Abstract

We study numerically the dependence of dispersive and birefringence properties of silicon nanowires on waveguide dimensions and show that they have a strong geometrical dependence when nanowire dimensions become comparable to the wavelength of light inside the device. We develop a graphical method for engineering two or more dispersion parameters simultaneously and use it to demonstrate the possibility of fabricating silicon nanowires with flattened dispersion curves over a wide spectral range with normal or anomalous nominal values. We quantify polarization-mode dispersion through the differential group delay and show that it can acquire large values for properly designed nanowires. Our analysis should help in designing silicon-based photonic integrated circuits.

© 2010 Optical Society of America

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References

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    [CrossRef] [PubMed]
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2009 (1)

J. Marconi, S. A. Cerqueira, Jr., J. Robinson, N. Sherwood-Droz, Y. Okawachi, H. Hernandez-Figueroa, M. Lipson, A. Gaeta, and H. Fragnito, Opt. Commun. 282, 849 (2009).
[CrossRef]

2008 (2)

B. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. Dadap, F. Xia, W. Green, L. Sekaric, Y. Vlasov, R. Osgood, Jr., and K. Bergman, IEEE Photon. Technol. Lett. 20, 398 (2008).
[CrossRef]

L. Christen, Y. K. Lizé, S. Nuccio, L. Paraschis, and A. E. Willner, IEEE Photon. Technol. Lett. 20, 1166 (2008).
[CrossRef]

2007 (3)

2006 (3)

2004 (1)

1994 (1)

P. Lüsse, P. Stuwe, J. Schüle, and H. Unger, J. Lightwave Technol. 12, 487 (1994).
[CrossRef]

Agrawal, G. P.

Bergman, K.

B. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. Dadap, F. Xia, W. Green, L. Sekaric, Y. Vlasov, R. Osgood, Jr., and K. Bergman, IEEE Photon. Technol. Lett. 20, 398 (2008).
[CrossRef]

Biberman, A.

B. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. Dadap, F. Xia, W. Green, L. Sekaric, Y. Vlasov, R. Osgood, Jr., and K. Bergman, IEEE Photon. Technol. Lett. 20, 398 (2008).
[CrossRef]

Bolten, J.

Cerqueira, S. A.

J. Marconi, S. A. Cerqueira, Jr., J. Robinson, N. Sherwood-Droz, Y. Okawachi, H. Hernandez-Figueroa, M. Lipson, A. Gaeta, and H. Fragnito, Opt. Commun. 282, 849 (2009).
[CrossRef]

Cheben, P.

D. Duchesne, P. Cheben, R. Morandotti, B. Lamontagne, D. Xu, S. Janz, and D. Christodoulides, Opt. Eng. 46, 104602 (2007).
[CrossRef]

Chen, X.

B. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. Dadap, F. Xia, W. Green, L. Sekaric, Y. Vlasov, R. Osgood, Jr., and K. Bergman, IEEE Photon. Technol. Lett. 20, 398 (2008).
[CrossRef]

Chou, C.

B. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. Dadap, F. Xia, W. Green, L. Sekaric, Y. Vlasov, R. Osgood, Jr., and K. Bergman, IEEE Photon. Technol. Lett. 20, 398 (2008).
[CrossRef]

Christen, L.

L. Christen, Y. K. Lizé, S. Nuccio, L. Paraschis, and A. E. Willner, IEEE Photon. Technol. Lett. 20, 1166 (2008).
[CrossRef]

Christodoulides, D.

D. Duchesne, P. Cheben, R. Morandotti, B. Lamontagne, D. Xu, S. Janz, and D. Christodoulides, Opt. Eng. 46, 104602 (2007).
[CrossRef]

Ctyroký, J.

Dadap, J.

B. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. Dadap, F. Xia, W. Green, L. Sekaric, Y. Vlasov, R. Osgood, Jr., and K. Bergman, IEEE Photon. Technol. Lett. 20, 398 (2008).
[CrossRef]

Duchesne, D.

D. Duchesne, P. Cheben, R. Morandotti, B. Lamontagne, D. Xu, S. Janz, and D. Christodoulides, Opt. Eng. 46, 104602 (2007).
[CrossRef]

Dulkeith, E.

Först, M.

Foster, M.

Foster, M. A.

Fragnito, H.

J. Marconi, S. A. Cerqueira, Jr., J. Robinson, N. Sherwood-Droz, Y. Okawachi, H. Hernandez-Figueroa, M. Lipson, A. Gaeta, and H. Fragnito, Opt. Commun. 282, 849 (2009).
[CrossRef]

Gaeta, A.

J. Marconi, S. A. Cerqueira, Jr., J. Robinson, N. Sherwood-Droz, Y. Okawachi, H. Hernandez-Figueroa, M. Lipson, A. Gaeta, and H. Fragnito, Opt. Commun. 282, 849 (2009).
[CrossRef]

A. Turner, C. Manolatou, B. Schmidt, M. Lipson, M. Foster, J. Sharping, and A. Gaeta, Opt. Express 14, 4357 (2006).
[CrossRef] [PubMed]

Gaeta, A. L.

Green, W.

B. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. Dadap, F. Xia, W. Green, L. Sekaric, Y. Vlasov, R. Osgood, Jr., and K. Bergman, IEEE Photon. Technol. Lett. 20, 398 (2008).
[CrossRef]

Green, W. M. J.

Hernandez-Figueroa, H.

J. Marconi, S. A. Cerqueira, Jr., J. Robinson, N. Sherwood-Droz, Y. Okawachi, H. Hernandez-Figueroa, M. Lipson, A. Gaeta, and H. Fragnito, Opt. Commun. 282, 849 (2009).
[CrossRef]

Houdré, R.

Hsieh, I.

B. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. Dadap, F. Xia, W. Green, L. Sekaric, Y. Vlasov, R. Osgood, Jr., and K. Bergman, IEEE Photon. Technol. Lett. 20, 398 (2008).
[CrossRef]

Jágerská, J.

Janz, S.

D. Duchesne, P. Cheben, R. Morandotti, B. Lamontagne, D. Xu, S. Janz, and D. Christodoulides, Opt. Eng. 46, 104602 (2007).
[CrossRef]

Lamontagne, B.

D. Duchesne, P. Cheben, R. Morandotti, B. Lamontagne, D. Xu, S. Janz, and D. Christodoulides, Opt. Eng. 46, 104602 (2007).
[CrossRef]

Le Thomas, N.

Lee, B.

B. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. Dadap, F. Xia, W. Green, L. Sekaric, Y. Vlasov, R. Osgood, Jr., and K. Bergman, IEEE Photon. Technol. Lett. 20, 398 (2008).
[CrossRef]

Lin, Q.

Lipson, M.

Liu, X.

B. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. Dadap, F. Xia, W. Green, L. Sekaric, Y. Vlasov, R. Osgood, Jr., and K. Bergman, IEEE Photon. Technol. Lett. 20, 398 (2008).
[CrossRef]

Lizé, Y. K.

L. Christen, Y. K. Lizé, S. Nuccio, L. Paraschis, and A. E. Willner, IEEE Photon. Technol. Lett. 20, 1166 (2008).
[CrossRef]

Lou, J.

Lüsse, P.

P. Lüsse, P. Stuwe, J. Schüle, and H. Unger, J. Lightwave Technol. 12, 487 (1994).
[CrossRef]

Manolatou, C.

Marconi, J.

J. Marconi, S. A. Cerqueira, Jr., J. Robinson, N. Sherwood-Droz, Y. Okawachi, H. Hernandez-Figueroa, M. Lipson, A. Gaeta, and H. Fragnito, Opt. Commun. 282, 849 (2009).
[CrossRef]

Mazur, E.

Moormann, C.

Morandotti, R.

D. Duchesne, P. Cheben, R. Morandotti, B. Lamontagne, D. Xu, S. Janz, and D. Christodoulides, Opt. Eng. 46, 104602 (2007).
[CrossRef]

Nuccio, S.

L. Christen, Y. K. Lizé, S. Nuccio, L. Paraschis, and A. E. Willner, IEEE Photon. Technol. Lett. 20, 1166 (2008).
[CrossRef]

Okawachi, Y.

J. Marconi, S. A. Cerqueira, Jr., J. Robinson, N. Sherwood-Droz, Y. Okawachi, H. Hernandez-Figueroa, M. Lipson, A. Gaeta, and H. Fragnito, Opt. Commun. 282, 849 (2009).
[CrossRef]

Osgood, R.

B. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. Dadap, F. Xia, W. Green, L. Sekaric, Y. Vlasov, R. Osgood, Jr., and K. Bergman, IEEE Photon. Technol. Lett. 20, 398 (2008).
[CrossRef]

Paraschis, L.

L. Christen, Y. K. Lizé, S. Nuccio, L. Paraschis, and A. E. Willner, IEEE Photon. Technol. Lett. 20, 1166 (2008).
[CrossRef]

Robinson, J.

J. Marconi, S. A. Cerqueira, Jr., J. Robinson, N. Sherwood-Droz, Y. Okawachi, H. Hernandez-Figueroa, M. Lipson, A. Gaeta, and H. Fragnito, Opt. Commun. 282, 849 (2009).
[CrossRef]

Salem, R.

Schares, L.

Schmidt, B.

Schüle, J.

P. Lüsse, P. Stuwe, J. Schüle, and H. Unger, J. Lightwave Technol. 12, 487 (1994).
[CrossRef]

Sekaric, L.

B. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. Dadap, F. Xia, W. Green, L. Sekaric, Y. Vlasov, R. Osgood, Jr., and K. Bergman, IEEE Photon. Technol. Lett. 20, 398 (2008).
[CrossRef]

Sharping, J.

Sherwood-Droz, N.

J. Marconi, S. A. Cerqueira, Jr., J. Robinson, N. Sherwood-Droz, Y. Okawachi, H. Hernandez-Figueroa, M. Lipson, A. Gaeta, and H. Fragnito, Opt. Commun. 282, 849 (2009).
[CrossRef]

Stuwe, P.

P. Lüsse, P. Stuwe, J. Schüle, and H. Unger, J. Lightwave Technol. 12, 487 (1994).
[CrossRef]

Tong, L.

Turner, A.

Turner, A. C.

Unger, H.

P. Lüsse, P. Stuwe, J. Schüle, and H. Unger, J. Lightwave Technol. 12, 487 (1994).
[CrossRef]

Vlasov, Y.

B. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. Dadap, F. Xia, W. Green, L. Sekaric, Y. Vlasov, R. Osgood, Jr., and K. Bergman, IEEE Photon. Technol. Lett. 20, 398 (2008).
[CrossRef]

Vlasov, Y. A.

Wahlbrink, T.

Waldow, M.

Weber, M. J.

M. J. Weber, Handbook of Optical Materials (CRC, 2003), p. 239.

Willner, A. E.

L. Christen, Y. K. Lizé, S. Nuccio, L. Paraschis, and A. E. Willner, IEEE Photon. Technol. Lett. 20, 1166 (2008).
[CrossRef]

Xia, F.

B. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. Dadap, F. Xia, W. Green, L. Sekaric, Y. Vlasov, R. Osgood, Jr., and K. Bergman, IEEE Photon. Technol. Lett. 20, 398 (2008).
[CrossRef]

E. Dulkeith, F. Xia, L. Schares, W. M. J. Green, and Y. A. Vlasov, Opt. Express 14, 3853 (2006).
[CrossRef] [PubMed]

Xu, D.

D. Duchesne, P. Cheben, R. Morandotti, B. Lamontagne, D. Xu, S. Janz, and D. Christodoulides, Opt. Eng. 46, 104602 (2007).
[CrossRef]

Yin, L.

IEEE Photon. Technol. Lett. (2)

B. Lee, X. Chen, A. Biberman, X. Liu, I. Hsieh, C. Chou, J. Dadap, F. Xia, W. Green, L. Sekaric, Y. Vlasov, R. Osgood, Jr., and K. Bergman, IEEE Photon. Technol. Lett. 20, 398 (2008).
[CrossRef]

L. Christen, Y. K. Lizé, S. Nuccio, L. Paraschis, and A. E. Willner, IEEE Photon. Technol. Lett. 20, 1166 (2008).
[CrossRef]

J. Lightwave Technol. (1)

P. Lüsse, P. Stuwe, J. Schüle, and H. Unger, J. Lightwave Technol. 12, 487 (1994).
[CrossRef]

Opt. Commun. (1)

J. Marconi, S. A. Cerqueira, Jr., J. Robinson, N. Sherwood-Droz, Y. Okawachi, H. Hernandez-Figueroa, M. Lipson, A. Gaeta, and H. Fragnito, Opt. Commun. 282, 849 (2009).
[CrossRef]

Opt. Eng. (1)

D. Duchesne, P. Cheben, R. Morandotti, B. Lamontagne, D. Xu, S. Janz, and D. Christodoulides, Opt. Eng. 46, 104602 (2007).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Other (1)

M. J. Weber, Handbook of Optical Materials (CRC, 2003), p. 239.

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Figures (5)

Fig. 1
Fig. 1

TE-mode group index at λ 0 = 1550   nm as a function of waveguide dimensions. The inset shows the waveguide geometry schematically.

Fig. 2
Fig. 2

DGD as a function of waveguide dimensions at λ 0 = 1550   nm .

Fig. 3
Fig. 3

TE-mode GVD at λ 0 = 1550   nm as a function of waveguide dimensions.

Fig. 4
Fig. 4

Contours in the w h plane showing locations where β 2 TE (solid curve), β 3 TE (dashed curve), and β 4 TE vanish at a wavelength of 1550 nm.

Fig. 5
Fig. 5

Spectral dependence of β 2 TE (solid lines) and β 3 TE (dashed lines) for a few dispersion-flattened geometries.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

× E = i ω μ 0 H ,
× H = i ω ε 0 n 2 ( x , y , ω ) E ,
E ( ω ; x , y , z ) = e ( ω ; x , y ) e i β ( ω ) z ,
H ( ω ; x , y , z ) = h ( ω ; x , y ) e i β ( ω ) z ,

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