Abstract

The formation of localized states or modes at defects in waveguide arrays is investigated both, theoretically and experimentally. If the effective index or the coupling of the defect guide to its neighbors is varied the number and character of respective modes bound to the defect can be altered. Waveguide arrays may be considered as tailor-made or metamaterials with new and unexpected properties as e.g. guiding staggered modes bound to defects with reduced index. Although the symmetric defect waveguide becomes multimode for increased coupling it does not support antisymmetric modes. All theoretical predictions are confirmed in excellent agreement with experimental observations in polymer waveguide arrays.

© 2003 Optical Society of America

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  1. Focus Issue: “Negative Refraction and Metamaterials,” ed. by J. B. Pendry, Opt. Express 11, 639 (2003), http://www.opticsexpress.org/issue.cfm?issue_id=186
    [CrossRef] [PubMed]
  2. M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
    [CrossRef]
  3. G. von Freymanna, W. Koch, D. C. Meisel, and M. Wegener, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614–616 (2003).
    [CrossRef]
  4. S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46–48 (1973).
    [CrossRef]
  5. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous Refraction and Diffraction in Discrete Optical Systems,” Phys. Rev. Lett. 88, 093901–093904 (2002).
    [CrossRef] [PubMed]
  6. 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]
  7. 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]
  8. R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, “Interactions of discrete solitons with structural defects,” Opt. Lett. 28, 834–836 (2003).
    [CrossRef] [PubMed]
  9. U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly Induced Escape from a Defect State,” Appl. Phys. Lett. 75, 1384–1386 (1999).
    [CrossRef]
  10. T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
    [CrossRef] [PubMed]
  11. P Russell, “Photonic Crystal Fibers,” Science 299, 358–363 (2003).
    [CrossRef] [PubMed]
  12. J. C. Knight, T. A. Birks, R. F. Cregan, P. ST. J. Russell, and J.-P. de Sandro, “Large Mode Area Photonic Crystal Fiber,” Electron. Lett. 34, 1347–1348 (1998).
    [CrossRef]
  13. D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Group-velocity dispersionin photonic crystal fibers,” Opt. Lett. 23, 1662–1664 (1998).
    [CrossRef]
  14. R. Houbertz, G. Domann, C. Cronauer, A. Schmitt, H. Martin, J.-U. Park, L. Fröhlich, R. Buestrich, M. Popall, U. Streppel, P. Dannberg, C. Wächter, and A. Bräuer, “Inorganic-organic hybrid materials for application in optical devices,” Thin Solid Films 422, 194–200 (2003)
    [CrossRef]
  15. U. Streppel, P. Dannberg, C. Wächter, A. Bräuer, L. Fröhlich, R. Houbertz, and M. Popall, “New wafer-scale fabrication method for stacked optical waveguide interconnects and 3D micro-optic structures using photo-responsive (inorganic-organic hybrid) polymers,” Opt. Mat. 21, 475–483 (2002).
    [CrossRef]

2003 (5)

Focus Issue: “Negative Refraction and Metamaterials,” ed. by J. B. Pendry, Opt. Express 11, 639 (2003), http://www.opticsexpress.org/issue.cfm?issue_id=186
[CrossRef] [PubMed]

G. von Freymanna, W. Koch, D. C. Meisel, and M. Wegener, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614–616 (2003).
[CrossRef]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, “Interactions of discrete solitons with structural defects,” Opt. Lett. 28, 834–836 (2003).
[CrossRef] [PubMed]

P Russell, “Photonic Crystal Fibers,” Science 299, 358–363 (2003).
[CrossRef] [PubMed]

R. Houbertz, G. Domann, C. Cronauer, A. Schmitt, H. Martin, J.-U. Park, L. Fröhlich, R. Buestrich, M. Popall, U. Streppel, P. Dannberg, C. Wächter, and A. Bräuer, “Inorganic-organic hybrid materials for application in optical devices,” Thin Solid Films 422, 194–200 (2003)
[CrossRef]

2002 (2)

U. Streppel, P. Dannberg, C. Wächter, A. Bräuer, L. Fröhlich, R. Houbertz, and M. Popall, “New wafer-scale fabrication method for stacked optical waveguide interconnects and 3D micro-optic structures using photo-responsive (inorganic-organic hybrid) polymers,” Opt. Mat. 21, 475–483 (2002).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous Refraction and Diffraction in Discrete Optical Systems,” Phys. Rev. Lett. 88, 093901–093904 (2002).
[CrossRef] [PubMed]

2000 (1)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
[CrossRef]

1999 (3)

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]

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]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly Induced Escape from a Defect State,” Appl. Phys. Lett. 75, 1384–1386 (1999).
[CrossRef]

1998 (2)

J. C. Knight, T. A. Birks, R. F. Cregan, P. ST. J. Russell, and J.-P. de Sandro, “Large Mode Area Photonic Crystal Fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

D. Mogilevtsev, T. A. Birks, and P. St. J. Russell, “Group-velocity dispersionin photonic crystal fibers,” Opt. Lett. 23, 1662–1664 (1998).
[CrossRef]

1997 (1)

1973 (1)

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46–48 (1973).
[CrossRef]

Aitchison, J. S.

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, “Interactions of discrete solitons with structural defects,” Opt. Lett. 28, 834–836 (2003).
[CrossRef] [PubMed]

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]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly Induced Escape from a Defect State,” Appl. Phys. Lett. 75, 1384–1386 (1999).
[CrossRef]

Birks, T. A.

Bräuer, A.

R. Houbertz, G. Domann, C. Cronauer, A. Schmitt, H. Martin, J.-U. Park, L. Fröhlich, R. Buestrich, M. Popall, U. Streppel, P. Dannberg, C. Wächter, and A. Bräuer, “Inorganic-organic hybrid materials for application in optical devices,” Thin Solid Films 422, 194–200 (2003)
[CrossRef]

U. Streppel, P. Dannberg, C. Wächter, A. Bräuer, L. Fröhlich, R. Houbertz, and M. Popall, “New wafer-scale fabrication method for stacked optical waveguide interconnects and 3D micro-optic structures using photo-responsive (inorganic-organic hybrid) polymers,” Opt. Mat. 21, 475–483 (2002).
[CrossRef]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous Refraction and Diffraction in Discrete Optical Systems,” Phys. Rev. Lett. 88, 093901–093904 (2002).
[CrossRef] [PubMed]

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]

Buestrich, R.

R. Houbertz, G. Domann, C. Cronauer, A. Schmitt, H. Martin, J.-U. Park, L. Fröhlich, R. Buestrich, M. Popall, U. Streppel, P. Dannberg, C. Wächter, and A. Bräuer, “Inorganic-organic hybrid materials for application in optical devices,” Thin Solid Films 422, 194–200 (2003)
[CrossRef]

Cregan, R. F.

J. C. Knight, T. A. Birks, R. F. Cregan, P. ST. J. Russell, and J.-P. de Sandro, “Large Mode Area Photonic Crystal Fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

Cronauer, C.

R. Houbertz, G. Domann, C. Cronauer, A. Schmitt, H. Martin, J.-U. Park, L. Fröhlich, R. Buestrich, M. Popall, U. Streppel, P. Dannberg, C. Wächter, and A. Bräuer, “Inorganic-organic hybrid materials for application in optical devices,” Thin Solid Films 422, 194–200 (2003)
[CrossRef]

Dannberg, P.

R. Houbertz, G. Domann, C. Cronauer, A. Schmitt, H. Martin, J.-U. Park, L. Fröhlich, R. Buestrich, M. Popall, U. Streppel, P. Dannberg, C. Wächter, and A. Bräuer, “Inorganic-organic hybrid materials for application in optical devices,” Thin Solid Films 422, 194–200 (2003)
[CrossRef]

U. Streppel, P. Dannberg, C. Wächter, A. Bräuer, L. Fröhlich, R. Houbertz, and M. Popall, “New wafer-scale fabrication method for stacked optical waveguide interconnects and 3D micro-optic structures using photo-responsive (inorganic-organic hybrid) polymers,” Opt. Mat. 21, 475–483 (2002).
[CrossRef]

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]

de Sandro, J.-P.

J. C. Knight, T. A. Birks, R. F. Cregan, P. ST. J. Russell, and J.-P. de Sandro, “Large Mode Area Photonic Crystal Fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

Domann, G.

R. Houbertz, G. Domann, C. Cronauer, A. Schmitt, H. Martin, J.-U. Park, L. Fröhlich, R. Buestrich, M. Popall, U. Streppel, P. Dannberg, C. Wächter, and A. Bräuer, “Inorganic-organic hybrid materials for application in optical devices,” Thin Solid Films 422, 194–200 (2003)
[CrossRef]

Eisenberg, H. S.

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, “Interactions of discrete solitons with structural defects,” Opt. Lett. 28, 834–836 (2003).
[CrossRef] [PubMed]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly Induced Escape from a Defect State,” Appl. Phys. Lett. 75, 1384–1386 (1999).
[CrossRef]

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]

Elflein, W.

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]

Fröhlich, L.

R. Houbertz, G. Domann, C. Cronauer, A. Schmitt, H. Martin, J.-U. Park, L. Fröhlich, R. Buestrich, M. Popall, U. Streppel, P. Dannberg, C. Wächter, and A. Bräuer, “Inorganic-organic hybrid materials for application in optical devices,” Thin Solid Films 422, 194–200 (2003)
[CrossRef]

U. Streppel, P. Dannberg, C. Wächter, A. Bräuer, L. Fröhlich, R. Houbertz, and M. Popall, “New wafer-scale fabrication method for stacked optical waveguide interconnects and 3D micro-optic structures using photo-responsive (inorganic-organic hybrid) polymers,” Opt. Mat. 21, 475–483 (2002).
[CrossRef]

Garmire, E.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46–48 (1973).
[CrossRef]

Garvin, H. L.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46–48 (1973).
[CrossRef]

Houbertz, R.

R. Houbertz, G. Domann, C. Cronauer, A. Schmitt, H. Martin, J.-U. Park, L. Fröhlich, R. Buestrich, M. Popall, U. Streppel, P. Dannberg, C. Wächter, and A. Bräuer, “Inorganic-organic hybrid materials for application in optical devices,” Thin Solid Films 422, 194–200 (2003)
[CrossRef]

U. Streppel, P. Dannberg, C. Wächter, A. Bräuer, L. Fröhlich, R. Houbertz, and M. Popall, “New wafer-scale fabrication method for stacked optical waveguide interconnects and 3D micro-optic structures using photo-responsive (inorganic-organic hybrid) polymers,” Opt. Mat. 21, 475–483 (2002).
[CrossRef]

Hunsperger, R. G.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46–48 (1973).
[CrossRef]

Knight, J. C.

J. C. Knight, T. A. Birks, R. F. Cregan, P. ST. J. Russell, and J.-P. de Sandro, “Large Mode Area Photonic Crystal Fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[CrossRef] [PubMed]

Koch, W.

G. von Freymanna, W. Koch, D. C. Meisel, and M. Wegener, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614–616 (2003).
[CrossRef]

Lederer, F.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous Refraction and Diffraction in Discrete Optical Systems,” Phys. Rev. Lett. 88, 093901–093904 (2002).
[CrossRef] [PubMed]

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]

Mandelik, D.

Martin, H.

R. Houbertz, G. Domann, C. Cronauer, A. Schmitt, H. Martin, J.-U. Park, L. Fröhlich, R. Buestrich, M. Popall, U. Streppel, P. Dannberg, C. Wächter, and A. Bräuer, “Inorganic-organic hybrid materials for application in optical devices,” Thin Solid Films 422, 194–200 (2003)
[CrossRef]

Meisel, D. C.

G. von Freymanna, W. Koch, D. C. Meisel, and M. Wegener, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614–616 (2003).
[CrossRef]

Modotto, D.

Mogilevtsev, D.

Morandotti, R.

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, “Interactions of discrete solitons with structural defects,” Opt. Lett. 28, 834–836 (2003).
[CrossRef] [PubMed]

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]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly Induced Escape from a Defect State,” Appl. Phys. Lett. 75, 1384–1386 (1999).
[CrossRef]

Notomi, M.

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
[CrossRef]

Park, J.-U.

R. Houbertz, G. Domann, C. Cronauer, A. Schmitt, H. Martin, J.-U. Park, L. Fröhlich, R. Buestrich, M. Popall, U. Streppel, P. Dannberg, C. Wächter, and A. Bräuer, “Inorganic-organic hybrid materials for application in optical devices,” Thin Solid Films 422, 194–200 (2003)
[CrossRef]

Pertsch, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous Refraction and Diffraction in Discrete Optical Systems,” Phys. Rev. Lett. 88, 093901–093904 (2002).
[CrossRef] [PubMed]

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]

Peschel, U.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous Refraction and Diffraction in Discrete Optical Systems,” Phys. Rev. Lett. 88, 093901–093904 (2002).
[CrossRef] [PubMed]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly Induced Escape from a Defect State,” Appl. Phys. Lett. 75, 1384–1386 (1999).
[CrossRef]

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]

Popall, M.

R. Houbertz, G. Domann, C. Cronauer, A. Schmitt, H. Martin, J.-U. Park, L. Fröhlich, R. Buestrich, M. Popall, U. Streppel, P. Dannberg, C. Wächter, and A. Bräuer, “Inorganic-organic hybrid materials for application in optical devices,” Thin Solid Films 422, 194–200 (2003)
[CrossRef]

U. Streppel, P. Dannberg, C. Wächter, A. Bräuer, L. Fröhlich, R. Houbertz, and M. Popall, “New wafer-scale fabrication method for stacked optical waveguide interconnects and 3D micro-optic structures using photo-responsive (inorganic-organic hybrid) polymers,” Opt. Mat. 21, 475–483 (2002).
[CrossRef]

Russell, P

P Russell, “Photonic Crystal Fibers,” Science 299, 358–363 (2003).
[CrossRef] [PubMed]

Russell, P. ST. J.

Schmitt, A.

R. Houbertz, G. Domann, C. Cronauer, A. Schmitt, H. Martin, J.-U. Park, L. Fröhlich, R. Buestrich, M. Popall, U. Streppel, P. Dannberg, C. Wächter, and A. Bräuer, “Inorganic-organic hybrid materials for application in optical devices,” Thin Solid Films 422, 194–200 (2003)
[CrossRef]

Silberberg, Y.

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, “Interactions of discrete solitons with structural defects,” Opt. Lett. 28, 834–836 (2003).
[CrossRef] [PubMed]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly Induced Escape from a Defect State,” Appl. Phys. Lett. 75, 1384–1386 (1999).
[CrossRef]

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]

Somekh, S.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46–48 (1973).
[CrossRef]

Sorel, M.

Stanley, C. R.

Streppel, U.

R. Houbertz, G. Domann, C. Cronauer, A. Schmitt, H. Martin, J.-U. Park, L. Fröhlich, R. Buestrich, M. Popall, U. Streppel, P. Dannberg, C. Wächter, and A. Bräuer, “Inorganic-organic hybrid materials for application in optical devices,” Thin Solid Films 422, 194–200 (2003)
[CrossRef]

U. Streppel, P. Dannberg, C. Wächter, A. Bräuer, L. Fröhlich, R. Houbertz, and M. Popall, “New wafer-scale fabrication method for stacked optical waveguide interconnects and 3D micro-optic structures using photo-responsive (inorganic-organic hybrid) polymers,” Opt. Mat. 21, 475–483 (2002).
[CrossRef]

von Freymanna, G.

G. von Freymanna, W. Koch, D. C. Meisel, and M. Wegener, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614–616 (2003).
[CrossRef]

Wächter, C.

R. Houbertz, G. Domann, C. Cronauer, A. Schmitt, H. Martin, J.-U. Park, L. Fröhlich, R. Buestrich, M. Popall, U. Streppel, P. Dannberg, C. Wächter, and A. Bräuer, “Inorganic-organic hybrid materials for application in optical devices,” Thin Solid Films 422, 194–200 (2003)
[CrossRef]

U. Streppel, P. Dannberg, C. Wächter, A. Bräuer, L. Fröhlich, R. Houbertz, and M. Popall, “New wafer-scale fabrication method for stacked optical waveguide interconnects and 3D micro-optic structures using photo-responsive (inorganic-organic hybrid) polymers,” Opt. Mat. 21, 475–483 (2002).
[CrossRef]

Wegener, M.

G. von Freymanna, W. Koch, D. C. Meisel, and M. Wegener, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614–616 (2003).
[CrossRef]

Yariv, A.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46–48 (1973).
[CrossRef]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous Refraction and Diffraction in Discrete Optical Systems,” Phys. Rev. Lett. 88, 093901–093904 (2002).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

G. von Freymanna, W. Koch, D. C. Meisel, and M. Wegener, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614–616 (2003).
[CrossRef]

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguide directional couplers,” Appl. Phys. Lett. 22, 46–48 (1973).
[CrossRef]

U. Peschel, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Nonlinearly Induced Escape from a Defect State,” Appl. Phys. Lett. 75, 1384–1386 (1999).
[CrossRef]

Electron. Lett. (1)

J. C. Knight, T. A. Birks, R. F. Cregan, P. ST. J. Russell, and J.-P. de Sandro, “Large Mode Area Photonic Crystal Fiber,” Electron. Lett. 34, 1347–1348 (1998).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Opt. Mat. (1)

U. Streppel, P. Dannberg, C. Wächter, A. Bräuer, L. Fröhlich, R. Houbertz, and M. Popall, “New wafer-scale fabrication method for stacked optical waveguide interconnects and 3D micro-optic structures using photo-responsive (inorganic-organic hybrid) polymers,” Opt. Mat. 21, 475–483 (2002).
[CrossRef]

Phys. Rev. B (1)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
[CrossRef]

Phys. Rev. Lett. (3)

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous Refraction and Diffraction in Discrete Optical Systems,” Phys. Rev. Lett. 88, 093901–093904 (2002).
[CrossRef] [PubMed]

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]

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]

Science (1)

P Russell, “Photonic Crystal Fibers,” Science 299, 358–363 (2003).
[CrossRef] [PubMed]

Thin Solid Films (1)

R. Houbertz, G. Domann, C. Cronauer, A. Schmitt, H. Martin, J.-U. Park, L. Fröhlich, R. Buestrich, M. Popall, U. Streppel, P. Dannberg, C. Wächter, and A. Bräuer, “Inorganic-organic hybrid materials for application in optical devices,” Thin Solid Films 422, 194–200 (2003)
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Cross section of a polymer waveguide array with a defect. The defect is introduced by reducing the waveguide spacing compared with the homogenous array.

Fig. 2.
Fig. 2.

Dispersion relation of Bloch modes and the formation of defect modes (a) diffraction relation of Bloch-waves (longitudinal vs. transverse wavenumber) in a homogeneous waveguide array (propagation constant of isolated waveguides: β0, coupling constant C). In the shaded regions only evanescent waves exist. (b) Shift of the band structure and formation of a staggered mode (wavenumber βD) around a defect with a wavenumber reduced by δβ. (c) Expansion of the band structure and formation of staggered and unstaggered modes around a defect with increased coupling (C 1>C) (d) Compression of the band structure around a defect with reduced coupling (C 1<C).

Fig. 3.
Fig. 3.

Field and intensity of a staggered and an unstaggered mode for a dominant change of the propagation constant of the defect. Field (a) and intensity (b) distribution of an unstaggered defect mode for δβ/C=2.0 and C 1/C=0.8 (cross 1 in Fig. 4), solid line: theory, dots: experiment. Field (c) and intensity (d) distribution of a staggered defect mode for δβ/C=-1.4 and C 1/C=1.1 (cross 2 in fig. 4), solid line: theory, dots: experiment.

Fig. 4.
Fig. 4.

Regions of existence for symmetric staggered and unstaggered modes in the (C1/C)2-δβ-plane. The crosses mark the parameters for the experiments (Figs. 3, 5 and 6).

Fig. 5.
Fig. 5.

Interference pattern of a staggered and an unstaggered defect mode for dominant change of the coupling constant (δβ/C=-0.3 and C 1/C=1.4, cross 3 in Fig. 4) of the defect at a propagation distance of 59,95mm. Dots: experiment, lines: theory, dashed line: position of the excitation. (b) Intensity distribution for an excitation of the defect waveguide. (a) and (c) Intensity distribution for an excitation of the left and right nearest neighbor waveguide of the defect. Insets: schematic diagrams of the modal amplitude of the unstaggered and staggered mode, the superposition of both modal fields produces the actual interference pattern.

Fig. 6.
Fig. 6.

Diffraction pattern for an excitation of a repulsive defect ((a) theory, (b) experiment) with reduced coupling (C 1/C=0.5, δβ/C=0, cross 4 in Fig.4) and in a homogeneous array ((c) theory, (d) experiment).

Equations (8)

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( i Z + β 0 ) A n + C ( A n + 1 + A n 1 ) = 0 ,
β = β 0 + 2 C cos ( κ ) .
( i Z + β 0 ) A ± 1 + C 1 A 0 + C A ± 2 = 0 ,
A n ( Z ) = a n exp ( i β D Z )
a ± n = a ± 1 γ n 1 for n 2
γ < 1
β D = β 0 + C ( γ + 1 γ )
1 γ = δβ 2 C ± ( δβ 2 C ) 2 + 2 ( C 1 C ) 2 1 .

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