1965).
[CrossRef]

Prog. Quantum Electron.

J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Sov. J. Quantum Electron.

V. A. Petrischev, V. I. Talanov, Sov. J. Quantum Electron. 6, 35 (1971).

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.


Figures (4)

Fig. 1
Fig. 1

Normalized probe beam diameter. Curve (a), no pump; curve (b), pump present and p = 1.

Fig. 2
Fig. 2

Probe longitudinal phase with pump present. p = 1.

Fig. 3
Fig. 3

Normalized probe beam diameter. A, p = 0; B, p = 0.1; C, p = 0.2; D, p = 0.3; E, p = 0.4; F, p = 0.5; G, p = 0.6; H, p = 0.7; I, p = 0.8; J, p = 0.9; K, p = 1.

Fig. 4
Fig. 4

Normalized probe beam diameter. A, p = 0; B, p = 0.1; C, p = 0.3; D, p = 0.5; E, p = 1.0; F, p = 1.3; G, p = 1.6; H, p = 2.0.

Equations (23)

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

T 2 A 1 - 2 i k 1 A 1 + n 2 k 1 2 n 0 ( A 1 2 A 1 + 2 A 2 2 A 1 ) = 0 ,
T 2 A 2 - 2 i k 2 A 2 + n 2 k 2 2 n 0 ( A 2 2 A 2 + 2 A 1 2 A 2 ) = 0 ,
A 1 , 2 ( r , 0 , u ) = A 1 , 2 0 exp ( - r 2 a 1 , 2 2 ) exp ( - u 2 2 τ 1 , 2 2 ) ,
A 1 , 2 ( r , z , u ) = A ˜ 1 , 2 0 ω 1 , 2 ( z , u ) exp [ - r 2 a 1 , 2 2 ω 1 , 2 2 ( z , u ) - i k 1 , 2 2 ρ 1 , 2 ( z , u ) r 2 + i k 1 , 2 α 1 , 2 ( z , u ) ] ,
ρ 1 , 2 = 1 ω 1 , 2 ω 1 , 2 z ,
α 1 z = a 1 2 2 ω 1 2 [ 4 a 1 4 k 1 2 - n 2 n ( A ˜ 1 0 ) 2 a 1 2 ] ,
α 2 z = a 2 2 2 [ 4 a 2 4 k 2 2 ω 2 2 - 2 n 2 n a 2 2 ( A ˜ 1 0 ) 2 ω 1 2 ] ,
2 ω 1 z 2 = [ 4 a 1 4 k 1 2 ω 1 3 - 2 n 2 n a 1 2 ( A ˜ 1 0 ) 2 ω 1 3 ] ,
2 ω 2 z 2 = [ 4 a 2 4 k 2 2 ω 2 3 - 4 n 2 n a 1 2 ( A ˜ 1 0 ) 2 ω 2 ω 1 4 ] .
Φ SPM = - k 1 n 2 ( A ˜ 1 0 ) 2 z 2 n .
ω 1 = [ 1 + y 1 2 ( 1 - p ) ] 1 / 2 ,
L 1 ρ 1 = y 1 ( 1 - p ) [ 1 + y 1 2 ( 1 - p ) ] ,
k 1 α 1 = ( 1 - 1 2 p ) ( 1 - p ) 1 / 2 arctan [ ( 1 - p ) 1 / 2 y 1 ] ,
p = p exp ( - u 2 / τ 2 ) ,             p = ( A 1 0 ) 2 / ( A 1 c ) 2 , y 1 = z / L 1 ,             ( A 1 c ) 2 = n a 1 2 2 n 2 L 1 2 ,
ω 2 = [ ξ cos ( χ z ) + η ] 1 / 2 ,
ρ 2 = - 1 2 ξ χ sin ( χ z ) [ ξ cos ( χ z ) + η ] ,
α 2 = { - a 1 2 2 L 1 2 z + a 2 2 L 2 2 1 χ ( η - ξ ) 1 / 2 × arctan [ ( η - ξ ) 1 / 2 tan χ z 2 ] } ,
ξ = 1 4 ( 2 - L 1 2 L 2 2 ) ,
η = 1 4 ( 2 + L 1 2 L 2 2 ) ,
χ = 2 2 L 1 ,
ω 2 = ( 1 + y 2 ) 1 / 2 ,
ρ 2 L 2 = y 2 [ ( 1 + y 2 2 ) ] - 1 ,
k 2 α 2 = arctan ( y 2 ) ,

Metrics