Abstract

We study nonlinear coupling of mutually incoherent beams associated with different Floquet-Bloch waves in a one-dimensional optically-induced photonic lattice. We demonstrate experimentally how such interactions lead to asymmetric mutual focusing and, for waves with opposite diffraction properties, to simultaneous focusing and defocusing as well as discreteness-induced beam localization and reshaping effects.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).
  2. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, �??Diffraction management,�?? Phys. Rev. Lett. 85, 1863�??1866 (2000).
    [CrossRef] [PubMed]
  3. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, �??Discrete spatial optical solitons in waveguide arrays,�?? Phys. Rev. Lett. 81, 3383�??3386 (1998).
    [CrossRef]
  4. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, �??Observation of discrete solitons in optically induced real time waveguide arrays,�?? Phys. Rev. Lett. 90, 023902�??4 (2003).
    [CrossRef] [PubMed]
  5. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, �??Spatial solitons in optically induced gratings,�?? Opt. Lett. 28, 710�??712 (2003).
    [CrossRef] [PubMed]
  6. J.W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, �??Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,�?? Nature 422, 147�??150 (2003).
    [CrossRef] [PubMed]
  7. D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, �??Gap solitons in waveguide arrays,�?? Phys. Rev. Lett. 92, 093904�??4 (2004).
    [CrossRef] [PubMed]
  8. D. Neshev, A. A. Sukhorukov, B. Hanna,W. Krolikowski, and Yu. S. Kivshar, �??Controlled generation and steering of spatial gap solitons,�?? Phys. Rev. Lett. 93, 083905�??4 (2004).
    [CrossRef]
  9. O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D. N. Christodoulides, �??Multiband vector lattice solitons,�?? Phys. Rev. Lett. 91, 113901�??4 (2003).
    [CrossRef] [PubMed]
  10. A. A. Sukhorukov and Yu. S. Kivshar, �??Multigap discrete vector solitons,�?? Phys. Rev. Lett. 91, 113902�??4 (2003).
    [CrossRef] [PubMed]
  11. H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, �??Random-phase solitons in nonlinear periodic lattices,�?? Phys. Rev. Lett. 92, 223901�??4 (2004).
    [CrossRef] [PubMed]
  12. K. Motzek, A. A. Sukhorukov, F. Kaiser, and Yu. S. Kivshar, �??Incoherent multi-gap optical solitons in nonlinear photonic lattices,�?? Opt. Express 13, 2916�??2923 (2005).
    [CrossRef] [PubMed]
  13. O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, �??Observation of random-phase lattice solitons,�?? Nature 433, 500�??503 (2005).
    [CrossRef] [PubMed]
  14. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, �??Observation of mutually trapped multiband optical breathers in waveguide arrays,�?? Phys. Rev. Lett. 90, 253902�??4 (2003).
    [CrossRef] [PubMed]
  15. Y. Lahini, D. Mandelik, Y. Silberberg, and R. Morandotti, �??Polarization dependent properties of waveguide arrays: band-structure anomaly and high-band localizations,�?? Opt. Express 13, 1762�??1773 (2005).
    [CrossRef] [PubMed]
  16. S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, �??Optical solitary waves induced by cross-phase modulation,�?? Opt. Lett. 13, 871�??873 (1988).
    [CrossRef] [PubMed]
  17. V. V. Afanasyev, Yu. S. Kivshar, V. V. Konotop, and V. N. Serkin, �??Dynamics of coupled dark and bright optical solitons,�?? Opt. Lett. 14, 805�??807 (1989).
    [CrossRef] [PubMed]
  18. Yu. S. Kivshar, D. Anderson, A. Hook, M. Lisak, A. A. Afanasjev, and V. N. Serkin, �??Symbiotic optical solitons and modulational instability,�?? Phys. Scr. 44, 195�??202 (1991).
    [CrossRef]
  19. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, �??Discrete solitons in photorefractive optically induced photonic lattices,�?? Phys. Rev. E 66, 046602�??5 (2002).
    [CrossRef]

Nature

J.W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, �??Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,�?? Nature 422, 147�??150 (2003).
[CrossRef] [PubMed]

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J. W. Fleischer, M. Segev, and D. N. Christodoulides, �??Observation of random-phase lattice solitons,�?? Nature 433, 500�??503 (2005).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. E

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, �??Discrete solitons in photorefractive optically induced photonic lattices,�?? Phys. Rev. E 66, 046602�??5 (2002).
[CrossRef]

Phys. Rev. Lett.

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, �??Observation of mutually trapped multiband optical breathers in waveguide arrays,�?? Phys. Rev. Lett. 90, 253902�??4 (2003).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, �??Diffraction management,�?? Phys. Rev. Lett. 85, 1863�??1866 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, �??Discrete spatial optical solitons in waveguide arrays,�?? Phys. Rev. Lett. 81, 3383�??3386 (1998).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, �??Observation of discrete solitons in optically induced real time waveguide arrays,�?? Phys. Rev. Lett. 90, 023902�??4 (2003).
[CrossRef] [PubMed]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, �??Gap solitons in waveguide arrays,�?? Phys. Rev. Lett. 92, 093904�??4 (2004).
[CrossRef] [PubMed]

D. Neshev, A. A. Sukhorukov, B. Hanna,W. Krolikowski, and Yu. S. Kivshar, �??Controlled generation and steering of spatial gap solitons,�?? Phys. Rev. Lett. 93, 083905�??4 (2004).
[CrossRef]

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D. N. Christodoulides, �??Multiband vector lattice solitons,�?? Phys. Rev. Lett. 91, 113901�??4 (2003).
[CrossRef] [PubMed]

A. A. Sukhorukov and Yu. S. Kivshar, �??Multigap discrete vector solitons,�?? Phys. Rev. Lett. 91, 113902�??4 (2003).
[CrossRef] [PubMed]

H. Buljan, O. Cohen, J. W. Fleischer, T. Schwartz, M. Segev, Z. H. Musslimani, N. K. Efremidis, and D. N. Christodoulides, �??Random-phase solitons in nonlinear periodic lattices,�?? Phys. Rev. Lett. 92, 223901�??4 (2004).
[CrossRef] [PubMed]

Phys. Scr.

Yu. S. Kivshar, D. Anderson, A. Hook, M. Lisak, A. A. Afanasjev, and V. N. Serkin, �??Symbiotic optical solitons and modulational instability,�?? Phys. Scr. 44, 195�??202 (1991).
[CrossRef]

Other

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic Press, San Diego, 2003).

Supplementary Material (1)

» Media 1: AVI (393 KB)     

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 (6)

Fig. 1.
Fig. 1.

(a) Dispersion of the Bloch waves in an optically-induced lattice; the bands are shaded. (b) Bloch-wave profiles at the gap edges (solid) and their leading-order Fourier components (dashed), superimposed on the normalized refractive index profile (shaded). (c) Schematic of (1) the Bloch-wave excitation with a single beam and (2) a pair of beams inclined at the Bragg angle. (d) Experimental intensity profiles of the optical lattice and the input beams.

Fig. 2.
Fig. 2.

Experimental results for interband mutual focusing of the beams generated at the top of the 2 nd band (orange) and top of the 1 st band (brown). (a) Both components at low power. (b) 1 st -band beam at high power and 2 i -band beam at low power (70 nW). (c) Beam width vs. power of the 1st-band mode. Solid curves are exponential fits to the data points.

Fig. 3.
Fig. 3.

Experimental results for interband mutual focusing of the beams generated at the top of the 1st band (brown) and top of the 2nd band (orange). (a) Both components at low power. (b) 2nd-band beam at high power (900 nW) and 1st-band beam at low power (100 nW). (c) Two-dimensional visualization of output profiles for increasing 2nd-band power.

Fig. 4.
Fig. 4.

Experimental results for coupling of beams at the top (brown) and bottom (blue) of the 1st band. (a) Both components at low power. (b) Bottom of 1st band at high power and top of 1st band at low power (100 nW). (c) Beam width vs. power of the 1st band bottom mode.

Fig. 5.
Fig. 5.

Experimental results for coupling of beams at the bottom (blue) and top (brown) of the 1st band. (a) Both components at low power (50 nW). (b) Top of 1st band at high power (4.0 µW) and bottom of 1st band at low power. (c) Movie (0.4 Mb) shows the fundamental beam self-focusing and the simultaneous appearance of a discrete localized peak and two decoupled outer lobes for the beam at the bottom of the band. The power of the fundamental beam is shown in the upper right corner.

Fig. 6.
Fig. 6.

Beam propagation method simulations of interband focusing (left) and interaction of focusing and defocusing 1st-band beams (right). The plot windows are 320 µm and 15 mm in the transverse (x) and propagation (z) directions, respectively. In (a,b) and (c,d) two beams co-propagate at low power and experience diffraction. In (e,f) the power of the beam at the top of the 1st band is increased, causing focusing of this beam and the low power 2nd-band beam. In (g,h) interaction between a high power fundamental beam and a low power beam at the bottom of the 1st band results in the formation of a complex beating pattern and the appearance of a localized discrete central peak and two diffracting outer lobes.

Equations (1)

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

i E n z + D 2 E n x 2 + 𝓕 ( x , I ) E n = 0 ,

Metrics