Light propagation behavior in a resonantly absorbing waveguide array is analyzed. Both a Lorentzian line shape and an inhomogeneous broadened absorbing line shape are considered, with their imaginary and real part of the refractive index determined by a Kramers–Kronig relationship. The diffracted wave is shown to have the frequency spectra determined by the material absorption, dispersion as well as the waveguide structure. An interesting phenomenon is that a spectral hole is produced and becomes deeper in the diffraction spectrum as the thickness of the resonantly absorbing waveguide array increases. The experimental measurements conducted in a waveguide array are found to be in good agreement with the numerical results.

© 2011 OSA

1. D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behavior in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003). [CrossRef] [PubMed]
2. Z. G. Chen, H. Martin, E. D. Eugenieva, J. J. Xu, and J. K. Yang, “Formation of discrete solitons in light-induced photonic lattices,” Opt. Express 13(6), 1816–1826 (2005). [CrossRef] [PubMed]
3. A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78(3), 031801 (2008). [CrossRef]
4. Y. Y. Li, W. Pang, Y. Z. Chen, Z. Q. Yu, J. Y. Zhou, and H. R. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80(4), 043824 (2009). [CrossRef]
5. T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007). [CrossRef] [PubMed]
6. A. Joushaghani, R. Iyer, J. K. S. Poon, J. S. Aitchison, C. M. de Sterke, J. Wan, and M. M. Dignam, “Quasi-BLOCH oscillations in curved coupled optical waveguides,” Phys. Rev. Lett. 103(14), 143903 (2009). [CrossRef] [PubMed]
7. S. Longhi, “Bloch dynamics of light waves in helical optical waveguide arrays,” Phys. Rev. B 76(19), 195119 (2007). [CrossRef]
8. 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(6928), 147–150 (2003). [CrossRef] [PubMed]
9. 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 Stat. Nonlin. Soft Matter Phys. 66(4 Pt 2), 046602 (2002). [CrossRef] [PubMed]
10. J. D. Liou, C. K. Lee, and K. C. Wu, “Photorefractive crystal-based holographic interferometry system for full-field wave propagation metrology,” Opt. Express 15(9), 5460–5472 (2007). [CrossRef] [PubMed]
11. A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete propagation and spatial solitons in nematic liquid crystals,” Opt. Lett. 29(13), 1530–1532 (2004). [CrossRef] [PubMed]
12. A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete light propagation and self-trapping in liquid crystals,” Opt. Express 13(6), 1808–1815 (2005). [CrossRef] [PubMed]
13. C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009). [CrossRef] [PubMed]
14. N.-C. Panoiu, B. A. Malomed, and R. M. Osgood, Jr., “Semidiscrete solitons in arrayed waveguide structures with Kerr nonlinearity,” Phys. Rev. A 78(1), 013801 (2008). [CrossRef]
15. D. Vujic and S. John, “Pulse reshaping in photonic crystal waveguides and microcavities with Kerr nonlinearity: critical issues for all-optical switching,” Phys. Rev. A 72(1), 013807 (2005). [CrossRef]
16. M. Blaauboer, B. A. Malomed, and G. Kurizki, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84(9), 1906–1909 (2000). [CrossRef] [PubMed]
17. J. P. Prineas, J. Y. Zhou, J. Kuhl, H. M. Gibbs, G. Khitrova, S. W. Koch, and A. Knorr, “Ultrafast ac Stark effect switching of the active photonic band gap from Bragg-periodic semiconductor quantum wells,” Appl. Phys. Lett. 81(23), 4332–4334 (2002). [CrossRef]
18. O. Toader, S. John, and K. Busch, “Optical trapping, field enhancement and laser cooling in photonic crystals,” Opt. Express 8(3), 217–222 (2001). [CrossRef] [PubMed]
19. J. Y. Zhou, H. G. Shao, J. Zhao, X. Yu, and K. S. Wong, “Storage and release of femtosecond laser pulses in a resonant photonic crystal,” Opt. Lett. 30(12), 1560–1562 (2005). [CrossRef] [PubMed]
20. I. V. Mel’nikov and J. S. Aitchison, “Gap soliton memory in a resonant photonic crystal,” Appl. Phys. Lett. 87(20), 201111 (2005). [CrossRef]
21. R. Khomeriki and J. Leon, “Driving light pulses with light in two-level media,” Phys. Rev. Lett. 99(18), 183601 (2007). [CrossRef] [PubMed]
22. J. T. Li and J. Y. Zhou, “Nonlinear optical frequency conversion with stopped short light pulses,” Opt. Express 14(7), 2811–2816 (2006). [CrossRef] [PubMed]
23. A. Kozhekin and G. Kurizki, “Self-induced transparency in Bragg reflectors: gap solitons near absorption resonances,” Phys. Rev. Lett. 74(25), 5020–5023 (1995). [CrossRef] [PubMed]
24. A. E. Kozhekin, G. Kurizki, and B. Malomed, “Standing and moving gap solitons in resonantly absorbing gratings,” Phys. Rev. Lett. 81(17), 3647–3650 (1998). [CrossRef]
25. M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(1 Pt A1 Pt A), R57–R59 (2000). [CrossRef] [PubMed]
26. J. Zhu, J. Y. Zhou, and J. Cheng, “Moving and stationary spatial-temporal solitons in a resonantly absorbing Bragg reflector,” Opt. Express 13(18), 7133–7138 (2005). [CrossRef] [PubMed]
27. Y. Y. Li, B. A. Malomed, M. N. Feng, and J. Y. Zhou, “Array and checkerboard optical waveguides controlled by the electromagnetically induced transparency,” Phys. Rev. A 82(6), 063813 (2010). [CrossRef]
28. J. T. Li, B. Liang, Y. K. Liu, P. Q. Zhang, J. Y. Zhou, S. O. Klimonsky, A. S. Slesarev, Y. D. Tretyakov, L. O’Faolain, and T. F. Krauss, “Photonic crystal formed by the imaginary part of the refractive index,” Adv. Mater. (Deerfield Beach Fla.) 22(24), 2676–2679 (2010). [CrossRef]
29. M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000). [CrossRef] [PubMed]
30. L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, “Fabrication of large area two- and three-dimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. 86(24), 241102 (2005). [CrossRef]
31. Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82(8), 1284–1286 (2003). [CrossRef]
32. O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, “Conical diffraction and gap solitons in honeycomb photonic lattices,” Phys. Rev. Lett. 98(10), 103901 (2007). [CrossRef] [PubMed]
33. O. B. Treidel, O. Peleg, and M. Segev, “Symmetry breaking in honeycomb photonic lattices,” Opt. Lett. 33, 2251–2253 (2009). [CrossRef]
34. B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440(7088), 1166–1169 (2006). [CrossRef] [PubMed]
35. R. Driben, B. A. Malomed, A. Gubeskys, and J. Zyss, “Cubic-quintic solitons in the checkerboard potential,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(6 Pt 2), 066604 (2007). [CrossRef]
36. R. Driben and B. A. Malomed, “Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials,” Eur. Phys. J. D 50(3), 317–323 (2008). [CrossRef]
37. F. Fedele, J. K. Yang, and Z. G. Chen, “Defect modes in one-dimensional photonic lattices,” Opt. Lett. 30(12), 1506–1508 (2005). [CrossRef] [PubMed]
38. X. S. Wang, Z. G. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96(8), 083904 (2006). [CrossRef] [PubMed]
39. J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, “Observation of vortex-ring “discrete” solitons in 2D photonic lattices,” Phys. Rev. Lett. 92(12), 123904 (2004). [CrossRef] [PubMed]
40. A. Argyros, I. M. Bassett, M. A. van Eijkelenborg, M. C. J. Large, J. Zagari, N. A. P. Nicorovici, R. C. McPhedran, and C. M. de Sterke, “Ring structures in microstructured polymer optical fibres,” Opt. Express 9(13), 813–820 (2001). [CrossRef] [PubMed]

Adv. Mater. (Deerfield Beach Fla.)

• J. T. Li, B. Liang, Y. K. Liu, P. Q. Zhang, J. Y. Zhou, S. O. Klimonsky, A. S. Slesarev, Y. D. Tretyakov, L. O’Faolain, and T. F. Krauss, “Photonic crystal formed by the imaginary part of the refractive index,” Adv. Mater. (Deerfield Beach Fla.) 22(24), 2676–2679 (2010). [CrossRef]

Appl. Phys. Lett.

• L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, and G. P. Wang, “Fabrication of large area two- and three-dimensional polymer photonic crystals using single refracting prism holographic lithography,” Appl. Phys. Lett. 86(24), 241102 (2005). [CrossRef]
• Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82(8), 1284–1286 (2003). [CrossRef]
• I. V. Mel’nikov and J. S. Aitchison, “Gap soliton memory in a resonant photonic crystal,” Appl. Phys. Lett. 87(20), 201111 (2005). [CrossRef]
• J. P. Prineas, J. Y. Zhou, J. Kuhl, H. M. Gibbs, G. Khitrova, S. W. Koch, and A. Knorr, “Ultrafast ac Stark effect switching of the active photonic band gap from Bragg-periodic semiconductor quantum wells,” Appl. Phys. Lett. 81(23), 4332–4334 (2002). [CrossRef]

Eur. Phys. J. D

• R. Driben and B. A. Malomed, “Stabilization of two-dimensional solitons and vortices against supercritical collapse by lattice potentials,” Eur. Phys. J. D 50(3), 317–323 (2008). [CrossRef]

Nature

• M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000). [CrossRef] [PubMed]
• D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behavior in linear and nonlinear waveguide lattices,” Nature 424(6950), 817–823 (2003). [CrossRef] [PubMed]
• T. Schwartz, G. Bartal, S. Fishman, and M. Segev, “Transport and Anderson localization in disordered two-dimensional photonic lattices,” Nature 446(7131), 52–55 (2007). [CrossRef] [PubMed]
• 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(6928), 147–150 (2003). [CrossRef] [PubMed]
• B. Freedman, G. Bartal, M. Segev, R. Lifshitz, D. N. Christodoulides, and J. W. Fleischer, “Wave and defect dynamics in nonlinear photonic quasicrystals,” Nature 440(7088), 1166–1169 (2006). [CrossRef] [PubMed]

Opt. Express

• A. Argyros, I. M. Bassett, M. A. van Eijkelenborg, M. C. J. Large, J. Zagari, N. A. P. Nicorovici, R. C. McPhedran, and C. M. de Sterke, “Ring structures in microstructured polymer optical fibres,” Opt. Express 9(13), 813–820 (2001). [CrossRef] [PubMed]
• Z. G. Chen, H. Martin, E. D. Eugenieva, J. J. Xu, and J. K. Yang, “Formation of discrete solitons in light-induced photonic lattices,” Opt. Express 13(6), 1816–1826 (2005). [CrossRef] [PubMed]
• O. Toader, S. John, and K. Busch, “Optical trapping, field enhancement and laser cooling in photonic crystals,” Opt. Express 8(3), 217–222 (2001). [CrossRef] [PubMed]
• J. D. Liou, C. K. Lee, and K. C. Wu, “Photorefractive crystal-based holographic interferometry system for full-field wave propagation metrology,” Opt. Express 15(9), 5460–5472 (2007). [CrossRef] [PubMed]
• A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete light propagation and self-trapping in liquid crystals,” Opt. Express 13(6), 1808–1815 (2005). [CrossRef] [PubMed]
• C. Monat, B. Corcoran, M. Ebnali-Heidari, C. Grillet, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Slow light enhancement of nonlinear effects in silicon engineered photonic crystal waveguides,” Opt. Express 17(4), 2944–2953 (2009). [CrossRef] [PubMed]
• J. T. Li and J. Y. Zhou, “Nonlinear optical frequency conversion with stopped short light pulses,” Opt. Express 14(7), 2811–2816 (2006). [CrossRef] [PubMed]
• J. Zhu, J. Y. Zhou, and J. Cheng, “Moving and stationary spatial-temporal solitons in a resonantly absorbing Bragg reflector,” Opt. Express 13(18), 7133–7138 (2005). [CrossRef] [PubMed]

Opt. Lett.

• F. Fedele, J. K. Yang, and Z. G. Chen, “Defect modes in one-dimensional photonic lattices,” Opt. Lett. 30(12), 1506–1508 (2005). [CrossRef] [PubMed]
• A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete propagation and spatial solitons in nematic liquid crystals,” Opt. Lett. 29(13), 1530–1532 (2004). [CrossRef] [PubMed]
• J. Y. Zhou, H. G. Shao, J. Zhao, X. Yu, and K. S. Wong, “Storage and release of femtosecond laser pulses in a resonant photonic crystal,” Opt. Lett. 30(12), 1560–1562 (2005). [CrossRef] [PubMed]
• O. B. Treidel, O. Peleg, and M. Segev, “Symmetry breaking in honeycomb photonic lattices,” Opt. Lett. 33, 2251–2253 (2009). [CrossRef]

Phys. Rev. A

• N.-C. Panoiu, B. A. Malomed, and R. M. Osgood, Jr., “Semidiscrete solitons in arrayed waveguide structures with Kerr nonlinearity,” Phys. Rev. A 78(1), 013801 (2008). [CrossRef]
• D. Vujic and S. John, “Pulse reshaping in photonic crystal waveguides and microcavities with Kerr nonlinearity: critical issues for all-optical switching,” Phys. Rev. A 72(1), 013807 (2005). [CrossRef]
• A. Szameit, I. L. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. A. Sukhorukov, T. Pertsch, D. N. Neshev, S. Nolte, W. Krolikowski, A. Tünnermann, A. Mitchell, and Y. S. Kivshar, “Observation of diffraction-managed discrete solitons in curved waveguide arrays,” Phys. Rev. A 78(3), 031801 (2008). [CrossRef]
• Y. Y. Li, W. Pang, Y. Z. Chen, Z. Q. Yu, J. Y. Zhou, and H. R. Zhang, “Defect-mediated discrete solitons in optically induced photorefractive lattices,” Phys. Rev. A 80(4), 043824 (2009). [CrossRef]
• Y. Y. Li, B. A. Malomed, M. N. Feng, and J. Y. Zhou, “Array and checkerboard optical waveguides controlled by the electromagnetically induced transparency,” Phys. Rev. A 82(6), 063813 (2010). [CrossRef]

Phys. Rev. B

• S. Longhi, “Bloch dynamics of light waves in helical optical waveguide arrays,” Phys. Rev. B 76(19), 195119 (2007). [CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

• 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 Stat. Nonlin. Soft Matter Phys. 66(4 Pt 2), 046602 (2002). [CrossRef] [PubMed]
• R. Driben, B. A. Malomed, A. Gubeskys, and J. Zyss, “Cubic-quintic solitons in the checkerboard potential,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(6 Pt 2), 066604 (2007). [CrossRef]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics

• M. Blaauboer, G. Kurizki, and B. A. Malomed, “Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62(1 Pt A1 Pt A), R57–R59 (2000). [CrossRef] [PubMed]

Phys. Rev. Lett.

• A. Kozhekin and G. Kurizki, “Self-induced transparency in Bragg reflectors: gap solitons near absorption resonances,” Phys. Rev. Lett. 74(25), 5020–5023 (1995). [CrossRef] [PubMed]
• A. E. Kozhekin, G. Kurizki, and B. Malomed, “Standing and moving gap solitons in resonantly absorbing gratings,” Phys. Rev. Lett. 81(17), 3647–3650 (1998). [CrossRef]
• R. Khomeriki and J. Leon, “Driving light pulses with light in two-level media,” Phys. Rev. Lett. 99(18), 183601 (2007). [CrossRef] [PubMed]
• X. S. Wang, Z. G. Chen, and P. G. Kevrekidis, “Observation of discrete solitons and soliton rotation in optically induced periodic ring lattices,” Phys. Rev. Lett. 96(8), 083904 (2006). [CrossRef] [PubMed]
• J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, “Observation of vortex-ring “discrete” solitons in 2D photonic lattices,” Phys. Rev. Lett. 92(12), 123904 (2004). [CrossRef] [PubMed]
• O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, and D. N. Christodoulides, “Conical diffraction and gap solitons in honeycomb photonic lattices,” Phys. Rev. Lett. 98(10), 103901 (2007). [CrossRef] [PubMed]
• A. Joushaghani, R. Iyer, J. K. S. Poon, J. S. Aitchison, C. M. de Sterke, J. Wan, and M. M. Dignam, “Quasi-BLOCH oscillations in curved coupled optical waveguides,” Phys. Rev. Lett. 103(14), 143903 (2009). [CrossRef] [PubMed]
• M. Blaauboer, B. A. Malomed, and G. Kurizki, “Spatiotemporally localized multidimensional solitons in self-induced transparency media,” Phys. Rev. Lett. 84(9), 1906–1909 (2000). [CrossRef] [PubMed]

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