Abstract

In this Letter, we report group index measurements of the supermodes of an array of two strongly coupled silicon-on-insulator waveguides. We observe coupling-induced dispersion that is greater than the material and waveguide dispersion of the individual waveguides. We demonstrate that the system transforms from supporting the two supermodes associated with two coupled waveguides to the single mode of a slot waveguide within the investigated spectral range. During the cutoff of the antisymmetric supermode, an anti-crossing between the symmetric TM and antisymmetric TE supermodes has been observed.

© 2010 Optical Society of America

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  1. R. M. Osgood, N. C. Paniou, J. I. Dadap, X. Liu, X. Chen, I. W. Hsieh, E. Dulkeith, W. M. Green, and Y. A. Vlasov, Adv. Opt. Photon. 1, 162 (2009).
    [CrossRef]
  2. Q. Lin, O. J. Painter, and G. P. Agrawal, Opt. Express 15, 16604 (2007).
    [CrossRef] [PubMed]
  3. M. A. Foster, A. C. Turner, M. Lipson, and A. L. Gaeta, Opt. Express 16, 1300 (2008).
    [CrossRef] [PubMed]
  4. W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorel, R. M. De La Rue, Opt. Express 16, 3310 (2008).
    [CrossRef] [PubMed]
  5. C. J. Benton, A. V. Gorbach, and D. V. Skryabin, Phys. Rev. A 78, 033818 (2008).
    [CrossRef]
  6. C. J. Benton and D. V. Skryabin, Opt. Express 17, 5879(2009).
    [CrossRef] [PubMed]
  7. E. Marom, O. G. Ramer, and S. Ruschin, IEEE J. Quantum Electron. 20, 1311 (1984).
    [CrossRef]
  8. M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Nanpartovice, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
    [CrossRef]
  9. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, Opt. Lett. 29, 1209 (2004).
    [CrossRef] [PubMed]
  10. C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
    [CrossRef]
  11. M. Gnan, S. Thorns, D. S. Macintyre, R. M. De La Rue, and M. Sorel, Electron. Lett. 44, 115 (2008).
    [CrossRef]
  12. C. E. de Nobriga, G. D. Hobbs, W. Ding, A. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CThB4.

2009 (3)

R. M. Osgood, N. C. Paniou, J. I. Dadap, X. Liu, X. Chen, I. W. Hsieh, E. Dulkeith, W. M. Green, and Y. A. Vlasov, Adv. Opt. Photon. 1, 162 (2009).
[CrossRef]

C. J. Benton and D. V. Skryabin, Opt. Express 17, 5879(2009).
[CrossRef] [PubMed]

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

2008 (4)

2007 (1)

2004 (1)

2000 (1)

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Nanpartovice, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

1984 (1)

E. Marom, O. G. Ramer, and S. Ruschin, IEEE J. Quantum Electron. 20, 1311 (1984).
[CrossRef]

Agrawal, G. P.

Almeida, V. R.

Baets, R.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Barrios, C. A.

Benton, C.

Benton, C. J.

C. J. Benton and D. V. Skryabin, Opt. Express 17, 5879(2009).
[CrossRef] [PubMed]

C. J. Benton, A. V. Gorbach, and D. V. Skryabin, Phys. Rev. A 78, 033818 (2008).
[CrossRef]

Biaggio, I.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Bogaerts, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Chen, X.

Dadap, J. I.

De La Rue, R. M.

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorel, R. M. De La Rue, Opt. Express 16, 3310 (2008).
[CrossRef] [PubMed]

M. Gnan, S. Thorns, D. S. Macintyre, R. M. De La Rue, and M. Sorel, Electron. Lett. 44, 115 (2008).
[CrossRef]

C. E. de Nobriga, G. D. Hobbs, W. Ding, A. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CThB4.

de Nobriga, C. E.

C. E. de Nobriga, G. D. Hobbs, W. Ding, A. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CThB4.

Diederich, F.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Ding, W.

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorel, R. M. De La Rue, Opt. Express 16, 3310 (2008).
[CrossRef] [PubMed]

C. E. de Nobriga, G. D. Hobbs, W. Ding, A. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CThB4.

Dulkeith, E.

Dumon, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Elkin, N. N.

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Nanpartovice, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

Esembeson, B.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Foster, M. A.

Freude, W.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Gaeta, A. L.

Glas, P.

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Nanpartovice, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

Gnan, M.

Gorbach, A.

C. E. de Nobriga, G. D. Hobbs, W. Ding, A. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CThB4.

Gorbach, A. V.

Green, W. M.

Hobbs, G. D.

C. E. de Nobriga, G. D. Hobbs, W. Ding, A. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CThB4.

Hsieh, I. W.

Knight, J. C.

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorel, R. M. De La Rue, Opt. Express 16, 3310 (2008).
[CrossRef] [PubMed]

C. E. de Nobriga, G. D. Hobbs, W. Ding, A. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CThB4.

Koos, C.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Leitner, M.

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Nanpartovice, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

Leuthold, J.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Lin, Q.

Lipson, M.

Liu, X.

Macintyre, D. S.

M. Gnan, S. Thorns, D. S. Macintyre, R. M. De La Rue, and M. Sorel, Electron. Lett. 44, 115 (2008).
[CrossRef]

Marom, E.

E. Marom, O. G. Ramer, and S. Ruschin, IEEE J. Quantum Electron. 20, 1311 (1984).
[CrossRef]

Michinobu, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Nanpartovice, A. P.

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Nanpartovice, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

Osgood, R. M.

Painter, O. J.

Paniou, N. C.

Ramer, O. G.

E. Marom, O. G. Ramer, and S. Ruschin, IEEE J. Quantum Electron. 20, 1311 (1984).
[CrossRef]

Ruschin, S.

E. Marom, O. G. Ramer, and S. Ruschin, IEEE J. Quantum Electron. 20, 1311 (1984).
[CrossRef]

Samarelli, A.

C. E. de Nobriga, G. D. Hobbs, W. Ding, A. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CThB4.

Sandrock, T.

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Nanpartovice, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

Skryabin, D. V.

C. J. Benton and D. V. Skryabin, Opt. Express 17, 5879(2009).
[CrossRef] [PubMed]

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorel, R. M. De La Rue, Opt. Express 16, 3310 (2008).
[CrossRef] [PubMed]

C. J. Benton, A. V. Gorbach, and D. V. Skryabin, Phys. Rev. A 78, 033818 (2008).
[CrossRef]

C. E. de Nobriga, G. D. Hobbs, W. Ding, A. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CThB4.

Sorel, M.

M. Gnan, S. Thorns, D. S. Macintyre, R. M. De La Rue, and M. Sorel, Electron. Lett. 44, 115 (2008).
[CrossRef]

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorel, R. M. De La Rue, Opt. Express 16, 3310 (2008).
[CrossRef] [PubMed]

C. E. de Nobriga, G. D. Hobbs, W. Ding, A. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CThB4.

Sukharev, A. G.

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Nanpartovice, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

Thorns, S.

M. Gnan, S. Thorns, D. S. Macintyre, R. M. De La Rue, and M. Sorel, Electron. Lett. 44, 115 (2008).
[CrossRef]

Turner, A. C.

Vallaitis, T.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Vlasov, Y. A.

Vorreau, P.

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Wadsworth, W. J.

W. Ding, C. Benton, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. Gnan, M. Sorel, R. M. De La Rue, Opt. Express 16, 3310 (2008).
[CrossRef] [PubMed]

C. E. de Nobriga, G. D. Hobbs, W. Ding, A. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CThB4.

Wrage, M.

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Nanpartovice, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

Xu, Q.

Adv. Opt. Photon. (1)

Electron. Lett. (1)

M. Gnan, S. Thorns, D. S. Macintyre, R. M. De La Rue, and M. Sorel, Electron. Lett. 44, 115 (2008).
[CrossRef]

IEEE J. Quantum Electron. (1)

E. Marom, O. G. Ramer, and S. Ruschin, IEEE J. Quantum Electron. 20, 1311 (1984).
[CrossRef]

Nat. Photon. (1)

C. Koos, P. Vorreau, T. Vallaitis, P. Dumon, W. Bogaerts, R. Baets, B. Esembeson, I. Biaggio, T. Michinobu, F. Diederich, W. Freude, and J. Leuthold, Nat. Photon. 3, 216 (2009).
[CrossRef]

Opt. Commun. (1)

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Nanpartovice, and A. G. Sukharev, Opt. Commun. 175, 97 (2000).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. A (1)

C. J. Benton, A. V. Gorbach, and D. V. Skryabin, Phys. Rev. A 78, 033818 (2008).
[CrossRef]

Other (1)

C. E. de Nobriga, G. D. Hobbs, W. Ding, A. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, A. Samarelli, M. Sorel, and R. M. De La Rue, in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CThB4.

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Figures (5)

Fig. 1
Fig. 1

Scanning electron microscope images showing the (a) sidewall verticality and (b) surface roughness of silicon photonic wires produced on the same chip as those used in the following experiments. (c) Schematic of the array used in the experiment. The waveguides are 380 nm × 220 nm in cross section and 3 mm long. The 160-nm-thick residual HSQ layer and the 20 nm silica pedestal created due to the complete etching of the silicon guiding layer are clearly shown.

Fig. 2
Fig. 2

(a) Group index of the symmetric and antisymmetric TE supermodes in a two-channel array. Experimental measurements of the quickest and slowest edges of the observed interferograms are shown by filled circles. The numerically modeled group index is also shown for the symmetric (solid curve) and antisymmetric (dashed curve) TE supermodes. The inset shows the computed dispersion of the TE supermode for a single 380 nm channel (dashed curve) compared to the coupling-induced dispersion (solid curve). (b) Example measured interferogram for the TE supermode at 1700 nm . The horizontal bar denotes the physical extent as described in the text.

Fig. 3
Fig. 3

Modeled field plots of the transverse electric field are shown for (a) the symmetric TE supermode and (b) the antisymmetric TE supermode at 1400 nm , long before the ridge–slot transition. For the antisymmetric mode, the left-hand lobe of the field plot and line plot is negative. The antisymmetric supermode is also shown in (d) as it approaches cutoff, at a wavelength of 1650 nm . After cutoff, only the symmetric TE supermode exists. This is shown at 1950 nm in (c). Below each plot is a line plot horizontally through the center of the waveguides.

Fig. 4
Fig. 4

Graph showing the modeled effective indices of the symmetric (solid curve) and antisymmetric (dashed curve) TE and TM supermodes of the two channel array, along with the refractive index of silica (dashed–dotted curve). An anticrossing between the symmetric TM and antisymmetric TE supermodes has been expanded (inset).

Fig. 5
Fig. 5

Field plots of the transverse magnetic component (parallel to the silica substrate) of the antisymmetric TE supermode as it passes through the anti-crossing [(a) at 1650 nm , (b) 1790 nm , and (c) 1950 nm ]. For comparison, the same component of the symmetric TM mode is shown in (d) at 1650 nm .

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