We investigate Landau-Zener all-optical tunneling in a voltage-controlled waveguide array realized in undoped nematic liquid crystals. From the material governing equations we derive the original Zener model and demonstrate a novel approach to Floquet-band tunneling.

© 2006 Optical Society of America

1. D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 13, 794-796 (1988). [CrossRef] [PubMed]
2. S. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, "Channel optical waveguide directional couplers," Appl. Phys. Lett. 22, 46-48 (1972). [CrossRef]
3. A. A. Sukhorukov and Y. S. Kivshar, "Spatial optical solitons in waveguide arrays," IEEE J. Quantum Electron. 39, 31-50 (2003). [CrossRef]
4. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from fibers to photonic crystals (Academic Press, San Diego, 2003).
5. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-4760 (1999). [CrossRef]
6. B. Wu and Q. Niu, "Nonlinear Landau-Zener tunneling," Phys. Rev. A 61, 023402 (2000). [CrossRef]
7. R. Khomeriki and S. Ruffo, "Nonadiabatic Landau-Zener Tunneling in Waveguide Arrays with a Step in the Refractive Index," Phys. Rev. Lett. 94, 113904 (2005). [CrossRef]
8. V. V. Konotop, P. G. Kevrekidis, and M. Salerno, "Landau-Zener tunneling of Bose-Einstein condensates in an optical lattice," Phys. Rev. A 72, 023611 (2005). [CrossRef]
9. S. Trillo and W. E. Torruellas, Spatial Solitons (Springer-Verlag, Berlin, 2001).
10. K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, Berlin, 2001).
11. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-Gap Structure ofWaveguide Arrays and Excitation of Floquet-Bloch Solitons," Phys. Rev. Lett. 90, 053902 (2003). [CrossRef]
12. H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, "Optical Bloch oscillations and Zener tunneling in two-dimensional photonic lattices," in Proc. Top. Meet. On Nonlinear Guided Waves and their Applications, ThD1 (Opt. Soc. Am., Dresden, Germany, 2005).
13. C. Zener, "Non-adiabatic crossing of energy levels," Proc. R. Soc. London Ser. A 137, 696-702 (1932). [CrossRef]
14. I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, New York, 1995).
15. F. Simoni, Nonlinear Optical Properties of Liquid Crystals (World Scientific, Singapore, 1997).
16. A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, "Discrete light propagation and self-trapping in liquid crystals," Opt. Express 13, 1808-1815 (2005), http://www.opticsexpress.org/abstract.cfm?id=82980. [CrossRef] [PubMed]
17. A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, "Discrete propagation and spatial solitons in nematic liquid crystals," Opt. Lett. 29, 1530-1532 (2004). [CrossRef] [PubMed]
18. A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, "Optical multiband vector breathers in tunable waveguide arrays," Opt. Lett. 30, 174-176 (2005). [CrossRef] [PubMed]
19. A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, "All-optical switching and beam steering in tunable waveguide arrays," Appl. Phys. Lett. 86, 051112 (2005). [CrossRef]
20. A. Fratalocchi and G. Assanto, "Discrete light localization in one dimensional nonlinear lattices with arbitrary non locality," Phys. Rev. E 72, 066608 (2005). [CrossRef]
21. A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, "Optically-induced Zener tunneling in one dimensional lattices," Opt. Lett., to be published. [PubMed]

Appl. Phys. Lett.

• S. Somekh, E. Garmire, A. Yariv, H. Garvin, and R. Hunsperger, "Channel optical waveguide directional couplers," Appl. Phys. Lett. 22, 46-48 (1972). [CrossRef]
• A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, "All-optical switching and beam steering in tunable waveguide arrays," Appl. Phys. Lett. 86, 051112 (2005). [CrossRef]

IEEE J. Quantum Electron.

• A. A. Sukhorukov and Y. S. Kivshar, "Spatial optical solitons in waveguide arrays," IEEE J. Quantum Electron. 39, 31-50 (2003). [CrossRef]

Opt. Express

• A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, "Discrete light propagation and self-trapping in liquid crystals," Opt. Express 13, 1808-1815 (2005), http://www.opticsexpress.org/abstract.cfm?id=82980. [CrossRef] [PubMed]

Opt. Lett.

• A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, "Discrete propagation and spatial solitons in nematic liquid crystals," Opt. Lett. 29, 1530-1532 (2004). [CrossRef] [PubMed]
• A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, "Optical multiband vector breathers in tunable waveguide arrays," Opt. Lett. 30, 174-176 (2005). [CrossRef] [PubMed]
• D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 13, 794-796 (1988). [CrossRef] [PubMed]

Phys. Rev. A

• B. Wu and Q. Niu, "Nonlinear Landau-Zener tunneling," Phys. Rev. A 61, 023402 (2000). [CrossRef]
• V. V. Konotop, P. G. Kevrekidis, and M. Salerno, "Landau-Zener tunneling of Bose-Einstein condensates in an optical lattice," Phys. Rev. A 72, 023611 (2005). [CrossRef]

Phys. Rev. E

• A. Fratalocchi and G. Assanto, "Discrete light localization in one dimensional nonlinear lattices with arbitrary non locality," Phys. Rev. E 72, 066608 (2005). [CrossRef]

Phys. Rev. Lett.

• D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-Gap Structure ofWaveguide Arrays and Excitation of Floquet-Bloch Solitons," Phys. Rev. Lett. 90, 053902 (2003). [CrossRef]
• R. Khomeriki and S. Ruffo, "Nonadiabatic Landau-Zener Tunneling in Waveguide Arrays with a Step in the Refractive Index," Phys. Rev. Lett. 94, 113904 (2005). [CrossRef]
• R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Experimental Observation of Linear and Nonlinear Optical Bloch Oscillations," Phys. Rev. Lett. 83, 4756-4760 (1999). [CrossRef]

Proc. R. Soc. London Ser. A

• C. Zener, "Non-adiabatic crossing of energy levels," Proc. R. Soc. London Ser. A 137, 696-702 (1932). [CrossRef]

Other

• I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, New York, 1995).
• F. Simoni, Nonlinear Optical Properties of Liquid Crystals (World Scientific, Singapore, 1997).
• H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, "Optical Bloch oscillations and Zener tunneling in two-dimensional photonic lattices," in Proc. Top. Meet. On Nonlinear Guided Waves and their Applications, ThD1 (Opt. Soc. Am., Dresden, Germany, 2005).
• A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, "Optically-induced Zener tunneling in one dimensional lattices," Opt. Lett., to be published. [PubMed]
• Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from fibers to photonic crystals (Academic Press, San Diego, 2003).
• S. Trillo and W. E. Torruellas, Spatial Solitons (Springer-Verlag, Berlin, 2001).
• K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, Berlin, 2001).

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