Nonlinear Bloch modes in two-dimensional photonic lattices

Optics Express

Volumn 14, Issue 5, 2006, Pages 1913-1923

  Träger, Denis ^a,b   Fischer, Robert ^a   Neshev, Dragomir N ^a   Sukhorukov, Andrey A ^a   Denz, Cornelia ^b   Królikowski, Wieslaw ^a   Kivshar, Yuri S ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b UNIVERSITY OF MÜNSTER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; CRYSTAL LATTICES; DIFFRACTIVE OPTICS; PHOTONS;

ANISOTROPIC DIFFRACTION; NONLINEAR BLOCH MODES; PHOTONIC LATTICES;

NONLINEAR OPTICS;

EID: 33644764071     PISSN: 10944087     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.14.001913     Document Type: Article

References (41)

1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, 1995).
2. P. S. Russell, "Bloch wave analysis of dispersion and pulse-propagation in pure distributed feedback structures," J. Mod. Opt. 38, 1599-1619 (1991).
3. P. St. J. Russell, T. A. Birks, and F. D. Lloyd Lucas, "Photonic Bloch waves and photonic band gaps," in Confined Electrons and Photons, E. Burstein and C. Weisbuch, eds., (1995), pp. 585-633.
4. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
5. T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901-4 (2002).
6. M. Lončar, D. Nedeljković, T. P. Pearsall, J. Vučković, A. Scherer, S. Kuchinsky, and D. C. Allan, "Experimental and theoretical confirmation of Bloch-mode light propagation in planar photonic crystal waveguides," Appl. Phys. Lett. 80, 1689-1691 (2002).
7. P. E. Barclay, K. Srinivasan, M. Borselli, and O. Painter, "Probing the dispersive and spatial properties of photonic crystal waveguides via highly efficient coupling from fiber tapers," Appl. Phys. Lett. 85, 4-6 (2004).
8. S. I. Bozhevolnyi, V. S. Volkov, T. Sondergaard, A. Boltasseva, P. I. Borel, and M. Kristensen, "Near-field imaging of light propagation in photonic crystal waveguides: explicit role of Bloch harmonics," Phys. Rev. B 66, 235204-9 (2002).
9. H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. Hulst, van, T. F. Krauss, and L. Kuipers, "Direct observation of Bloch harmonics and negative phase velocity in photonic crystal waveguides," Phys. Rev. Lett. 94, 123901-4 (2005).
10. R. J. P. Engelen, T. T. Karle, H. Gersen, T. P. Korterik, T. F. Krauss, L. Kuipers, and N. F. Hulst, van, "Local probing of Bloch mode dispersion in a photonic crystal waveguide," Opt. Express 13, 4457-4464 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4457.
11. Yu. I. Voloshchenko, Yu. N. Ryzhov, and V. E. Sotin, "Stationary waves in non-linear, periodically modulated media with higher group retardation," Zh. Tekh. Fiz. 51, 902-907 (1981) (in Russian)
12. [English translation: Tech. Phys. 26, 541-544 (1981)].
13. W. Chen and D. L. Mills, "Gap solitons and Ihe nonlinear optical-response of superlattices," Phys. Rev. Lett. 58, 160-163 (1987).
14. D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled wave-guides," Opt. Lett. 13, 794-796 (1988).
15. C. M. de Sterke and J. E. Sipe, "Gap solitons," in Progress in Optics, E. Wolf, ed., (North-Holland, Amsterdam, 1994), Vol. XXXIII, pp. 203-260.
16. J. Feng, "Alternative scheme for studying gap solitons in an infinite periodic Kerr medium," Opt. Lett. 18, 1302-1304 (1993).
17. R. F. Nabiev, P. Yeh, and D. Botez, "Spatial gap solitons in periodic nonlinear structures," Opt. Lett. 18, 1612-1614 (1993).
18. S. John and N. Akozbek, "Nonlinear-optical solitary waves in a photonic band-gap," Phys. Rev. Lett. 71, 1168-1171 (1993).
19. N. Akozbek and S. John, "Optical solitary waves in two- and three-dimensional nonlinear photonic band-gap structures," Phys. Rev. E 57, 2287-2319 (1998).
20. S. F. Mingaleev and Yu. S. Kivshar, "Self-trapping and stable localized modes in nonlinear photonic crystals," Phys. Rev. Lett. 86, 5474-5477 (2001).
21. B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, "Nonlinear pulse propagation in Bragg gratings," J. Opt. Soc. Am. B 14, 2980-2993 (1997).
22. Y. V. Kartashov, V. A. Vysloukh and L. Torner, "Soliton trains in photonic lattices," Opt. Express 12, 2831 (2004), http://www.opticsexpress. org/abstract.cfm?URI=OPEX-12-13-2831.
23. J. Hudock, N. K. Efremidis and D. N. Christodoulides, "Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays," Opt. Lett. 29, 268-270 (2004).
24. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 053902-4 (2003).
25. A. A. Sukhorukov, D. Neshev, W. Królikowski, and Yu. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices," Phys. Rev. Lett. 92, 093901-4 (2004).
26. C. M. de Sterke, "Theory of modulational instability in fiber Bragg gratings," J. Opt. Soc. Am. B 15, 2660-2667 (1998).
27. J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, "Experimental observation of discrete modulational instability," Phys. Rev. Lett. 92, 163902-4 (2004).
28. R. Iwanow, G. I. Stegeman, R. Schick, Y. Min, and W. Sohler, "Discrete modulational instability in periodically poled lithium niobate waveguide arrays," Opt. Express 13, 7794-7799 (2005), http://www. opticsexpress.org/abstract.cfm?URI=OPEX-13-20-7794.
29. M. Stepić, C. Wirth, C. Rüter, and D. Kip, "Experimental observation of modulational instability in self-detbcusing nonlinear waveguide arrays," Opt. Lett. 31, 247-249 (2006).
30. M. Chauvet, G. Fu, G. Salamo, T. W. Fleischer, and M. Segev, "Experimental Observation of Discrete Modulation Instability in 1-D Nonlinear Waveguide Arrays," In Nonlinear Guided Waves und Their Applications, Postconference ed. OSA p. WD39 (Optical Society of America, Washington DC, 2005).
31. B. J. Eggleton, C. M. de Sterke, A. B. Aceves, J. E. Sipe, T. A. Strasser, and R. E. Slusher, "Modulational instability and tunable multiple soliton generation in apodized fiber gratings," Opt. Commun. 149, 267-271 (1998).
32. G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Leu. 94, 163902-4 (2005).
33. 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).
34. Nonlinear Photonic Crystals, Vol. 10 of Springer Series in Photonics, R. E. Slusher and B. J. Eggleton, eds., (Springer-Verlag, Berlin, 2003).
35. 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).
36. H. Martin, E. D. Eugenieva, Z. G. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902-4 (2004).
37. O. Cohen, B. Freedman, J. W. Fleischer, M. Segev, and D. N. Christodoulides, "Grating-mediated waveguiding," Phys. Rev. Lett. 93, 103902-4 (2004).
38. B. Freedman, O. Cohen, O. Manela, M. Segev, J. W. Fleischer, and D. N. Christodoulides, "Grating-mediated wave guiding and holographic solitons," J. Opt. Soc. Am. B 22, 1349-1355 (2005).
39. R. Fischer, D. Träger, D. N. Neshev, A. A. Sukhorukov, W. Królikowski, C. Denz, and Yu. S. Kivshar, "Reduced-symmerry two-dimensional solitons in photonic lattices," Phys. Rev. Lett. 96, 023905-4 (2006).
40. O. Matiela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29, 2049-2051 (2004).
41. O. Bartal, O. Manela, O. Cohen, J. W. Fleischer, and M. Segev, "Observation of second-band vortex solitons in 2D photonic lattices," Phys. Rev. Lett. 95, 053904-4 (2005).