Abstract

We find conditions for collimation and guiding of two light beams in a nonlinear bulk medium. The spatial parameters of each beam of the symbiotically coupled pair depend critically on the cross-phase modulation from the complementary beam. The diffraction divergence and self-phase modulation can be offset by proper choice of the wavelength, the value, and the sign of the nonlinear susceptibility of the medium.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. For a review see, for example, J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
    [CrossRef]
  2. R. R. Alfano, Q. Li, T. Jimbo, J. Manassah, P. P. Ho, “Induced spectral broadening of a weak picosecond pulse in glass produced by an intense picosecond pulse,” Opt. Lett. 11, 626–628 (1986).
    [CrossRef] [PubMed]
  3. G. P. Agrawal, P. L. Baldeck, R. R. Alfano, “Temporal and spectral effects of XPM on copropagating pulses in optical fibers,” Phys. Rev. A 40, 5063–5072 (1989).
    [CrossRef] [PubMed]
  4. P. P. Ho, D. Ji, Q. Z. Wang, R. R. Alfano, “Temporal behavior of cross-phase-modulated second-harmonic generation of ultrashort laser pulses in nonlinear-optical media,” J. Opt. Soc. Am. B 7, 276–284 (1990).
    [CrossRef]
  5. S. G. Dinev, A. A. Dreischuh, “The induced phase modulation in the UV,” J. Phys. B 24, 319–323 (1991).
    [CrossRef]
  6. D. Schadt, B. Jaskorzynska, “Suppression of the Raman self-frequency shift by cross-phase modulation,” J. Opt. Soc. Am. B 5, 2374–2378 (1988).
    [CrossRef]
  7. M. Lisak, A. Höök, D. Anderson, “Symbiotic solitary-wave pairs sustained by cross-phase modulation in optical fibers,” J. Opt. Soc. Am. B 7, 810–814 (1990).
    [CrossRef]
  8. J. T. Manassah, “Focusing effects of induced phase modulation on a probe pulse propagating in a χ(3) medium,” Opt. Lett. 14, 396–398 (1989).
    [CrossRef] [PubMed]
  9. R. R. Alfano, P. L. Baldeck, P. P. Ho, G. P. Agrawal, “Cross-phase modulation and induced focusing due to optical nonlinearities in optical fibers and bulk materials,” J. Opt. Soc. Am. B 6, 824–829 (1989).
    [CrossRef]
  10. G. P. Agrawal, “Induced focusing of optical beams in self-defocusing nonlinear media,” Phys. Rev. Lett. 64, 2487–2490 (1990).
    [CrossRef] [PubMed]
  11. G. P. Agrawal, Nonlinear Fiber Optics (Academic, London, 1989), Chap. 7, p. 193.
  12. P. V. Mamyshev, S. V. Cherikov, E. M. Dianov, A. M. Prokhorov, “Generation of a high-repetition-rate train of practically noninteracting solitons by using the induced modulational instability and Raman self-scattering effects,” Opt. Lett. 15, 1365–1367 (1990).
    [CrossRef] [PubMed]
  13. Y. Silberberg, “The collapse of optical pulses,” Opt. Lett. 15, 1282–1284 (1990).
    [CrossRef] [PubMed]
  14. D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
    [CrossRef]
  15. S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses(Nauka, Moscow, 1988), Chap. 2, p. 104.
  16. W. I. Bespalov, W. I. Talanow, “On the filament structure of a light beam in nonlinear liquids,” JETP Lett. 3, 471 (1966).
  17. G. P. Agrawal, P. L. Baldeck, R. R. Alfano, “Modulation instability induced by XPM in optical fibers,” Phys. Rev. A 39, 3406–3413 (1989).
    [CrossRef] [PubMed]
  18. J. S. Aitchison, A. M. Weiner, Y. Sylberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, P. W. E. Smith, “Observations of spatial optical solitons in a nonlinear glass waveguide,” Opt. Lett. 15, 471–473 (1990).
    [CrossRef] [PubMed]
  19. V. G. Arkhipkin, Yu. I. Heller, A. K. Popov, A. S. Provorov, “Frequency mixing in a gas-filled waveguide for VUV light generation,” Appl. Phys. B 37, 93–97 (1985).
    [CrossRef]

1991 (1)

S. G. Dinev, A. A. Dreischuh, “The induced phase modulation in the UV,” J. Phys. B 24, 319–323 (1991).
[CrossRef]

1990 (6)

1989 (4)

R. R. Alfano, P. L. Baldeck, P. P. Ho, G. P. Agrawal, “Cross-phase modulation and induced focusing due to optical nonlinearities in optical fibers and bulk materials,” J. Opt. Soc. Am. B 6, 824–829 (1989).
[CrossRef]

J. T. Manassah, “Focusing effects of induced phase modulation on a probe pulse propagating in a χ(3) medium,” Opt. Lett. 14, 396–398 (1989).
[CrossRef] [PubMed]

G. P. Agrawal, P. L. Baldeck, R. R. Alfano, “Modulation instability induced by XPM in optical fibers,” Phys. Rev. A 39, 3406–3413 (1989).
[CrossRef] [PubMed]

G. P. Agrawal, P. L. Baldeck, R. R. Alfano, “Temporal and spectral effects of XPM on copropagating pulses in optical fibers,” Phys. Rev. A 40, 5063–5072 (1989).
[CrossRef] [PubMed]

1988 (1)

1986 (1)

1985 (1)

V. G. Arkhipkin, Yu. I. Heller, A. K. Popov, A. S. Provorov, “Frequency mixing in a gas-filled waveguide for VUV light generation,” Appl. Phys. B 37, 93–97 (1985).
[CrossRef]

1983 (1)

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
[CrossRef]

1975 (1)

For a review see, for example, J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

1966 (1)

W. I. Bespalov, W. I. Talanow, “On the filament structure of a light beam in nonlinear liquids,” JETP Lett. 3, 471 (1966).

Agrawal, G. P.

G. P. Agrawal, “Induced focusing of optical beams in self-defocusing nonlinear media,” Phys. Rev. Lett. 64, 2487–2490 (1990).
[CrossRef] [PubMed]

G. P. Agrawal, P. L. Baldeck, R. R. Alfano, “Temporal and spectral effects of XPM on copropagating pulses in optical fibers,” Phys. Rev. A 40, 5063–5072 (1989).
[CrossRef] [PubMed]

G. P. Agrawal, P. L. Baldeck, R. R. Alfano, “Modulation instability induced by XPM in optical fibers,” Phys. Rev. A 39, 3406–3413 (1989).
[CrossRef] [PubMed]

R. R. Alfano, P. L. Baldeck, P. P. Ho, G. P. Agrawal, “Cross-phase modulation and induced focusing due to optical nonlinearities in optical fibers and bulk materials,” J. Opt. Soc. Am. B 6, 824–829 (1989).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, London, 1989), Chap. 7, p. 193.

Aitchison, J. S.

Akhmanov, S. A.

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses(Nauka, Moscow, 1988), Chap. 2, p. 104.

Alfano, R. R.

Anderson, D.

M. Lisak, A. Höök, D. Anderson, “Symbiotic solitary-wave pairs sustained by cross-phase modulation in optical fibers,” J. Opt. Soc. Am. B 7, 810–814 (1990).
[CrossRef]

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
[CrossRef]

Arkhipkin, V. G.

V. G. Arkhipkin, Yu. I. Heller, A. K. Popov, A. S. Provorov, “Frequency mixing in a gas-filled waveguide for VUV light generation,” Appl. Phys. B 37, 93–97 (1985).
[CrossRef]

Baldeck, P. L.

R. R. Alfano, P. L. Baldeck, P. P. Ho, G. P. Agrawal, “Cross-phase modulation and induced focusing due to optical nonlinearities in optical fibers and bulk materials,” J. Opt. Soc. Am. B 6, 824–829 (1989).
[CrossRef]

G. P. Agrawal, P. L. Baldeck, R. R. Alfano, “Temporal and spectral effects of XPM on copropagating pulses in optical fibers,” Phys. Rev. A 40, 5063–5072 (1989).
[CrossRef] [PubMed]

G. P. Agrawal, P. L. Baldeck, R. R. Alfano, “Modulation instability induced by XPM in optical fibers,” Phys. Rev. A 39, 3406–3413 (1989).
[CrossRef] [PubMed]

Bespalov, W. I.

W. I. Bespalov, W. I. Talanow, “On the filament structure of a light beam in nonlinear liquids,” JETP Lett. 3, 471 (1966).

Cherikov, S. V.

Chirkin, A. S.

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses(Nauka, Moscow, 1988), Chap. 2, p. 104.

Dianov, E. M.

Dinev, S. G.

S. G. Dinev, A. A. Dreischuh, “The induced phase modulation in the UV,” J. Phys. B 24, 319–323 (1991).
[CrossRef]

Dreischuh, A. A.

S. G. Dinev, A. A. Dreischuh, “The induced phase modulation in the UV,” J. Phys. B 24, 319–323 (1991).
[CrossRef]

Heller, Yu. I.

V. G. Arkhipkin, Yu. I. Heller, A. K. Popov, A. S. Provorov, “Frequency mixing in a gas-filled waveguide for VUV light generation,” Appl. Phys. B 37, 93–97 (1985).
[CrossRef]

Ho, P. P.

Höök, A.

Jackel, J. L.

Jaskorzynska, B.

Ji, D.

Jimbo, T.

Leaird, D. E.

Li, Q.

Lisak, M.

Mamyshev, P. V.

Manassah, J.

Manassah, J. T.

Marburger, J. H.

For a review see, for example, J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Oliver, M. K.

Popov, A. K.

V. G. Arkhipkin, Yu. I. Heller, A. K. Popov, A. S. Provorov, “Frequency mixing in a gas-filled waveguide for VUV light generation,” Appl. Phys. B 37, 93–97 (1985).
[CrossRef]

Prokhorov, A. M.

Provorov, A. S.

V. G. Arkhipkin, Yu. I. Heller, A. K. Popov, A. S. Provorov, “Frequency mixing in a gas-filled waveguide for VUV light generation,” Appl. Phys. B 37, 93–97 (1985).
[CrossRef]

Schadt, D.

Silberberg, Y.

Smith, P. W. E.

Sylberberg, Y.

Talanow, W. I.

W. I. Bespalov, W. I. Talanow, “On the filament structure of a light beam in nonlinear liquids,” JETP Lett. 3, 471 (1966).

Vogel, E. M.

Vysloukh, V. A.

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses(Nauka, Moscow, 1988), Chap. 2, p. 104.

Wang, Q. Z.

Weiner, A. M.

Appl. Phys. B (1)

V. G. Arkhipkin, Yu. I. Heller, A. K. Popov, A. S. Provorov, “Frequency mixing in a gas-filled waveguide for VUV light generation,” Appl. Phys. B 37, 93–97 (1985).
[CrossRef]

J. Opt. Soc. Am. B (4)

J. Phys. B (1)

S. G. Dinev, A. A. Dreischuh, “The induced phase modulation in the UV,” J. Phys. B 24, 319–323 (1991).
[CrossRef]

JETP Lett. (1)

W. I. Bespalov, W. I. Talanow, “On the filament structure of a light beam in nonlinear liquids,” JETP Lett. 3, 471 (1966).

Opt. Lett. (5)

Phys. Rev. A (3)

G. P. Agrawal, P. L. Baldeck, R. R. Alfano, “Modulation instability induced by XPM in optical fibers,” Phys. Rev. A 39, 3406–3413 (1989).
[CrossRef] [PubMed]

D. Anderson, “Variational approach to nonlinear pulse propagation in optical fibers,” Phys. Rev. A 27, 3135–3145 (1983).
[CrossRef]

G. P. Agrawal, P. L. Baldeck, R. R. Alfano, “Temporal and spectral effects of XPM on copropagating pulses in optical fibers,” Phys. Rev. A 40, 5063–5072 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

G. P. Agrawal, “Induced focusing of optical beams in self-defocusing nonlinear media,” Phys. Rev. Lett. 64, 2487–2490 (1990).
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

For a review see, for example, J. H. Marburger, Prog. Quantum Electron. 4, 35 (1975).
[CrossRef]

Other (2)

S. A. Akhmanov, V. A. Vysloukh, A. S. Chirkin, Optics of Femtosecond Laser Pulses(Nauka, Moscow, 1988), Chap. 2, p. 104.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, London, 1989), Chap. 7, p. 193.

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 (1)

Fig. 1
Fig. 1

Dispersion and sign of the χ SPM ( 3 ) nonlinear coefficient in Xe i, near the 5p6–6p resonances. The wavelength pairs (λ1, λ2) are denoted for the three cases considered.

Equations (28)

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

i ψ 1 x + α 1 2 ψ 1 r 2 + k SPM ( λ 1 ) ψ 1 2 ψ 1 + k XPM ( λ 1 ) ψ 2 2 ψ 1 = 0 , i ψ 1 x + α 2 2 ψ 2 r 2 + k SPM ( λ 2 ) ψ 2 2 ψ 2 + k XPM ( λ 2 ) ψ 1 2 ψ 2 = 0 ,
k SPM ( λ i ) = - n 2 SPM ( λ i ) k i 2 n 0 i = - k i 2 n 0 i 3 π N χ SPM ( 3 ) ( λ i ) n 0 i , k XPM ( λ i ) = - n 2 XPM ( λ i ) k i 2 n 0 i = - k i 2 n 0 i 6 π N χ XPM ( 3 ) ( λ i ) n 0 i .
L = L 1 + L 2 + L XPM ,
L 1 = ( i / 2 ) ( ψ 1 * ψ 1 x - ψ 1 ψ 1 * x ) - α 1 | ψ 1 r | 2 + k SPM ( λ 1 ) 2 ψ 1 4 ,
L 2 = ( i / 2 ) ( ψ 2 * ψ 2 x - ψ 2 ψ 2 * x ) - α 2 | ψ 2 | 2 + k SPM ( λ 2 ) 2 ψ 2 4 ,
L XPM = k XPM ψ 1 2 ψ 2 2 .
ψ 1 ( r , x ) = A 1 ( x ) ω 1 ( x ) exp [ - r 2 a 1 2 ω 1 2 ( x ) - i k 1 ρ 1 ( x ) r 2 2 ] ,
ψ 2 ( r , x ) = A 2 ( x ) ω 2 ( x ) exp [ - r 2 a 2 2 ω 2 2 ( x ) - i k 2 ρ 2 ( x ) r 2 2 ] ,
d ρ 1 d x = - ρ 1 2 + 4 k 1 2 a 1 4 ω 1 4 + 2 k SPM ( λ 1 ) A 1 2 a 1 2 ω 1 4 k 1 + 4 k XPM A 2 2 a 2 ω 2 k 1 ( a 1 2 ω 1 2 + a 2 2 ω 2 2 ) 3 / 2 ,
d ρ 2 d x = - ρ 2 2 + 4 k 2 2 a 2 4 ω 2 4 + 2 k SPM ( λ 2 ) A 2 2 a 2 2 ω 2 4 k 2 + 4 k XPM A 1 2 a 1 ω 1 k 2 ( a 1 2 ω 1 2 + a 2 2 ω 2 2 ) 3 / 2 ,
d ω 1 d x = ω 1 ρ 1 ,
d ω 2 d x = ω 2 ρ 2 .
k SPM ( λ 1 ) A 1 2 + k XPM A 2 2 = - 2 2 k 1 a 2 ,
k SPM ( λ 2 ) A 2 2 + k XPM A 1 2 = - 2 2 k 2 a 2 .
P 1 = - 2 2 c 8.10 7 { [ k SPM ( λ 2 ) / k 1 ] - ( k XPM / k 2 ) } k SPM ( λ 1 ) k SPM ( λ 2 ) - ( k XPM ) 2 ,
P 2 = - 2 2 c 8.10 7 { [ k SPM ( λ 1 ) / k 2 ] - ( k XPM / k 1 ) } k SPM ( λ 1 ) k SPM ( λ 2 ) - ( k XPM ) 2 .
A i ( r , x ) = [ A i + δ A i ( r , x ) ] exp ( - Γ i x ) ,
{ x - α 1 2 r 2 } δ A 1 = k SPM ( λ 1 ) A 1 2 ( δ A 1 + δ A 1 * ) + k XPM ( A 1 2 A 2 2 ) 1 / 2 × ( δ A 2 + δ A 2 * ) ,
{ x - α 2 2 r 2 } δ A 2 = k SPM ( λ 2 ) A 2 2 ( δ A 2 + δ A 2 * ) + k XPM ( A 1 2 A 2 2 ) 1 / 2 × ( δ A 1 + δ A 1 * ) .
δ A i = δ A i 0 exp [ i ( K ( i ) t - h i x ) ] + c . c . ,             i = 1 , 2 ,
K ( i ) K crit ( i ) ,             i = 1 , 2.
K     crit ( 1 ) = { 2 α 1 [ k SPM ( λ 1 ) A 1 2 + k XPM ( A 1 2 A 2 2 ) 1 / 2 ] } 1 / 2 ,
K     crit ( 2 ) = { 2 α 2 [ k SPM ( λ 2 ) A 2 2 + k XPM ( A 1 2 A 2 2 ) 1 / 2 ] } 1 / 2 .
F r G A 2 r A F 2 ( ω G F - ω i - ω j - i γ F ) [ ( ω G A - ω i ) - 2 + ( ω G A - ω j ) - 2 ] ,             i , j = 1 , 2 ,
χ SPM ( 3 ) ( λ 1 ) = 1.8 × 10 - 33 esu ,             χ SPM ( 3 ) ( λ 2 ) = 1.4 × 10 - 33 esu , χ SPM ( 3 ) = 10 - 32 esu .
χ SPM ( 3 ) ( λ 1 ) = 2.4 × 10 - 33 esu , χ SPM ( 3 ) ( λ 2 ) = 1.7 × 10 - 32 esu , χ SPM ( 3 ) = - 1.1 × 10 - 33 esu .
η i = [ k SPM ( λ i ) A i 2 + k SPM ( A 1 2 A 2 2 ) 1 / 2 k SPM ( λ i ) A i 2 ] 1 / 2 ,             i = 1 , 2.
χ SPM ( 3 ) ( λ 1 ) = - 8.5 × 10 - 35 esu , χ SPM ( 3 ) ( λ 2 ) = - 5.9 × 10 - 35 esu , χ SPM ( 3 ) = 5.1 × 10 - 33 esu ,

Metrics