Interlaced linear-nonlinear optical waveguide arrays

Interlaced linear-nonlinear optical waveguide arrays Kyriakos Hizanidis, 1,* Yannis Kominis, 1 and Nikolaos K. Efremidis2 1 School of Electrical and Computer Engineering, National Technical University of Athens, Athens, Greece 2 Department of Applied Mathematics, University of Crete, Crete, Greece *Corresponding author: kyriakos@central.ntua.gr Abstract: The system of coupled discrete equations describing a two- component superlattice with interlaced linear and nonlinear constituents is revisited as a basis for investigating binary waveguide arrays, such as ribbed AlGaAs structures, among others. Compared to the single nonlinear lattice, the interlaced system exhibits an extra band-gap controlled by the, suitably chosen by design, relative detuning. In more general physics settings, this system represents a discretization scheme for the single-equation-based continuous models in media with transversely modulated linear and nonlinear properties. Continuous wave solutions and the associated modulational instability are fully analytically investigated and numerically tested for focusing and defocusing nonlinearity. The propagation dynamics and the stability of periodic modes are also analytically investigated for the case of zero Bloch momentum. In the band-gaps a variety of stable discrete solitary modes, dipole or otherwise, in-phase or of staggered type are found and discussed. ©2008 Optical Society of America OCIS codes: (190.4390) Nonlinear optics, integrated optics; (190.4420) Nonlinear optics, transverse effects in; (190.5530) Nonlinear Optics Pulse propagation and solitons; (190.6135) Spatial solitons; (190.5940) Self-action effects. References and links 1. D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled waveguides," Opt. Lett. 13, 794 (1988). 2. A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays”, IEEE J. Quantum Electron. 39, 31 (2003). 3. J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freeman, M. Segev, H. Buljan, and N. K. Efremidis, “Spatial photonics in nonlinear waveguide arrays,” Opt. Express 13, 1780–1796 (2005). 4. D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, “Gap Solitons inWaveguide Arrays,” Phys. Rev. Lett. 92, 093,904–1–4 (2004). 5. D.N. Christodoulides and E. D. Eugenieva, “Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays,” Phys. Rev. Lett. 87, 233901 (2001). 6. D. N. Christodouldes and E. D. Eugenieva, “Minimizing bending losses in two-dimensional discrete soliton networks, Opt. Lett. 23, 1876, (2001). 7. E. D. Eugenieva, N. Efremidis, and D. N. Christodoulides “Design of switching junctions for two-dimensional discrete soliton network”, Opt. Lett. 26, 1978 (2001). 8. R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, “Controlled switching of discrete solitons in waveguide arrays”, Opt. Lett. 28, 1942 (2003). 9. R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, “All-optical switching and amplification of discrete vector solitons in nonlinear cubic birefrigent wave guide arrays”, Opt. Lett. 29, 2905 (2004). 10. Y. V. Kartashov, L. Torner, and V. A. Vysloukh, “Parametric amplification of soliton steering in optical lattices”, Opt. Lett. 29, 1102 (2004). 11. F. Kh. Abdullaev, B. B. Baizakov, S. A. Darmanyan, V. V. Konotop, and M. Salerno, “Nonlinear excitations in arrays in Bose-Einstein condensates”, Phys. Rev. A 64, 043606 (2001). 12. G. L. Alfimov, V. V. Konotop, and M. Salerno, “Matter solitons in Bose-Einstein condensates with optical lattices”, Europhys. Lett. 58, 7 (2002). 13. V. V. Konotop and M. Salerno, “Modulational instability in Bose-Einstein condensates in optical lattices”, “Phys. Rev. A 65, 021602(R) (2002). 14. N. K. Efremidis and D. N. Christodoulides, “Lattice solitons in Bose-Einstein condensates,” Phys. Rev. A 67, 063,608–1–9 (2003). 15. P. J. Y. Louis, E. A. Ostrovskaya, and Y. S. Kivshar, “Matter-wave dark solitons in optical lattices”, J. Opt. B 6, S309 (2004). 16. Y. S. Kivshar, W. Krolikowsi, and O. A. Chubykalo, “Dark solitons in discrete lattices”, Phys. Rev. E 50, 5020 (1994). 17. M. Johansson and Y. S. Kivshar, “Discreteness-induced oscillatory instabilities in dark solitons”, Phys. Rev. Lett. 82, 85 (1999). 18. V. V. Konotop and S. Takeno, “Stationary dark localized modes: Discrete nonlinear Schrödinger equations“, Phys. Rev. E 60, 1001 (1999). 19. B. Sanchez-Rey and M. Johansson, “Exact numerical solutions for dark waves on the discrete nonlinear Schrödinger equation”, Phys. Rev. E 71, 036627 (2005). 20. H. Susanto and M. Johansson, “Discrete dark solitons with multiple holes”, Phys. Rev. E 72, 016605 (2005). 21. Y. Kominis and K. Hizanidis, “Power dependent soliton location and stability in complex photonic structures”. Opt. Express 16, 12124 (2008). 22. S. Theodorakis and E. Leontidis, “Bou

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