Discrete diffraction and shape-invariant beams in optical waveguide arrays

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 79, Issue 3, 2009, Pages

  Longhi, Stefano ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

BEAM COLLIMATIONS; BEAM SPREADING; BESSEL BEAMS; BLOCH OSCILLATIONS; CONTINUOUS MEDIAS; CURVED WAVEGUIDES; DISCRETE DIFFRACTIONS; FAR-FIELD PATTERNS; GENERAL LAWS; GLOBAL BEAMS; INVARIANT BEAMS; LINEAR PROPAGATION; OPTICAL WAVEGUIDE ARRAYS; PARAXIAL; Q PARAMETERS; STEEPEST-DESCENT METHODS; WAVEGUIDE ARRAYS;

DIFFRACTION; GAUSSIAN BEAMS; INTEGRATED OPTOELECTRONICS; LASER BEAMS; LIGHT; WAVEGUIDES;

METHOD OF MOMENTS;

EID: 64349121099     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.79.033847     Document Type: Article

References (62)

1. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature (London) 424, 817 (2003). 10.1038/nature01936
2. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008). 10.1016/j.physrep.2008.04.004
3. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000). 10.1103/PhysRevLett.85.1863
4. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002). 10.1103/PhysRevLett.88.093901
5. R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, Phys. Rev. Lett. 95, 053902 (2005). 10.1103/PhysRevLett.95. 053902
6. A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007). 10.1063/1.2735953
7. U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998). 10.1364/OL.23.001701
8. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999) 10.1103/PhysRevLett.83.4756
9. T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999). 10.1103/PhysRevLett.83.4752
10. G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999). 10.1103/PhysRevLett.83.963
11. B. A. Usievich, V. A. Sychugov, J. Kh. Nirligareev, and K. M. Golant, Opt. Spectrosc. 97, 790 (2004) 10.1134/1.1828630
12. N. Chiodo, G. DellaValle, R. Osellame, S. Longhi, G. Cerullo, R. Ramponi, P. Laporta, and U. Morgner, Opt. Lett. 31, 1651 (2006) 10.1364/OL.31.001651
13. H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Bräuer, and U. Peschel, Phys. Rev. Lett. 96, 023901 (2006) 10.1103/PhysRevLett.96.023901
14. H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Yu. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, Phys. Rev. Lett. 96, 053903 (2006). 10.1103/PhysRevLett.96.053903
15. A. Szameit, T. Pertsch, S. Nolte, A. Tünnermann, U. Peschel, and F. Lederer, J. Opt. Soc. Am. B 24, 2632 (2007). 10.1364/JOSAB.24.002632
16. G. Lenz, R. Parker, M. C. Wanke, and C. M. Sterke, Opt. Commun. 218, 87 (2003) 10.1016/S0030-4018(03)01172-6
17. J. Wan, M. Laforest, C. M. de Sterke, and M. M. Dignam, Opt. Commun. 247, 353 (2005). 10.1016/j.optcom.2004.11.075
18. S. Longhi, Opt. Lett. 30, 2137 (2005) 10.1364/OL.30.002137
19. S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006) 10.1103/PhysRevLett.96. 243901
20. S. Longhi, M. Lobino, M. Marangoni, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti, Phys. Rev. B 74, 155116 (2006) 10.1103/PhysRevB.74.155116
21. R. Iyer, J. S. Aitchison, J. Wan, M. M. Dignam, and C. M. de Sterke, Opt. Express 15, 3212 (2007) 10.1364/OE.15.003212
22. F. Dreisow, M. Heinrich, A. Szameit, S. Döring, S. Nolte, A. Tünnermann, S. Fahr, and F. Lederer, Opt. Express 16, 3474 (2008). 10.1364/OE.16.003474
23. I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. E 74, 066609 (2006) 10.1103/PhysRevE.74.066609
24. I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, Opt. Express 15, 9547 (2007) 10.1364/OE.15.009547
25. I. L. Garanovich, Phys. Lett. A 372, 3922 (2008). 10.1016/j.physleta. 2008.02.078
26. I. L. Garanovich, A. Szameit, A. A. Sukhorukov, T. Pertsch, W. Krolikowski, S. Nolte, D. Neshev, A. Tünnermann, and Y. S. Kivshar, Opt. Express 15, 9737 (2007). 10.1364/OE.15.009737
27. M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 87, 254102 (2001) 10.1103/PhysRevLett.87.254102
28. 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, Phys. Rev. A 78, 031801 (R) (2008). 10.1103/PhysRevA.78.031801
29. K. G. Makris and D. N. Christodoulides, Phys. Rev. E 73, 036616 (2006) 10.1103/PhysRevE.73.036616
30. S. Longhi, Phys. Rev. E 74, 026602 (2006) 10.1103/PhysRevE.74.026602
31. A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tünnermann, U. Peschel, and F. Lederer, Phys. Rev. A 75, 053814 (2007). 10.1103/PhysRevA.75. 053814
32. R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004) 10.1103/PhysRevLett.93.113902
33. S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006) 10.1103/PhysRevLett.96.063901
34. Y. V. Kartashov, V. A. Vysloukh and, L. Torner, Phys. Rev. Lett. 96, 073901 (2006) 10.1103/PhysRevLett.96.073901
35. M. Molina, Y. Kartashov, L. Torner, and Y. Kivshar, Opt. Lett. 32, 2668 (2007) 10.1364/OL.32.002668
36. A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007) 10.1103/PhysRevLett.98.173903
37. X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007). 10.1103/PhysRevLett.98. 123903
38. I. L. Garanovich, A. A. Sukhorukov, and Y. S. Kivshar, Phys. Rev. Lett. 100, 203904 (2008) 10.1103/PhysRevLett.100.203904
39. A. Szameit, I. L. Garanovich, M. Heinrich, A. A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and Yu. S. Kivshar, Phys. Rev. Lett. 101, 203902 (2008). 10.1103/PhysRevLett.101.203902
40. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, Appl. Phys. Lett. 74, 1212 (1999) 10.1063/1.123502
41. J. Witzens, M. Loncar, and A. Scherer, IEEE J. Sel. Top. Quantum Electron. 8, 1246 (2002) 10.1109/JSTQE.2002.806693
42. Z. Lu, S. Shi, J. A. Murakowski, G. J. Schneider, C. A. Schuetz, and D. W. Prather, Phys. Rev. Lett. 96, 173902 (2006) 10.1103/PhysRevLett.96.173902
43. P. T. Rakich, M. S. Dahlem, S. Tandon, M. Ibanescu, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, L. A. Kolodziejski, and E. P. Ippen, Nature Mater. 5, 93 (2006). 10.1038/nmat1568
44. See, for instance, J. M. Ziman, Principles of the Theory of Solids, 2nd ed. (Cambridge University Press, Cambridge, 1979).
45. S. G. Krivoshlykov, Quantum-Theoretical Formalism for Inhomogeneous Graded-IndexWaveguides (Akademie-Verlag, Berlin, 1994).
46. J. R. Klein, Am. J. Phys. 48, 1035 (1980) 10.1119/1.12300
47. D. F. Styer, Am. J. Phys. 58, 742 (1990) 10.1119/1.16396
48. P. A. Bélanger, Opt. Lett. 16, 196 (1991) 10.1364/OL.16.000196
49. V. M. Pérez-García, P. Torres, J. J. García-Ripoll, and H. Michinel, J. Opt. B: Quantum Semiclassical Opt. 2, 353 (2000) 10.1088/1464-4266/2/3/320
50. S. Longhi, G. Della Valle, and D. Janner, Phys. Rev. E 69, 056608 (2004) 10.1103/PhysRevE.69.056608
51. A. K. Potemkin and E. A. Khazanov, Quantum Electron. 35, 1042 (2005). 10.1070/QE2005v035n11ABEH012788
52. F. W. J. Olver, Asymptotics and Special Functions (Academic, New York, 1974).
53. It should be noted that for special initial field distributions with low decaying tails, yet carrying a finite power, the spectrum F (k) may diverge, and the decay law may be slower than ∼1/z [see K. Unnikrishnan, Am. J. Phys. 65, 526 (1997) 10.1119/1.18583
54. F. Lillo and R. N. Mantegna, Phys. Rev. Lett. 84, 1061 (2000)]. This curious circumstance happens, for instance, for beams with power-law decay tails. However, for such special beams the moment x2 is unbounded. In this paper we will limit ourselves to consider beams with a bounded variance, for which the corresponding spectrum F (k) is not singular. 10.1103/PhysRevLett.84.1061
55. A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, E. Suran, F. Louradour, A. Barthélémy, and S. Longhi, Appl. Phys. Lett. 93, 181109 (2008). 10.1063/1.2999624
56. A. E. Siegman, Lasers (University Science, Mill Valley, CA, 1986).
57. H. L. Haroutyunyan and G. Nienhuis, Phys. Rev. A 64, 033424 (2001). 10.1103/PhysRevA.64.033424
58. H. J. Korsch and S. Mossmann, Phys. Lett. A 317, 54 (2003). 10.1016/j.physleta.2003.08.038
59. S. Mossmann, A. Schulze, D. Witthaut, and H. J. Korsch, J. Phys. A 38, 3381 (2005). 10.1088/0305-4470/38/15/010
60. T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, Opt. Lett. 29, 468 (2004). 10.1364/OL.29.000468
61. Analytical results can be also provided for a more general two-dimensional lattice model, in which nearest diagonal coupling terms are accounted for in Hamiltonian 38 (see Ref.). However, the resulting equations are very cumbersome, and this case will not be considered here.
62. D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986). 10.1103/PhysRevB.34.3625