Abstract

We investigate interactions between vectorial solitary waves through type  II second-harmonic generation. We demonstrate that one can tune the collision distance of two initially codirectional solitary waves changing their polarization state. Moreover, by adiabatic perturbation analysis, it is possible to predict such a collision distance as a function of solitary-wave separation, in good agreement with numerical simulations.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Berg̀ano, J. Lightwave Technol. 10, 28 (1992).
    [CrossRef]
  2. C. De Angelis, S. Wabnitz, and M. Haelterman, Electron. Lett. 29, 1568 (1993).
    [CrossRef]
  3. K. Iwatsuki, K. Suzuki, S. Nishi, and S. Saruwatari, IEEE Photon. Technol. Lett. 5, 245 (1993).
    [CrossRef]
  4. L. F. Mollenauer, P. V. Mamyshev, and M. J. Neubelt, Opt. Lett. 19, 704 (1994).
    [CrossRef] [PubMed]
  5. M. J. Werner and P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993).
    [CrossRef]
  6. A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).
    [CrossRef] [PubMed]
  7. D. M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).
    [CrossRef]
  8. C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
    [CrossRef]
  9. G. Leo, G. Assanto, and W. E. Torrruellas, Opt. Lett. 22, 7 (1997).
    [CrossRef] [PubMed]
  10. C. Balslev Clausen, P. L. Christiansen, and L. Torner, Opt. Commun. 136, 185 (1997).
    [CrossRef]
  11. L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
    [CrossRef] [PubMed]
  12. V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
    [CrossRef]

1997 (2)

G. Leo, G. Assanto, and W. E. Torrruellas, Opt. Lett. 22, 7 (1997).
[CrossRef] [PubMed]

C. Balslev Clausen, P. L. Christiansen, and L. Torner, Opt. Commun. 136, 185 (1997).
[CrossRef]

1996 (1)

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

1995 (4)

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).
[CrossRef] [PubMed]

D. M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).
[CrossRef]

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
[CrossRef]

1994 (1)

1993 (3)

M. J. Werner and P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993).
[CrossRef]

C. De Angelis, S. Wabnitz, and M. Haelterman, Electron. Lett. 29, 1568 (1993).
[CrossRef]

K. Iwatsuki, K. Suzuki, S. Nishi, and S. Saruwatari, IEEE Photon. Technol. Lett. 5, 245 (1993).
[CrossRef]

1992 (1)

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Berg̀ano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

Assanto, G.

Baboiu, D. M.

Balslev Clausen, C.

C. Balslev Clausen, P. L. Christiansen, and L. Torner, Opt. Commun. 136, 185 (1997).
[CrossRef]

Berg`ano, N. S.

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Berg̀ano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

Buryak, A. V.

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).
[CrossRef] [PubMed]

Christiansen, P. L.

C. Balslev Clausen, P. L. Christiansen, and L. Torner, Opt. Commun. 136, 185 (1997).
[CrossRef]

De Angelis, C.

C. De Angelis, S. Wabnitz, and M. Haelterman, Electron. Lett. 29, 1568 (1993).
[CrossRef]

Drummond, P. D.

Etrich, C.

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
[CrossRef]

Evangelides, S. G.

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Berg̀ano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

Gordon, J. P.

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Berg̀ano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

Haelterman, M.

C. De Angelis, S. Wabnitz, and M. Haelterman, Electron. Lett. 29, 1568 (1993).
[CrossRef]

Iwatsuki, K.

K. Iwatsuki, K. Suzuki, S. Nishi, and S. Saruwatari, IEEE Photon. Technol. Lett. 5, 245 (1993).
[CrossRef]

Kivshar, Y. S.

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).
[CrossRef] [PubMed]

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

Lederer, F.

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
[CrossRef]

Leo, G.

Lisak, M.

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

Malomed, B.

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
[CrossRef]

Malomed, B. A.

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

Mamyshev, P. V.

Mazilu, D.

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

Mihalache, D.

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

Mollenauer, L. F.

L. F. Mollenauer, P. V. Mamyshev, and M. J. Neubelt, Opt. Lett. 19, 704 (1994).
[CrossRef] [PubMed]

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Berg̀ano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

Neubelt, M. J.

Nishi, S.

K. Iwatsuki, K. Suzuki, S. Nishi, and S. Saruwatari, IEEE Photon. Technol. Lett. 5, 245 (1993).
[CrossRef]

Peschel, U.

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
[CrossRef]

Saruwatari, S.

K. Iwatsuki, K. Suzuki, S. Nishi, and S. Saruwatari, IEEE Photon. Technol. Lett. 5, 245 (1993).
[CrossRef]

Steblina, V. V.

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).
[CrossRef] [PubMed]

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

Stegeman, G. I.

Suzuki, K.

K. Iwatsuki, K. Suzuki, S. Nishi, and S. Saruwatari, IEEE Photon. Technol. Lett. 5, 245 (1993).
[CrossRef]

Torner, L.

C. Balslev Clausen, P. L. Christiansen, and L. Torner, Opt. Commun. 136, 185 (1997).
[CrossRef]

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

D. M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).
[CrossRef]

Torrruellas, W. E.

Wabnitz, S.

C. De Angelis, S. Wabnitz, and M. Haelterman, Electron. Lett. 29, 1568 (1993).
[CrossRef]

Werner, M. J.

Electron. Lett. (1)

C. De Angelis, S. Wabnitz, and M. Haelterman, Electron. Lett. 29, 1568 (1993).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. Iwatsuki, K. Suzuki, S. Nishi, and S. Saruwatari, IEEE Photon. Technol. Lett. 5, 245 (1993).
[CrossRef]

J. Lightwave Technol. (1)

S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Berg̀ano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

C. Balslev Clausen, P. L. Christiansen, and L. Torner, Opt. Commun. 136, 185 (1997).
[CrossRef]

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (2)

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
[CrossRef]

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, Phys. Rev. A 52, 1670 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

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 (3)

Fig. 1
Fig. 1

Collision distance versus SW separation: numeri-cal results. Solid curve, θA=θB=45°, Δθ=0; dashed curve, θAB=45°±Δθ/2, Δθ=9°; dotted curve, θAB=45°±Δθ/2, Δθ=18°.

Fig. 2
Fig. 2

Collision distance versus SW separation: comparison between analytical (curves) and numerical (circles) results. Solid curve and filled circles, θA=θB=45°, Δθ=0; dashed curve and open circles, θAB=45°±Δθ/2, Δθ=9°.

Fig. 3
Fig. 3

Contour plots of component FF1 of two adjacent SW’s (the orthogonal component FF2 shows the same behavior and the second harmonic follows adiabatically): (a) SW separation 2s0=10 and Δθ=0, (b) SW separation as in (a) and Δθ=18°.

Equations (8)

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

iUjz-bj22Ujs2+U3U3-j*=0, iU3z-b322U3s2+U1U22+ΔkU3=0,
U1s|z=0=A1s+S0, z|z=0+B1s-S0, z|z=0=A102 cosθAexp-s+S02α12+B102 cosθBexp-s-S02β12,
U2s|z=0=A2s+S0, z|z=0+B2s-S0, z|z=0=A202 sinθAexp-s+S02α22+B202 sinθBexp-s-S02β22,
U3s|z=0=A3s+S0, z|z=0+B3s-S0, z|z=0=A30 exp-s+S02α32+B30 exp-s-S02β32,
Ujs, z=Ajs, z+Bjs, z=ajhs+S0zexpiλjz×expikzs+S0z+bjhs-S0z×expiγjzexp-ikzs-S0z, U3s, z=A3s, z+B3s, z=a3gs+S0zexpiλ3z×expi2kzs+S0z+b3gs-S0z×expiγ3zexp-i2kzs-S0z,
S0=--+sA1A1*+A2A2*+4A3A3*dsIA,
M0=i-+A1sA1*-A1A1s*+A2sA2*-A2A2s*+2A3sA3*-A3A3s*ds,
dS0dz=-kz+2-+sImP1A1*+P2A2*+4P3A3*dsIAdkdz=-2-+ReP1A1s*+P2A2s*+P3A3s*dsIA,

Metrics