Bandgap lattices: low index solitons and linear properties
Optics Express, Vol. 13, Issue 26, pp. 10571-10588 (2005)
http://dx.doi.org/10.1364/OPEX.13.010571
Acrobat PDF (733 KB)
Abstract
A new type of waveguide lattice that relies on the effect of bandgap guidance, rather than total internal reflection, in the regions between the waveguide defects is proposed. Two different setting, for low index and high index defects are suggested. We analyze the linear bandgap and diffraction properties of such lattices. In the nonlinear regime the Kerr effect can counteract diffraction leading to the formation of gap lattice solitons. Interestingly enough, in the case of low index defects, stable soliton solutions are localized in the low index areas. This finding challenges the widely accepted idea that stable solitons can be sustained in high refractive index regions. In addition, in the case of high index defects, the coupling coefficient can become negative. Physical settings where the linear and nonlinear properties for bandgap lattices can be experimentally realized are presented.
© 2005 Optical Society of America
1 Introduction
1 . E. Yablonovitch , “ Inhibited Spontaneous Emission in Solid-State Physics and Electronics ,” Phys. Rev. Lett. 58 , 2059 – 2062 ( 1987 ). [CrossRef] [PubMed]
4 . J. Knight , J. Broeng , T. A. Birks , and P. Russell , “ Photonic band gap guidance in optical fibers ,” Science 282 , 1476 – 1478 ( 1998 ). [CrossRef] [PubMed]
5 . P. Russell , “ Photonic crystal fibers ,” Science 299 , 358 – 362 ( 2003 ). [CrossRef] [PubMed]
6 . D. N. Christodoulides and R. I. Joseph , “ Discrete self-focusing in nonlinear arrays of coupled waveguides ,” Opt. Lett. 13 , 794 – 796 ( 1988 ). [CrossRef] [PubMed]
1 . E. Yablonovitch , “ Inhibited Spontaneous Emission in Solid-State Physics and Electronics ,” Phys. Rev. Lett. 58 , 2059 – 2062 ( 1987 ). [CrossRef] [PubMed]
2 . S. John , “ Strong Localization of Photons in Certain Disordered Dielectric Superlattices ,” Phys. Rev. Lett. 58 , 2486 – 2489 ( 1987 ). [CrossRef] [PubMed]
9 . A. Mekis , J. C. Chen , I. Kurland , S. Fan , P. R. Villeneuve , and J. D. Joannopoulos , “ High Transmission through Sharp Bends in Photonic Crystal Waveguides ,” Phys. Rev. Lett. 77 , 3787 – 3790 ( 1996 ). [CrossRef] [PubMed]
10 . S. L. McCall , P. M. Platzman , R. Dalichaouch , D. Smith , and S. Schultz , “ Microwave Propagation in Two-Dimensional Dielectric Lattices ,” Phys. Rev. Lett. 67 , 2017 – 2020 ( 1991 ). [CrossRef] [PubMed]
11 . E. Yablonovitch , T. J. Gmitter , R. D. Meade , A. M. Rappe , K. D. Brommer , and J. D. Joannopoulos , “ Donor and Acceptor Modes in Photonic Band Strucure ,” Phys. Rev. Lett. 67 , 3380 – 3383 ( 1991 ). [CrossRef] [PubMed]
12 . N. Stefanou and A. Modinos , “ Impurity bands in photonic insulators ,” Phys. Rev. B 57 , 12, 127 –12, 133 ( 1998 ). [CrossRef]
7 . 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]
15 . R. Morandotti , U. Peschel , J. S. Aitchison , H. S. Eisenberg , and Y. Silberberg , “ Dynamics of Discrete Solitons in Optical Waveguide Arrays ,” Phys. Rev. Lett. ( 1999 ). [CrossRef]
6 . D. N. Christodoulides and R. I. Joseph , “ Discrete self-focusing in nonlinear arrays of coupled waveguides ,” Opt. Lett. 13 , 794 – 796 ( 1988 ). [CrossRef] [PubMed]
8 . D. N. Christodoulides , F. Lederer , and Y. Silberberg , “ Discretizing light behaviour in linear and nonlinear waveguide lattices ,” Nature 424 , 817 – 823 ( 2003 ). [CrossRef] [PubMed]
6 . D. N. Christodoulides and R. I. Joseph , “ Discrete self-focusing in nonlinear arrays of coupled waveguides ,” Opt. Lett. 13 , 794 – 796 ( 1988 ). [CrossRef] [PubMed]
7 . 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]
16 . R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. ederer , Y. Min , and W. Sohler , “ Observation of Discrete Quadratic Solitons ,” Phys. Rev. Lett. 93 , 113 , 902 –1–4 ( 2004 ). [CrossRef]
17 . T. Pertsch , P. Dannberg , W. Elflein , A. Bräuer , and F. Lederer , “ Optical Bloch Oscillations in Temperature Tuned Waveguide Arrays ,” Phys. Rev. Lett. 83 , 4752 – 4755 ( 1999 ). [CrossRef]
18 . 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 – 4759 ( 1999 ). [CrossRef]
19 . J. Meier , J. Hudock , D. Christodoulides , G. Stegeman , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays ,” Phys. Rev. Lett. 91 , 143 , 907 –1–4 ( 2003 ). [CrossRef]
20 . 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 , 053 , 902 –1–4 ( 2003 ). [CrossRef]
20 . 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 , 053 , 902 –1–4 ( 2003 ). [CrossRef]
21 . 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 , 023 , 902 –1–4 ( 2003 ). [CrossRef]
22 . J. Feng , “ Alternative scheme for studying gap solitons in an infinite periodic Kerr medium ,” Opt. Lett. 18 , 1302 – 1304 ( 1993 ). [CrossRef] [PubMed]
23 . D. D. Mandelik , R. Morandotti , J. S. Aitchison , and Y. Silberberg , “ Gap Solitons in Waveguide Arrays ,” Phys. Rev. Lett. 92 , 093 , 904 –1–4 ( 2004 ). [CrossRef]
24 . D. Neshev , A. A. Sukhorukov , B. Hanna , W. Krolikowski , and Y. S. Kivshar , “ Controlled Generation and Steering of Spatial Gap Solitons ,” Phys. Rev. Lett. 93 , 083 , 905 –1–4 ( 2004 ). [CrossRef]
25 . P. J. Y. Louis , E. A. Ostrovskaya , C. M. Savage , and Y. S. Kivshar , “ Bose-Einstein condensates in optical lattices: Band-gap structure and solitons ,” Phys. Rev. A 67 , 013 , 602 –1–9 ( 2003 ). [CrossRef]
26 . N. K. Efremidis and D. N. Christodoulides , “ Lattice solitons in Bose-Einstein condensates ,” Phys. Rev. A 67 , 063 , 608 –1–9 ( 2003 ). [CrossRef]
27 . Y. V. Kartashov , V. A. Vysloukh , and L. Torner , “ Soliton trains in photonic lattices ,” Opt. Express 12 , 2831 – 2837 ( 2004 ). [CrossRef] [PubMed]
28 . J. Wang , F. Ye , L. Dong , T. Cai , and Y.-P. Li , “ Lattice solitons supported by competing cubic-quintic nonlinearity ,” Phys. Lett. A 339 , 74 – 82 ( 2005 ). [CrossRef]
29 . P. Kevrekidis , B. Malomed , and Z. Musslimani , “ Discrete gap solitons in a diffraction-managed waveguide array ,” Eur. Phys. J. D 23 , 421 – 436 ( 2003 ). [CrossRef]
30 . D. N. Christodoulides and R. I. Joseph , “ Slow Bragg Solitons in Nonlinear Periodic Structures ,” Phys. Rev. Lett. 62 , 1746 – 1749 ( 1989 ). [CrossRef] [PubMed]
34 . F. Fedele , J. Yang , and Z. Chen , “ Defect modes in one-dimensional photonic lattices ,” Opt. Lett. 30 , 1506 – 1508 ( 2005 ). [CrossRef] [PubMed]
35 . Y. V. Kartashov , L. Torner , and V. A. Vysloukh , “ Diffraction management of focused light beams in optical lattices with a quadratic frequency modulation ,” Opt. Express 13 , 4244 – 4249 ( 2005 ). [CrossRef] [PubMed]
21 . 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 , 023 , 902 –1–4 ( 2003 ). [CrossRef]
36 . N. K. Efremidis , D. N. Christodoulides , S. Sears , J. W. Fleischer , and M. Segev , “ Discrete Solitons in Photorefractive Optically-Induced Photonic Lattices ,” Phys. Rev. E 66 , 046 , 602 –1–5 ( 2002 ). [CrossRef]
37 . 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]
38 . N. K. Efremidis , J. Hudock , D. N. Christodoulides , J. W. Fleischer , O. Cohen , and M. Segev , “ Two-dimensional optical lattice solitons ,” Phys. Rev. Lett. 91 , 213 , 906 –1–4 ( 2003 ). [CrossRef]
25 . P. J. Y. Louis , E. A. Ostrovskaya , C. M. Savage , and Y. S. Kivshar , “ Bose-Einstein condensates in optical lattices: Band-gap structure and solitons ,” Phys. Rev. A 67 , 013 , 602 –1–9 ( 2003 ). [CrossRef]
26 . N. K. Efremidis and D. N. Christodoulides , “ Lattice solitons in Bose-Einstein condensates ,” Phys. Rev. A 67 , 063 , 608 –1–9 ( 2003 ). [CrossRef]
38 . N. K. Efremidis , J. Hudock , D. N. Christodoulides , J. W. Fleischer , O. Cohen , and M. Segev , “ Two-dimensional optical lattice solitons ,” Phys. Rev. Lett. 91 , 213 , 906 –1–4 ( 2003 ). [CrossRef]
39 . J. Yang and Z. H. Musslimani , “ Fundamental and vortex solitons in a two-dimensional optical lattice ,” Opt. Lett. 21 , 2094 – 2096 ( 2003 ). [CrossRef]
39 . J. Yang and Z. H. Musslimani , “ Fundamental and vortex solitons in a two-dimensional optical lattice ,” Opt. Lett. 21 , 2094 – 2096 ( 2003 ). [CrossRef]
42 . 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 , 123 , 904 –1–4 ( 2004 ). [CrossRef]
43 . D. N. Neshev , T. J. Alexander , E. A. Ostrovskaya , Y. S. Kivshar , H. Martin , I. Makasyuk , and Z. Chen , “ Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices ,” Phys. Rev. Lett. 92 , 123 , 903 –1–4 ( 2004 ). [CrossRef]
44 . Y. V. Kartashov , V. A. Vysloukh , and L. Torner , “ Rotary Solitons in Bessel Optical Lattices ,” Phys. Rev. Lett. 93 , 093 , 904 –1–4 ( 2004 ). [CrossRef]
45 . Y. V. Kartashov , A. A. Egorov , L. Torner , and D. N. Christodoulides , “ Stable soliton complexes in two-dimensional photonic lattices ,” Opt. Lett. 29 , 1918 – 1920 ( 2004 ). [CrossRef] [PubMed]
46 . 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 ). [CrossRef] [PubMed]
6 . D. N. Christodoulides and R. I. Joseph , “ Discrete self-focusing in nonlinear arrays of coupled waveguides ,” Opt. Lett. 13 , 794 – 796 ( 1988 ). [CrossRef] [PubMed]
26 . N. K. Efremidis and D. N. Christodoulides , “ Lattice solitons in Bose-Einstein condensates ,” Phys. Rev. A 67 , 063 , 608 –1–9 ( 2003 ). [CrossRef]
12 . N. Stefanou and A. Modinos , “ Impurity bands in photonic insulators ,” Phys. Rev. B 57 , 12, 127 –12, 133 ( 1998 ). [CrossRef]
13 . A. Yariv , Y. Xu , R. K. Lee , and A. Scherer , “ Coupled-resonator optical waveguide: a proposal and analysis ,” Opt. Lett. 24 , 711 – 713 ( 1999 ). [CrossRef]
4 . J. Knight , J. Broeng , T. A. Birks , and P. Russell , “ Photonic band gap guidance in optical fibers ,” Science 282 , 1476 – 1478 ( 1998 ). [CrossRef] [PubMed]
11 . E. Yablonovitch , T. J. Gmitter , R. D. Meade , A. M. Rappe , K. D. Brommer , and J. D. Joannopoulos , “ Donor and Acceptor Modes in Photonic Band Strucure ,” Phys. Rev. Lett. 67 , 3380 – 3383 ( 1991 ). [CrossRef] [PubMed]
34 . F. Fedele , J. Yang , and Z. Chen , “ Defect modes in one-dimensional photonic lattices ,” Opt. Lett. 30 , 1506 – 1508 ( 2005 ). [CrossRef] [PubMed]
47 . P. Yeh and A. Yariv , “ Bragg reflection waveguides ,” Opt. Commun. 19 , 427 – 430 ( 1976 ). [CrossRef]
2 Physical Settings
2.1 Low index guidance
47 . P. Yeh and A. Yariv , “ Bragg reflection waveguides ,” Opt. Commun. 19 , 427 – 430 ( 1976 ). [CrossRef]
48 . A. Y. Cho , A. Yariv , and P. Yeh , “ Observation of confined propagation in Bragg waveguides ,” Appl. Phys. Lett. 30 , 471 ( 1977 ). [CrossRef]
50 . S. Linden , J. P. Mondia , H. M. V. Driel , T. C. Kleckner , C. R. Stanley , D. Modotto , A. Locatelli , C. D. An-gelis , R. Morandotti , and J. S. Aitchison , “ Nonlinear transmission properties of a deep-etched microstructured waveguide ,” Appl. Phys. Lett. 84 , 5437 – 5439 ( 2004 ). [CrossRef]
4 . J. Knight , J. Broeng , T. A. Birks , and P. Russell , “ Photonic band gap guidance in optical fibers ,” Science 282 , 1476 – 1478 ( 1998 ). [CrossRef] [PubMed]
5 . P. Russell , “ Photonic crystal fibers ,” Science 299 , 358 – 362 ( 2003 ). [CrossRef] [PubMed]
21 . 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 , 023 , 902 –1–4 ( 2003 ). [CrossRef]
36 . N. K. Efremidis , D. N. Christodoulides , S. Sears , J. W. Fleischer , and M. Segev , “ Discrete Solitons in Photorefractive Optically-Induced Photonic Lattices ,” Phys. Rev. E 66 , 046 , 602 –1–5 ( 2002 ). [CrossRef]
51 . H. Martin , E. D. Eugenieva , Z. Chen , and D. N. Christodoulides , “ Discrete Solitons and Soliton-Induced Dislocations in Partially Coherent Photonic Lattices ,” Phys. Rev. Lett. 92 , 123 , 902 –1–4 ( 2004 ). [CrossRef]
34 . F. Fedele , J. Yang , and Z. Chen , “ Defect modes in one-dimensional photonic lattices ,” Opt. Lett. 30 , 1506 – 1508 ( 2005 ). [CrossRef] [PubMed]
2.2 High index guidance
2.3 Paraxial model 1
52 . T. M. Monro , D. J. Richardson , N. G. R. Broderick , and P. J. Bennett , “ Holey Optical Fibers: An Efficient Modal Model ,” J. Lightwave Technol. 17 , 1093 – 1102 ( 1999 ). [CrossRef]
53 . R. d. L. Kronig and W. G. Penney , “ Quantum Mechanics of Electrons in Crystal Lattices ,” P. Roy. Soc. Lond. A Mat. 814 , 499 – 513 ( 1931 ). [CrossRef]
54 . S. Theodorakis and E. Leontidis , “ Bound states in a nonlinear Kronig-Penney model ,” J. Phys. A 30 , 4835 – 4849 ( 1997 ). [CrossRef]
3 Low index guidance
3.1 Single defect
3.2 Bandgap lattice and coupled mode theory
58 . H. S. Eisenberg , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Diffraction Management ,” Phys. Rev. Lett. 85 , 1863 – 1866 ( 2000 ). [CrossRef] [PubMed]
12 . N. Stefanou and A. Modinos , “ Impurity bands in photonic insulators ,” Phys. Rev. B 57 , 12, 127 –12, 133 ( 1998 ). [CrossRef]
13 . A. Yariv , Y. Xu , R. K. Lee , and A. Scherer , “ Coupled-resonator optical waveguide: a proposal and analysis ,” Opt. Lett. 24 , 711 – 713 ( 1999 ). [CrossRef]
59 . S. F. Mingaleev , R. A. Kivshar , S. Yuri , and Sammut , “ Long-range interaction and nonlinear localized modes in photonic crystal waveguides ,” Phys. Rev. E 62 , 5777 – 5782 ( 2000 ). [CrossRef]
3.3 Low index solitons
60 . J. Sipe and H. G. Winful , “ Nonlinear Schrödinger solitons in a periodic structure ,” Opt. Lett. 13 , 132 – 133 ( 1988 ). [CrossRef] [PubMed]
4 High refractive index guidance
5 Conclusions
Acknowledgments
References and links
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2 . | S. John , “ Strong Localization of Photons in Certain Disordered Dielectric Superlattices ,” Phys. Rev. Lett. 58 , 2486 – 2489 ( 1987 ). [CrossRef] [PubMed] |
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4 . | J. Knight , J. Broeng , T. A. Birks , and P. Russell , “ Photonic band gap guidance in optical fibers ,” Science 282 , 1476 – 1478 ( 1998 ). [CrossRef] [PubMed] |
5 . | P. Russell , “ Photonic crystal fibers ,” Science 299 , 358 – 362 ( 2003 ). [CrossRef] [PubMed] |
6 . | D. N. Christodoulides and R. I. Joseph , “ Discrete self-focusing in nonlinear arrays of coupled waveguides ,” Opt. Lett. 13 , 794 – 796 ( 1988 ). [CrossRef] [PubMed] |
7 . | 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] |
8 . | D. N. Christodoulides , F. Lederer , and Y. Silberberg , “ Discretizing light behaviour in linear and nonlinear waveguide lattices ,” Nature 424 , 817 – 823 ( 2003 ). [CrossRef] [PubMed] |
9 . | A. Mekis , J. C. Chen , I. Kurland , S. Fan , P. R. Villeneuve , and J. D. Joannopoulos , “ High Transmission through Sharp Bends in Photonic Crystal Waveguides ,” Phys. Rev. Lett. 77 , 3787 – 3790 ( 1996 ). [CrossRef] [PubMed] |
10 . | S. L. McCall , P. M. Platzman , R. Dalichaouch , D. Smith , and S. Schultz , “ Microwave Propagation in Two-Dimensional Dielectric Lattices ,” Phys. Rev. Lett. 67 , 2017 – 2020 ( 1991 ). [CrossRef] [PubMed] |
11 . | E. Yablonovitch , T. J. Gmitter , R. D. Meade , A. M. Rappe , K. D. Brommer , and J. D. Joannopoulos , “ Donor and Acceptor Modes in Photonic Band Strucure ,” Phys. Rev. Lett. 67 , 3380 – 3383 ( 1991 ). [CrossRef] [PubMed] |
12 . | N. Stefanou and A. Modinos , “ Impurity bands in photonic insulators ,” Phys. Rev. B 57 , 12, 127 –12, 133 ( 1998 ). [CrossRef] |
13 . | A. Yariv , Y. Xu , R. K. Lee , and A. Scherer , “ Coupled-resonator optical waveguide: a proposal and analysis ,” Opt. Lett. 24 , 711 – 713 ( 1999 ). [CrossRef] |
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16 . | R. Iwanow , R. Schiek , G. I. Stegeman , T. Pertsch , F. ederer , Y. Min , and W. Sohler , “ Observation of Discrete Quadratic Solitons ,” Phys. Rev. Lett. 93 , 113 , 902 –1–4 ( 2004 ). [CrossRef] |
17 . | T. Pertsch , P. Dannberg , W. Elflein , A. Bräuer , and F. Lederer , “ Optical Bloch Oscillations in Temperature Tuned Waveguide Arrays ,” Phys. Rev. Lett. 83 , 4752 – 4755 ( 1999 ). [CrossRef] |
18 . | 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 – 4759 ( 1999 ). [CrossRef] |
19 . | J. Meier , J. Hudock , D. Christodoulides , G. Stegeman , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Discrete Vector Solitons in Kerr Nonlinear Waveguide Arrays ,” Phys. Rev. Lett. 91 , 143 , 907 –1–4 ( 2003 ). [CrossRef] |
20 . | 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 , 053 , 902 –1–4 ( 2003 ). [CrossRef] |
21 . | 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 , 023 , 902 –1–4 ( 2003 ). [CrossRef] |
22 . | J. Feng , “ Alternative scheme for studying gap solitons in an infinite periodic Kerr medium ,” Opt. Lett. 18 , 1302 – 1304 ( 1993 ). [CrossRef] [PubMed] |
23 . | D. D. Mandelik , R. Morandotti , J. S. Aitchison , and Y. Silberberg , “ Gap Solitons in Waveguide Arrays ,” Phys. Rev. Lett. 92 , 093 , 904 –1–4 ( 2004 ). [CrossRef] |
24 . | D. Neshev , A. A. Sukhorukov , B. Hanna , W. Krolikowski , and Y. S. Kivshar , “ Controlled Generation and Steering of Spatial Gap Solitons ,” Phys. Rev. Lett. 93 , 083 , 905 –1–4 ( 2004 ). [CrossRef] |
25 . | P. J. Y. Louis , E. A. Ostrovskaya , C. M. Savage , and Y. S. Kivshar , “ Bose-Einstein condensates in optical lattices: Band-gap structure and solitons ,” Phys. Rev. A 67 , 013 , 602 –1–9 ( 2003 ). [CrossRef] |
26 . | N. K. Efremidis and D. N. Christodoulides , “ Lattice solitons in Bose-Einstein condensates ,” Phys. Rev. A 67 , 063 , 608 –1–9 ( 2003 ). [CrossRef] |
27 . | Y. V. Kartashov , V. A. Vysloukh , and L. Torner , “ Soliton trains in photonic lattices ,” Opt. Express 12 , 2831 – 2837 ( 2004 ). [CrossRef] [PubMed] |
28 . | J. Wang , F. Ye , L. Dong , T. Cai , and Y.-P. Li , “ Lattice solitons supported by competing cubic-quintic nonlinearity ,” Phys. Lett. A 339 , 74 – 82 ( 2005 ). [CrossRef] |
29 . | P. Kevrekidis , B. Malomed , and Z. Musslimani , “ Discrete gap solitons in a diffraction-managed waveguide array ,” Eur. Phys. J. D 23 , 421 – 436 ( 2003 ). [CrossRef] |
30 . | D. N. Christodoulides and R. I. Joseph , “ Slow Bragg Solitons in Nonlinear Periodic Structures ,” Phys. Rev. Lett. 62 , 1746 – 1749 ( 1989 ). [CrossRef] [PubMed] |
31 . | A. B. Aceves and S. Wabnitz , “ Self-induced transparency solitons in nonlinear refractive periodic media ,” Phys. Lett. A 141 , 37 – 42 ( 1989 ). [CrossRef] |
32 . | B. J. Eggleton , R. E. Slusher , C. M. de Sterke , P. A. Krug , and J. E. Sipe , “ Bragg Grating Solitons ,” Phys. Rev. Lett. 76 , 1627 – 1630 ( 1996 ). [CrossRef] [PubMed] |
33 . | C. M. de Sterke and J. E. Sipe , “ Gap solitons ,” in Progress in Optics , E. Wolf , ed., vol. XXXIII, p. 203 ( North-Holland, Amsterdam , 1994 ). |
34 . | F. Fedele , J. Yang , and Z. Chen , “ Defect modes in one-dimensional photonic lattices ,” Opt. Lett. 30 , 1506 – 1508 ( 2005 ). [CrossRef] [PubMed] |
35 . | Y. V. Kartashov , L. Torner , and V. A. Vysloukh , “ Diffraction management of focused light beams in optical lattices with a quadratic frequency modulation ,” Opt. Express 13 , 4244 – 4249 ( 2005 ). [CrossRef] [PubMed] |
36 . | N. K. Efremidis , D. N. Christodoulides , S. Sears , J. W. Fleischer , and M. Segev , “ Discrete Solitons in Photorefractive Optically-Induced Photonic Lattices ,” Phys. Rev. E 66 , 046 , 602 –1–5 ( 2002 ). [CrossRef] |
37 . | 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] |
38 . | N. K. Efremidis , J. Hudock , D. N. Christodoulides , J. W. Fleischer , O. Cohen , and M. Segev , “ Two-dimensional optical lattice solitons ,” Phys. Rev. Lett. 91 , 213 , 906 –1–4 ( 2003 ). [CrossRef] |
39 . | J. Yang and Z. H. Musslimani , “ Fundamental and vortex solitons in a two-dimensional optical lattice ,” Opt. Lett. 21 , 2094 – 2096 ( 2003 ). [CrossRef] |
40 . | B. A. Malomed and P. G. Kevrekidis , “ Discrete vortex solitons ,” Prys. Rev. E 64 , 026 , 601 –1–6 ( 2001 ). |
41 . | B. B. Baizakov , B. A. Malomed , and M. Salerno , “ Multidimensional solitons in periodic potentials ,” Europhys. Lett. 63 , 642 – 648 ( 2003 ). [CrossRef] |
42 . | 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 , 123 , 904 –1–4 ( 2004 ). [CrossRef] |
43 . | D. N. Neshev , T. J. Alexander , E. A. Ostrovskaya , Y. S. Kivshar , H. Martin , I. Makasyuk , and Z. Chen , “ Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices ,” Phys. Rev. Lett. 92 , 123 , 903 –1–4 ( 2004 ). [CrossRef] |
44 . | Y. V. Kartashov , V. A. Vysloukh , and L. Torner , “ Rotary Solitons in Bessel Optical Lattices ,” Phys. Rev. Lett. 93 , 093 , 904 –1–4 ( 2004 ). [CrossRef] |
45 . | Y. V. Kartashov , A. A. Egorov , L. Torner , and D. N. Christodoulides , “ Stable soliton complexes in two-dimensional photonic lattices ,” Opt. Lett. 29 , 1918 – 1920 ( 2004 ). [CrossRef] [PubMed] |
46 . | 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 ). [CrossRef] [PubMed] |
47 . | P. Yeh and A. Yariv , “ Bragg reflection waveguides ,” Opt. Commun. 19 , 427 – 430 ( 1976 ). [CrossRef] |
48 . | A. Y. Cho , A. Yariv , and P. Yeh , “ Observation of confined propagation in Bragg waveguides ,” Appl. Phys. Lett. 30 , 471 ( 1977 ). [CrossRef] |
49 . | A. Yariv , “ Coupled-wave formalism for optical waveguiding by transverse Bragg reflection ,” Opt. Lett. 27 , 936 – 938 ( 2002 ). [CrossRef] |
50 . | S. Linden , J. P. Mondia , H. M. V. Driel , T. C. Kleckner , C. R. Stanley , D. Modotto , A. Locatelli , C. D. An-gelis , R. Morandotti , and J. S. Aitchison , “ Nonlinear transmission properties of a deep-etched microstructured waveguide ,” Appl. Phys. Lett. 84 , 5437 – 5439 ( 2004 ). [CrossRef] |
51 . | H. Martin , E. D. Eugenieva , Z. Chen , and D. N. Christodoulides , “ Discrete Solitons and Soliton-Induced Dislocations in Partially Coherent Photonic Lattices ,” Phys. Rev. Lett. 92 , 123 , 902 –1–4 ( 2004 ). [CrossRef] |
52 . | T. M. Monro , D. J. Richardson , N. G. R. Broderick , and P. J. Bennett , “ Holey Optical Fibers: An Efficient Modal Model ,” J. Lightwave Technol. 17 , 1093 – 1102 ( 1999 ). [CrossRef] |
53 . | R. d. L. Kronig and W. G. Penney , “ Quantum Mechanics of Electrons in Crystal Lattices ,” P. Roy. Soc. Lond. A Mat. 814 , 499 – 513 ( 1931 ). [CrossRef] |
54 . | S. Theodorakis and E. Leontidis , “ Bound states in a nonlinear Kronig-Penney model ,” J. Phys. A 30 , 4835 – 4849 ( 1997 ). [CrossRef] |
55 . | W. Li and A. Smerzi , “ Nonlinear Krönig-Penney model ,” Phys. Rev. E 70 , 016 , 605 –1–4 ( 2004 ). [CrossRef] |
56 . | I. M. Merhasin , B. V. Gisin , R. Driben , and B. A. Malomed , “ Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity ,” Phys. Rev. E 71 , 016 , 613 –1–12 ( 2005 ). [CrossRef] |
57 . | C. Kittel , Introduction to Solid State Physics ( Wiley, New York , 1986 ). |
58 . | H. S. Eisenberg , Y. Silberberg , R. Morandotti , and J. S. Aitchison , “ Diffraction Management ,” Phys. Rev. Lett. 85 , 1863 – 1866 ( 2000 ). [CrossRef] [PubMed] |
59 . | S. F. Mingaleev , R. A. Kivshar , S. Yuri , and Sammut , “ Long-range interaction and nonlinear localized modes in photonic crystal waveguides ,” Phys. Rev. E 62 , 5777 – 5782 ( 2000 ). [CrossRef] |
60 . | J. Sipe and H. G. Winful , “ Nonlinear Schrödinger solitons in a periodic structure ,” Opt. Lett. 13 , 132 – 133 ( 1988 ). [CrossRef] [PubMed] |
OCIS Codes
(130.2790) Integrated optics : Guided waves
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
ToC Category:
Research Papers
Citation
Nikolaos K. Efremidis and Kyriakos Hizanidis, "Bandgap lattices: low index solitons and linear properties," Opt. Express 13, 10571-10588 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-26-10571
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