Abstract

We numerically investigate the lateral leakage loss behavior for TM-like modes in silicon-on-insulator ridge waveguides. In order to improve the leakage loss properties, we propose a novel ridge waveguide structure where a dimple is introduced at the ridge center. It is shown that the ridge waveguide with a dimple is both low loss and fabrication tolerant. This behavior is predicted by not only an accurate finite-element-based analysis but also a simple, phenomenological effective-index-based analysis.

© 2008 Optical Society of America

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  1. J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
    [CrossRef]
  2. F. Ohno, K. Sasaki, A. Motegi, and T. Baba, Jpn. J. Appl. Phys. 45, 6126 (2006).
    [CrossRef]
  3. A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
    [CrossRef] [PubMed]
  4. H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
    [CrossRef] [PubMed]
  5. M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, Appl. Phys. Lett. 87, 231108 (2005).
    [CrossRef]
  6. M. A. Webster, R. M. Pafchek, A. Mitchell, and T. L. Koch, IEEE Photonics Technol. Lett. 19, 429 (2007).
    [CrossRef]
  7. A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, IEEE Trans. Microwave Theory Tech. 29, 855 (1981).
    [CrossRef]
  8. K. Saitoh and M. Koshiba, IEEE J. Quantum Electron. 38, 927 (2002).
    [CrossRef]
  9. C. A. Barrios and M. Lipson, Opt. Express 13, 10092 (2005).
    [CrossRef] [PubMed]
  10. P. Muellner, N. Finger, and R. Hainberger, Opt. Express 16, 287 (2008).
    [CrossRef] [PubMed]

2008 (1)

2007 (1)

M. A. Webster, R. M. Pafchek, A. Mitchell, and T. L. Koch, IEEE Photonics Technol. Lett. 19, 429 (2007).
[CrossRef]

2006 (1)

F. Ohno, K. Sasaki, A. Motegi, and T. Baba, Jpn. J. Appl. Phys. 45, 6126 (2006).
[CrossRef]

2005 (3)

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[CrossRef] [PubMed]

M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, Appl. Phys. Lett. 87, 231108 (2005).
[CrossRef]

C. A. Barrios and M. Lipson, Opt. Express 13, 10092 (2005).
[CrossRef] [PubMed]

2004 (1)

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[CrossRef] [PubMed]

2002 (1)

K. Saitoh and M. Koshiba, IEEE J. Quantum Electron. 38, 927 (2002).
[CrossRef]

1997 (1)

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

1981 (1)

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, IEEE Trans. Microwave Theory Tech. 29, 855 (1981).
[CrossRef]

Baba, T.

F. Ohno, K. Sasaki, A. Motegi, and T. Baba, Jpn. J. Appl. Phys. 45, 6126 (2006).
[CrossRef]

Barrios, C. A.

Cohen, O.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[CrossRef] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[CrossRef] [PubMed]

Fan, S.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Fang, A.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[CrossRef] [PubMed]

Ferrera, J.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Finger, N.

Foresi, J. S.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Hainberger, R.

Hak, D.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[CrossRef] [PubMed]

Hsu, T. I.

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, IEEE Trans. Microwave Theory Tech. 29, 855 (1981).
[CrossRef]

Ippen, E. P.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Joannopoulos, J. D.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Jones, R.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[CrossRef] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[CrossRef] [PubMed]

Kimerling, L. C.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Koch, T. L.

M. A. Webster, R. M. Pafchek, A. Mitchell, and T. L. Koch, IEEE Photonics Technol. Lett. 19, 429 (2007).
[CrossRef]

M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, Appl. Phys. Lett. 87, 231108 (2005).
[CrossRef]

Koshiba, M.

K. Saitoh and M. Koshiba, IEEE J. Quantum Electron. 38, 927 (2002).
[CrossRef]

Liao, L.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[CrossRef] [PubMed]

Lipson, M.

Liu, A.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[CrossRef] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[CrossRef] [PubMed]

Mitchell, A.

M. A. Webster, R. M. Pafchek, A. Mitchell, and T. L. Koch, IEEE Photonics Technol. Lett. 19, 429 (2007).
[CrossRef]

Motegi, A.

F. Ohno, K. Sasaki, A. Motegi, and T. Baba, Jpn. J. Appl. Phys. 45, 6126 (2006).
[CrossRef]

Muellner, P.

Nicolaescu, R.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[CrossRef] [PubMed]

Ohno, F.

F. Ohno, K. Sasaki, A. Motegi, and T. Baba, Jpn. J. Appl. Phys. 45, 6126 (2006).
[CrossRef]

Oliner, A. A.

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, IEEE Trans. Microwave Theory Tech. 29, 855 (1981).
[CrossRef]

Pafchek, R. M.

M. A. Webster, R. M. Pafchek, A. Mitchell, and T. L. Koch, IEEE Photonics Technol. Lett. 19, 429 (2007).
[CrossRef]

M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, Appl. Phys. Lett. 87, 231108 (2005).
[CrossRef]

Paniccia, M.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[CrossRef] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[CrossRef] [PubMed]

Peng, S. T.

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, IEEE Trans. Microwave Theory Tech. 29, 855 (1981).
[CrossRef]

Rong, H.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[CrossRef] [PubMed]

Rubin, D.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[CrossRef] [PubMed]

Saitoh, K.

K. Saitoh and M. Koshiba, IEEE J. Quantum Electron. 38, 927 (2002).
[CrossRef]

Samara-Rubio, D.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[CrossRef] [PubMed]

Sanchez, A.

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, IEEE Trans. Microwave Theory Tech. 29, 855 (1981).
[CrossRef]

Sasaki, K.

F. Ohno, K. Sasaki, A. Motegi, and T. Baba, Jpn. J. Appl. Phys. 45, 6126 (2006).
[CrossRef]

Smith, H. I.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Steinmeyer, G.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Sukumaran, G.

M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, Appl. Phys. Lett. 87, 231108 (2005).
[CrossRef]

Thoen, E. R.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Villeneuve, P. R.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Webster, M. A.

M. A. Webster, R. M. Pafchek, A. Mitchell, and T. L. Koch, IEEE Photonics Technol. Lett. 19, 429 (2007).
[CrossRef]

M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, Appl. Phys. Lett. 87, 231108 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, Appl. Phys. Lett. 87, 231108 (2005).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Saitoh and M. Koshiba, IEEE J. Quantum Electron. 38, 927 (2002).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

M. A. Webster, R. M. Pafchek, A. Mitchell, and T. L. Koch, IEEE Photonics Technol. Lett. 19, 429 (2007).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

A. A. Oliner, S. T. Peng, T. I. Hsu, and A. Sanchez, IEEE Trans. Microwave Theory Tech. 29, 855 (1981).
[CrossRef]

Jpn. J. Appl. Phys. (1)

F. Ohno, K. Sasaki, A. Motegi, and T. Baba, Jpn. J. Appl. Phys. 45, 6126 (2006).
[CrossRef]

Nature (3)

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, Nature 427, 615 (2004).
[CrossRef] [PubMed]

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, Nature 433, 725 (2005).
[CrossRef] [PubMed]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, Nature 390, 143 (1997).
[CrossRef]

Opt. Express (2)

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic representation of the SOI ridge waveguide with a dimple at the ridge center. (b) Propagation process of the TM-like mode in a ridge waveguide with a top view, where the main field components of the TM-like hybrid mode are the y component of electric fields, E y , and the x component of magnetic fields, H x , and the TE- and TM-slab modes (intrinsically propagating in two-dimensional, planar waveguides) have no y component of electric and magnetic fields, E y and H y , respectively.

Fig. 2
Fig. 2

Waveguide-width dependence of (a) the normalized intensity I of the transmitted TE-slab waves obtained from Eq. (1) and (b) the leakage losses of the TM-like mode obtained from finite-element method simulation in the ridge waveguide in Fig. 1a.

Fig. 3
Fig. 3

Leakage losses of TM-like modes as a function of wavelength for (a) the conventional ridge waveguide ( d = 0 ) and (b) the proposed ridge waveguide with a dimple.

Fig. 4
Fig. 4

Wavelength dependence of the leakage losses with (a) dimple-width and (b) dimple-depth variations at an interval of 1 nm for the waveguide width of w = 1720 nm .

Equations (4)

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

I = 4 ϕ 0 2 [ 1 cos k 1 ( w d ) 2 ] [ 1 + cos k 1 ( w d ) + 2 k 2 d 2 ] ,
k 1 = k 0 n TE 2 ( t 1 ) N eff , TM 2 ,
k 2 = k 0 n TE 2 ( t 2 ) N eff , TM 2 ,
I = 2 ϕ 0 2 ( 1 cos k 1 w ) ,

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