Discrete Optics in Femtosecond Laser Written Waveguide Arrays

Chapter
Part of the Topics in Applied Physics book series (TAP, volume 123)

Abstract

The miniaturization of integrated optical devices can achieve geometric dimensions where crosstalk between adjacent waveguides is no longer negligible. In discrete optics, such interactions can be explained using the well-known coupled mode theory [1]. Based on this fundamental theory, systems of coupled waveguides are reduced to systems of discrete, i.e. countable, cells, and the spatial electromagnetic field is separated into the transverse mode profile of each waveguide and a longitudinal dependent amplitude. In the last years, femtosecond laser waveguide writing has been established as a versatile technique to fabricate three-dimensional optical waveguide systems. The following chapter begins with an overview of the basic principles of discrete light propagation. Linear propagation effects are envisaged in the second section. Here, straight and curved lattices are discussed. In the last section, third order nonlinearity is introduced to comprehend nonlinear propagation effects, which provide essential concepts for the development of ultrafast switching and routing devices.

Keywords

Femtosecond Laser Dynamic Localization Nonlinear Refractive Index Waveguide Array Bloch Oscillation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    A. Yariv, Optical Electronics, 4th edn. (Saunders College Publ., 1991)Google Scholar
  2. 2.
    J. Frenkel, T. Kontorova, J. Phys. (USSR) 1, 137 (1939)MathSciNetGoogle Scholar
  3. 3.
    A. Jones, J. Opt. Soc. Am. 55, 261 (1965)ADSCrossRefGoogle Scholar
  4. 4.
    S. Somekh, E. Garmire, A. Yariv, H. Garvin, R. Hunsperger, Appl. Phys. Lett. 22, 46 (1973)ADSCrossRefGoogle Scholar
  5. 5.
    D. Christodoulides, F. Lederer, Y. Silberberg, Nature 424, 817 (2003)ADSCrossRefGoogle Scholar
  6. 6.
    F. Lederer, G. Stegeman, D. Christodoulides, G. Assanto, M. Segev, Y. Silberberg, Physics Reports 463, 1 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    H. Eisenberg, Y. Silberberg, R. Morandotti, J. Aitchison, Phys. Rev. Lett. 85(9), 1863 (2000)ADSCrossRefGoogle Scholar
  8. 8.
    T. Pertsch, T. Zentgraf, U. Peschel, A. Braeuer, F. Lederer, Phys. Rev. Lett. 88(9), 093901 (2002)ADSCrossRefGoogle Scholar
  9. 9.
    R. Gordon, Opt. Lett. 29(23), 2752 (2004)ADSCrossRefGoogle Scholar
  10. 10.
    U. Peschel, T. Pertsch, F. Lederer, Opt. Lett. 23(21), 1701 (1998)ADSCrossRefGoogle Scholar
  11. 11.
    T. Pertsch, P. Dannberg, W. Elflein, A. Braeuer, F. Lederer, Phys. Rev. Lett. 83(23), 4752 (1999)ADSCrossRefGoogle Scholar
  12. 12.
    R. Morandotti, U. Peschel, J. Aitchinson, H. Eisenberg, Y. Silberberg, Phys. Rev. Lett. 83(23), 4756 (1999)ADSCrossRefGoogle Scholar
  13. 13.
    G. Lenz, I. Talanina, M. de Sterke, Phys. Rev. Lett. 83(5), 963 (1999)ADSCrossRefGoogle Scholar
  14. 14.
    N. Chiodo, G.D. Valle, R. Osellame, S. Longhi, G. Cerullo, R. Ramponi, P. Laporta, U. Morgner, Opt. Lett. 31(11), 1651 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    H. Trompeter, W. Krolikowski, D. Neshev, A. Desyatnikov, A. Sukhorukov, Y. Kivshar, T. Pertsch, U. Peschel, F. Lederer, Phys. Rev. Lett. 96(5), 053903 (2006)ADSCrossRefGoogle Scholar
  16. 16.
    H. Trompeter, T. Pertsch, F. Lederer, D. Michaelis, U. Streppel, A. Braeuer, U. Peschel, Phys. Rev. Lett. 96(2), 023901 (2006)ADSCrossRefGoogle Scholar
  17. 17.
    R. Iwanow, D. May-Arrioja, D. Christodoulides, G. Stegeman, Y. Min, W. Sohler, Phys. Rev. Lett. 95(5), 053902 (2005)ADSCrossRefGoogle Scholar
  18. 18.
    K. Makris, D. Christodoulides, Phys. Rev. E 73, 036616 (2006)ADSCrossRefGoogle Scholar
  19. 19.
    A. Szameit, T. Pertsch, F. Dreisow, S. Nolte, A. Tuennermann, U. Peschel, F. Lederer, Phys. Rev. A 75, 053814 (2007)ADSCrossRefGoogle Scholar
  20. 20.
    H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, A. Braeuer, Opt. Exp. 11(25), 3404 (2003)ADSCrossRefGoogle Scholar
  21. 21.
    S. Jensen, IEEE J. Quantum Electron. 18, 1580 (1982)ADSCrossRefGoogle Scholar
  22. 22.
    D. Christodoulides, R. Joseph, Opt. Lett. 13(9), 794 (1988)ADSCrossRefGoogle Scholar
  23. 23.
    H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, J. Aitchison, Phys. Rev. Lett. 81(16), 3383 (1998)ADSCrossRefGoogle Scholar
  24. 24.
    H. Eisenberg, R. Morandotti, Y. Silberberg, J. Arnold, G. Pennelli, J. Aitchison, J. Opt. Soc. Am. B 19(12), 2938 (2002)ADSCrossRefGoogle Scholar
  25. 25.
    U. Peschel, R. Morandotti, J. Arnold, J. Aitchison, H. Eisenberg, Y. Silberberg, T. Pertsch, F. Lederer, J. Opt. Soc. Am. B 19(11), 2637 (2002)ADSCrossRefGoogle Scholar
  26. 26.
    S. Flach, C. Willis, Physics Reports 295, 181 (1988)MathSciNetADSCrossRefGoogle Scholar
  27. 27.
    T. Pertsch, U. Peschel, F. Lederer, Phys. Rev. E 66, 066604 (2002)MathSciNetADSCrossRefGoogle Scholar
  28. 28.
    Y. Kivshar, W. Krolikowski, O. Chubykalo, Phys. Rev. E 50(6), 5020 (1994)ADSCrossRefGoogle Scholar
  29. 29.
    D. Mandelik, H. Eisenberg, Y. Silberberg, R. Morandotti, J. Aitchison, Phys. Rev. Lett. 90(5), 053902 (2003)ADSCrossRefGoogle Scholar
  30. 30.
    K. Makris, S. Suntsov, D. Christodoulides, G. Stegeman, Opt. Lett. 30(18), 2466 (2005)ADSCrossRefGoogle Scholar
  31. 31.
    K. Makris, J. Hudock, D. Christodoulides, G. Stegeman, O. Manela, M. Segev, Opt. Lett. 31(18), 2774 (2006)ADSCrossRefGoogle Scholar
  32. 32.
    N. Efremidis, J. Hudock, D. Christodoulides, J. Fleischer, O. Cohen, M. Segev, Phys. Rev. Lett. 92(21), 213906 (2003)ADSCrossRefGoogle Scholar
  33. 33.
    J. Fleischer, M. Segev, N. Efremidis, D. Christodoulides, Nature 422, 147 (2003)ADSCrossRefGoogle Scholar
  34. 34.
    N. Efremidis, S. Sears, D. Christodoulides, J. Fleischer, M. Segev, Phys. Rev. E 66, 046602 (2002)ADSCrossRefGoogle Scholar
  35. 35.
    B. Malomed, P. Kevrekidis, Phys. Rev. E 64, 026601 (2001)MathSciNetADSCrossRefGoogle Scholar
  36. 36.
    D. Traeger, R. Fischer, D. Neshev, A. Sukhorukov, C. Denz, W. Krolikowski, Y. Kivshar, Opt. Exp. 14(5), 1913 (2006)ADSCrossRefGoogle Scholar
  37. 37.
    S. Longhi, Opt. Lett. 30(16), 2137 (2005)ADSCrossRefGoogle Scholar
  38. 38.
    A. Szameit, F. Dreisow, T. Pertsch, S. Nolte, A. Tuennermann, Opt. Exp. 15(4), 1579 (2007)ADSCrossRefGoogle Scholar
  39. 39.
    D. Blomer, A. Szameit, F. Dreisow, T. Schreiber, S. Nolte, A. Tuennermann, Opt. Exp. 14(6), 2151 (2006)ADSCrossRefGoogle Scholar
  40. 40.
    A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tuennermann, F. Lederer, Appl. Phys. Lett. 90, 241113 (2007)ADSCrossRefGoogle Scholar
  41. 41.
    F. Dreisow, A. Szameit, T. Pertsch, S. Nolte, A. Tuennermann, (SPIE, 2007), vol. 6460, p. 64601C. DOI 10.1117/12.711446. URL http://link.aip.org/link/?PSI/6460/64601C/1
  42. 42.
    M. Mizuguchi, L. Skuja, ∗ Hideo Hosono, T. Ogawa, Opt. Lett. 24(13), 863 (1999). URL http://ol.osa.org/abstract.cfm?URI=ol-24-13-863
  43. 43.
    L. Skuja, J. Non-Cryst. Solids 179, 51 (1995)ADSCrossRefGoogle Scholar
  44. 44.
    H. Herzig, Micro-optics: Elements, systems and applications (Crc Pr Inc, 1997)Google Scholar
  45. 45.
    S. Sinzinger, J. Jahns, Microoptics, 2nd edn. (Wiley-VCH, 2003)Google Scholar
  46. 46.
    A. Szameit, H. Hartung, F. Dreisow, S. Nolte, A. Tuennermann, Appl. Phys. B. 87, 17 (2007)ADSCrossRefGoogle Scholar
  47. 47.
    F. Dreisow, M. Heinrich, A. Szameit, S. Doering, S. Nolte, A. Tuennermann, S. Fahr, F. Lederer, Opt. Express 16(5), 3474 (2008)ADSCrossRefGoogle Scholar
  48. 48.
    F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tünnermann, S. Longhi, Phys. Rev. Lett. 101(143602) (2008)Google Scholar
  49. 49.
    N. Efremidis, D. Christodoulides, Phys. Rev. E 65, 056607 (2002)ADSCrossRefGoogle Scholar
  50. 50.
    F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tuennermann, Opt. Lett. 33(22), 2689 (2008). URL http://ol.osa.org/abstract.cfm?URI=ol-33-22-2689 Google Scholar
  51. 51.
    A. Szameit, H. Trompeter, M. Heinrich, F. Dreisow, U. Peschel, T. Pertsch, S. Nolte, F. Lederer, A. Tuennermann, New Journal of Physics 10(10), 103020 (2008). URL http://stacks.iop.org/1367-2630/10/103020 Google Scholar
  52. 52.
    S. Longhi, Opt. Lett. 33(5), 473 (2008). URL http://ol.osa.org/abstract.cfm?URI=ol-33-5-473
  53. 53.
    A. Szameit, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tuennermann, E. Suran, F. Louradour, A. Barthelemy, S. Longhi, Appl. Phys. Lett. 93(18), 181109 (2008). DOI 10.1063/1.2999624. URL http://link.aip.org/link/?APL/93/181109/1
  54. 54.
    A. Szameit, D. Bloemer, J. Burghoff, T. Pertsch, S. Nolte, A. Tuennermann, Appl. Phys. B. 82(4), 507 (2006)ADSCrossRefGoogle Scholar
  55. 55.
    W. Karthe, R. Mueller, Integrierte Optik (Akademische Verlagsgesellschaft, 1991)Google Scholar
  56. 56.
    L. Tong, R.R. Gattass, I. Maxwell, J.B. Ashcom, E. Mazur, Opt. Comm. 259(2), 626 (2006). DOI DOI:10.1016/j.optcom.2005.09.040. URL http://www.sciencedirect.com/science/article/B6TVF-4H6XNDS-1/2/d3aff92f775e65065fdb4a17e0413082 Google Scholar
  57. 57.
    D. Dunlap, V. Kenkre, Phys. Rev. B 34, 3625 (1986)ADSCrossRefGoogle Scholar
  58. 58.
    S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, V. Foglietti, Phys. Rev. Lett. 96, 243901 (2006)ADSCrossRefGoogle Scholar
  59. 59.
    I. Garanovich, A. Sukhorukov, Y. Kivshar, Phys. Rev. E 74, 066609 (2006)ADSCrossRefGoogle Scholar
  60. 60.
    A. Szameit, I. Garanovich, M. Heinrich, A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tuennermann, Y. Kivshar, Nature Phys. 5(4), 271 (2009)ADSCrossRefGoogle Scholar
  61. 61.
    I. Tamm, Phys. Z. Soviet Union 1, 733 (1932)MATHGoogle Scholar
  62. 62.
    W. Shockley, Phys. Rev. 56(4), 317 (1939). DOI 10.1103/PhysRev.56.317ADSMATHCrossRefGoogle Scholar
  63. 63.
    A. Szameit, I. Garanovich, M. Heinrich, A. Sukhorukov, F. Dreisow, T. Pertsch, S. Nolte, A. Tuennermann, Y. Kivshar, Phys. Rev. Lett. 101(20), 203902 (2008). DOI 10.1103/PhysRevLett.101.203902. URL http://link.aps.org/abstract/PRL/v101/e203902
  64. 64.
    F. Bloch, Z. Phys. 52, 555 (1928)ADSGoogle Scholar
  65. 65.
    F. Dreisow, A. Szameit, M. Heinrich, T. Pertsch, S. Nolte, A. Tuennermann, S. Longhi, Phys. Rev. Lett. 102(7), 076802 (2009). DOI 10.1103/PhysRevLett.102. 076802ADSCrossRefGoogle Scholar
  66. 66.
    D. Gloge, D. Macruse, J. Opt. Soc. Am. 59(12), 1629 (1969). URL http://www.opticsinfobase.org/abstract.cfm?URI=josa-59-12-1629 Google Scholar
  67. 67.
    S. Longhi, Laser & Photonics Reviews 3(3), 243 (2009)MathSciNetCrossRefGoogle Scholar
  68. 68.
    F. Dreisow, A. Szameit, M. Heinrich, S. Nolte, A. Tuennermann, M. Ornigotti, S. Longhi, Phys. Rev. A 79(5), 055802 (2009). DOI 10.1103/PhysRevA.79.055802. URL http://link.aps.org/abstract/PRA/v79/e055802
  69. 69.
    P. Facchi, S. Pascazio, Journal of Physics A: Mathematical and Theoretical 41(49), 493001 (45pp) (2008). URL http://stacks.iop.org/1751-8121/41/493001
  70. 70.
    P. Butcher, D. Cotter, The Elements of Nonlinear Optics, 1st edn. (Cambridge University Press, 1990)Google Scholar
  71. 71.
    D. Milam, Appl. Opt. 37(3), 546 (1998)ADSCrossRefGoogle Scholar
  72. 72.
    R. Chiao, E. Garmire, C. Townes, Phys. Rev. Lett. 13(15), 479 (1964)ADSCrossRefGoogle Scholar
  73. 73.
    A. Barthelemy, S. Maneuf, C. Froehly, Opt. Commun. 55, 201 (1985)ADSCrossRefGoogle Scholar
  74. 74.
    A. Szameit, D. Bloemer, J. Burghoff, T. Schreiber, T. Pertsch, S. Nolte, A. Tuennermann, F. Lederer, Opt. Exp. 13(26), 10552 (2005)ADSCrossRefGoogle Scholar
  75. 75.
    A. Szameit, I. Garanovich, M. Heinrich, A. Minovich, F. Dreisow, A. Sukhorukov, T. Pertsch, D. Neshev, S. Nolte, W. Krolikowski, A. Tuennermann, A. Mitchell, Y. Kivshar, Phys. Rev. A 78(3), 031801(R) (2008)Google Scholar
  76. 76.
    A. Szameit, Y. Kartashov, F. Dreisow, M. Heinrich, T. Pertsch, S. Nolte, A. Tuennermann, V. Vysloukh, F. Lederer, L. Torner, Phys. Rev. Lett. 102(5), 153901 (2009)ADSCrossRefGoogle Scholar
  77. 77.
    T. Pertsch, U. Peschel, S. Nolte, A. Tuennermann, F. Lederer, J. Kobelke, K. Schuster, H. Bartelt, Phys. Rev. Lett. 93(5), 053901 (2004)ADSCrossRefGoogle Scholar
  78. 78.
    A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tuennermann, F. Lederer, Opt. Exp. 14(13), 6055 (2006)ADSCrossRefGoogle Scholar
  79. 79.
    A. Szameit, Y. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tuennermann, L. Torner, Phys. Rev. Lett. 98, 173903 (2007)ADSCrossRefGoogle Scholar
  80. 80.
    A. Szameit, Y. Kartashov, F. Dreisow, M. Heinrich, V. Vysloukh, T. Pertsch, S. Nolte, A. Tuennermann, F. Lederer, L. Torner, Opt. Lett. 33(7), 663 (2008). URL http://ol.osa.org/abstract.cfm?URI=ol-33-7-663 Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alexander Szameit
    • 1
  • Felix Dreisow
    • 1
  • Stefan Nolte
    • 1
  1. 1.Institute of Applied PhysicsFriedrich-Schiller-Universität JenaJenaGermany

Personalised recommendations