Abstract

The statistics of backscattering induced by sidewall roughness in dielectric optical waveguides is experimentally investigated. We demonstrate that waveguide backscattering is a wavelength-dependent random process, whose statistics follows the rules of single scattering systems, independently of shape, size, and refractive index contrast of the waveguide, and of the light polarization state. The intensity of backscattering is distributed according to an exponential probability density function, and its mean delay corresponds to a reflection at half the effective length of the waveguide.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2010 (2)

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, Phys. Rev. Lett. 104, 033902(2010).
[CrossRef] [PubMed]

F. Morichetti, A. Melloni, A. Canciamilla, A. Samarelli, M. Sorel, R. M. De La Rue, and M. Martinelli, Appl. Phys. Lett. 96, 081112 (2010).
[CrossRef]

2009 (1)

M. Patterson, S. Hughes, S. Combie, N.-V. Q. Tran, A. De Rossi, R. Gabet, and Y. Jaouen, Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef] [PubMed]

2008 (2)

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

A. Melloni, F. Morichetti, C. Ferrari, and M. Martinelli, Opt. Lett. 33, 2389 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, IEEE J. Sel. Top. Quantum Electron. 12, 1306 (2006).
[CrossRef]

2001 (1)

1996 (1)

1995 (1)

W. Yun-ping and Z. Dian-lin, Phys. Rev. A 52, 2597 (1995).
[CrossRef] [PubMed]

1990 (1)

P. Gysel and K. Stabuli, J. Lightwave Technol. 8, 561 (1990).
[CrossRef]

1987 (1)

P. Healey, IEEE Trans. Commun. 35, 210 (1987).
[CrossRef]

Borreman, A.

Canciamilla, A.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, Phys. Rev. Lett. 104, 033902(2010).
[CrossRef] [PubMed]

F. Morichetti, A. Melloni, A. Canciamilla, A. Samarelli, M. Sorel, R. M. De La Rue, and M. Martinelli, Appl. Phys. Lett. 96, 081112 (2010).
[CrossRef]

Cerrina, F.

Combie, S.

M. Patterson, S. Hughes, S. Combie, N.-V. Q. Tran, A. De Rossi, R. Gabet, and Y. Jaouen, Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef] [PubMed]

De La Rue, R. M.

F. Morichetti, A. Melloni, A. Canciamilla, A. Samarelli, M. Sorel, R. M. De La Rue, and M. Martinelli, Appl. Phys. Lett. 96, 081112 (2010).
[CrossRef]

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

De Rossi, A.

M. Patterson, S. Hughes, S. Combie, N.-V. Q. Tran, A. De Rossi, R. Gabet, and Y. Jaouen, Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef] [PubMed]

Dian-lin, Z.

W. Yun-ping and Z. Dian-lin, Phys. Rev. A 52, 2597 (1995).
[CrossRef] [PubMed]

Ferrari, C.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, Phys. Rev. Lett. 104, 033902(2010).
[CrossRef] [PubMed]

A. Melloni, F. Morichetti, C. Ferrari, and M. Martinelli, Opt. Lett. 33, 2389 (2008).
[CrossRef] [PubMed]

Freude, W.

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, IEEE J. Sel. Top. Quantum Electron. 12, 1306 (2006).
[CrossRef]

Fujii, M.

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, IEEE J. Sel. Top. Quantum Electron. 12, 1306 (2006).
[CrossRef]

Gabet, R.

M. Patterson, S. Hughes, S. Combie, N.-V. Q. Tran, A. De Rossi, R. Gabet, and Y. Jaouen, Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef] [PubMed]

Geuzebroek, D. H.

Gnan, M.

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

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley-Interscience, 1985).

Gysel, P.

P. Gysel and K. Stabuli, J. Lightwave Technol. 8, 561 (1990).
[CrossRef]

Healey, P.

P. Healey, IEEE Trans. Commun. 35, 210 (1987).
[CrossRef]

Heideman, R. G.

Hughes, S.

M. Patterson, S. Hughes, S. Combie, N.-V. Q. Tran, A. De Rossi, R. Gabet, and Y. Jaouen, Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef] [PubMed]

Jaouen, Y.

M. Patterson, S. Hughes, S. Combie, N.-V. Q. Tran, A. De Rossi, R. Gabet, and Y. Jaouen, Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef] [PubMed]

Kimerling, L. C.

Koos, C.

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, IEEE J. Sel. Top. Quantum Electron. 12, 1306 (2006).
[CrossRef]

Ladouceur, F.

Lee, K. K.

Leinse, A.

Leuthold, J.

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, IEEE J. Sel. Top. Quantum Electron. 12, 1306 (2006).
[CrossRef]

Lim, D. R.

Macintyre, D. S.

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

Martinelli, M.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, Phys. Rev. Lett. 104, 033902(2010).
[CrossRef] [PubMed]

F. Morichetti, A. Melloni, A. Canciamilla, A. Samarelli, M. Sorel, R. M. De La Rue, and M. Martinelli, Appl. Phys. Lett. 96, 081112 (2010).
[CrossRef]

A. Melloni, F. Morichetti, C. Ferrari, and M. Martinelli, Opt. Lett. 33, 2389 (2008).
[CrossRef] [PubMed]

F. Morichetti, A. Melloni, M. Martinelli, R. G. Heideman, A. Leinse, D. H. Geuzebroek, and A. Borreman, J. Lightwave Technol. 25, 2579 (2007).
[CrossRef]

Melloni, A.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, Phys. Rev. Lett. 104, 033902(2010).
[CrossRef] [PubMed]

F. Morichetti, A. Melloni, A. Canciamilla, A. Samarelli, M. Sorel, R. M. De La Rue, and M. Martinelli, Appl. Phys. Lett. 96, 081112 (2010).
[CrossRef]

A. Melloni, F. Morichetti, C. Ferrari, and M. Martinelli, Opt. Lett. 33, 2389 (2008).
[CrossRef] [PubMed]

F. Morichetti, A. Melloni, M. Martinelli, R. G. Heideman, A. Leinse, D. H. Geuzebroek, and A. Borreman, J. Lightwave Technol. 25, 2579 (2007).
[CrossRef]

Morichetti, F.

F. Morichetti, A. Melloni, A. Canciamilla, A. Samarelli, M. Sorel, R. M. De La Rue, and M. Martinelli, Appl. Phys. Lett. 96, 081112 (2010).
[CrossRef]

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, Phys. Rev. Lett. 104, 033902(2010).
[CrossRef] [PubMed]

A. Melloni, F. Morichetti, C. Ferrari, and M. Martinelli, Opt. Lett. 33, 2389 (2008).
[CrossRef] [PubMed]

F. Morichetti, A. Melloni, M. Martinelli, R. G. Heideman, A. Leinse, D. H. Geuzebroek, and A. Borreman, J. Lightwave Technol. 25, 2579 (2007).
[CrossRef]

Patterson, M.

M. Patterson, S. Hughes, S. Combie, N.-V. Q. Tran, A. De Rossi, R. Gabet, and Y. Jaouen, Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef] [PubMed]

Pfrang, A.

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, IEEE J. Sel. Top. Quantum Electron. 12, 1306 (2006).
[CrossRef]

Poladian, L.

Poulton, C. G.

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, IEEE J. Sel. Top. Quantum Electron. 12, 1306 (2006).
[CrossRef]

Samarelli, A.

F. Morichetti, A. Melloni, A. Canciamilla, A. Samarelli, M. Sorel, R. M. De La Rue, and M. Martinelli, Appl. Phys. Lett. 96, 081112 (2010).
[CrossRef]

Schimmel, T.

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, IEEE J. Sel. Top. Quantum Electron. 12, 1306 (2006).
[CrossRef]

Shin, J.

Sorel, M.

F. Morichetti, A. Melloni, A. Canciamilla, A. Samarelli, M. Sorel, R. M. De La Rue, and M. Martinelli, Appl. Phys. Lett. 96, 081112 (2010).
[CrossRef]

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

Stabuli, K.

P. Gysel and K. Stabuli, J. Lightwave Technol. 8, 561 (1990).
[CrossRef]

Thoms, S.

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

Torregiani, M.

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, Phys. Rev. Lett. 104, 033902(2010).
[CrossRef] [PubMed]

Tran, N.-V. Q.

M. Patterson, S. Hughes, S. Combie, N.-V. Q. Tran, A. De Rossi, R. Gabet, and Y. Jaouen, Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef] [PubMed]

Yun-ping, W.

W. Yun-ping and Z. Dian-lin, Phys. Rev. A 52, 2597 (1995).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

F. Morichetti, A. Melloni, A. Canciamilla, A. Samarelli, M. Sorel, R. M. De La Rue, and M. Martinelli, Appl. Phys. Lett. 96, 081112 (2010).
[CrossRef]

Electron. Lett. (1)

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

IEEE J. Sel. Top. Quantum Electron. (1)

C. G. Poulton, C. Koos, M. Fujii, A. Pfrang, T. Schimmel, J. Leuthold, and W. Freude, IEEE J. Sel. Top. Quantum Electron. 12, 1306 (2006).
[CrossRef]

IEEE Trans. Commun. (1)

P. Healey, IEEE Trans. Commun. 35, 210 (1987).
[CrossRef]

J. Lightwave Technol. (2)

Opt. Lett. (3)

Phys. Rev. A (1)

W. Yun-ping and Z. Dian-lin, Phys. Rev. A 52, 2597 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

M. Patterson, S. Hughes, S. Combie, N.-V. Q. Tran, A. De Rossi, R. Gabet, and Y. Jaouen, Phys. Rev. Lett. 102, 253903 (2009).
[CrossRef] [PubMed]

F. Morichetti, A. Canciamilla, C. Ferrari, M. Torregiani, A. Melloni, and M. Martinelli, Phys. Rev. Lett. 104, 033902(2010).
[CrossRef] [PubMed]

Other (1)

J. W. Goodman, Statistical Optics (Wiley-Interscience, 1985).

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic of a rough optical waveguide, (b) measured PSD of the backscattering of a 1-mm-long SOI waveguide with w = 490 nm for TE (solid curve) and TM (dotted curve) input polarization.

Fig. 2
Fig. 2

Mean backscattering level (averaged in the 1520 1580 nm wavelength range) of three SOI waveguides with w = 300 , 350, and 490 nm versus the waveguide length L w : measurements (dots) and theoretical model (dashed curves). The arrow indicates the waveguide of Fig. 1b.

Fig. 3
Fig. 3

Probability density function of the measured backscattering power | H R | 2 of 1-mm-long SOI waveguides with different w for (a) TE and (b) TM input polarization. Mean and standard deviation of | H R | 2 are indicated in the insets.

Fig. 4
Fig. 4

Probability density function of the normalized measured backscattering length of 12-mm-long SOI waveguides with different w for (a) TE and (b) TM input polarization.

Fig. 5
Fig. 5

Probability density function of the (a) real and (b) imaginary parts of the normalized backscattering H R / σ R in a SOI nanowire (circles), a SiON square buried waveguide (diamonds), and a box-shaped TriPleX waveguide (squares) for TE input polarization.

Equations (1)

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L w > L ln H 0 L [ 1 + H 0 2 L 2 ] 1 2 1 L ln 2 H 0 L ,

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