Abstract

We present the first prediction of lateral leakage behavior of the TM-like mode in thin-ridge SOI curved waveguides and ring resonators. A simple phenomenological model is first presented which predicts that the lateral leakage in these structures is significantly impacted by both the ring radius and waveguide width. This prediction is verified using full vectorial mode matching and finite element methods. We show that specific combinations of waveguide width and ring radius can lead to very low-loss propagation in the TM-like mode. This finding is critical for the design of high-Q resonators on such waveguide platforms and will have major impact on the field of silicon lasers and sensing applications.

© 2010 Optical Society of America

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  1. B. Jalali and S. Fathpour, "Silicon Photonics," J. Lightwave Technol. 24(12), 4600-4615 (2006).
    [CrossRef]
  2. M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, "Low-loss quasi-planar ridge waveguides formed on thin silicon-on-insulator," Appl. Phys. Lett. 87(23), 231108-231110 (2005).
    [CrossRef]
  3. T. L. Koch, R. M. Pafchek, and M. A. Webster, "Fabrication of Optical Waveguides," US Patent App. 20060098928, (2006).
  4. R. Pafchek, R. Tummidi, J. Li, M. A. Webster, E. Chen, and T. L. Koch, "Low-loss silicon-on-insulator shallow ridge TE and TM waveguides formed using thermal oxidation," Appl. Opt. 48(5), 958-963 (2009). URL http://ao.osa.org/abstract.cfm?URI=ao-48-5-958.
    [CrossRef] [PubMed]
  5. A. A. Oliner, S.-T. Peng, T.-I. Hsu, and A. Sanchez, "Guidance and Leakage Properties of a Class of Open Dielectric Waveguides: Part II-New Physical Effects," IEEE Trans. Microwave Theory Tech. 29(9), 855-869 (1981).
    [CrossRef]
  6. K. Ogusu, "Optical strip waveguide-A detailed analysis including leaky modes," J. Opt. Soc. Am. 73, 353-357 (1983).
    [CrossRef]
  7. M. Webster, R. Pafchek, A. Mitchell, and T. Koch, "Width dependence of inherent TM-mode lateral leakage loss in silicon-on-insulator ridge waveguides," IEEE Photon. Technol. Lett. 19(6), 429-431 (2007).
    [CrossRef]
  8. R. S. Tummidi, T. Nguyen, A. Mitchell, and T. L. Koch, "Anomalous Losses in Curved Waveguides and Directional Couplers at "Magic Widths"," in 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society, pp.521-522, (2008).
  9. T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, "Rigorous Modeling of Lateral Leakage Loss in SOI Thin-Ridge Waveguides and Couplers," IEEE Photon. Technol. Lett. 21(7), 486 (2009).
    [CrossRef]
  10. T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, "Lateral leakage in TM-like whispering gallery mode of thin-ridge silicon-on-insulator disk resonators," Opt. Lett. 34(7), 980-982 (2009). URL http://ol.osa.org/abstract.cfm?URI=ol-34-7-980.
    [CrossRef] [PubMed]
  11. T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, "Thin-Ridge SOI Disk and Ring Resonators with "Magic Radius" and "Magic Width" Phenomena," in IEEE/OSA Conference on Lasers and Electro-Optics (CLEO) 2009 (Baltimore, MD, 2009).
  12. A. S. Sudbo, "Improved formulation of the film mode matching method for mode field calculations in dielectric waveguides," J. Opt. A, Pure Appl. Opt. 3, 381-388 (1994).
  13. L. Prkna, M. Hubálek, and J. Ctyroký, "Field modeling of circular microresonators by film mode matching," IEEE J. Sel. Top. Quantum Electron. 11(1), 217-223 (2005).
    [CrossRef]
  14. J. Jin, The finite element method in electromagnetics, 2nd ed. (Wiley-IEEE press, 2002).
  15. Comsol, Inc. URL http://www.comsol.com.

2009 (1)

T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, "Rigorous Modeling of Lateral Leakage Loss in SOI Thin-Ridge Waveguides and Couplers," IEEE Photon. Technol. Lett. 21(7), 486 (2009).
[CrossRef]

2007 (1)

M. Webster, R. Pafchek, A. Mitchell, and T. Koch, "Width dependence of inherent TM-mode lateral leakage loss in silicon-on-insulator ridge waveguides," IEEE Photon. Technol. Lett. 19(6), 429-431 (2007).
[CrossRef]

2006 (1)

2005 (2)

L. Prkna, M. Hubálek, and J. Ctyroký, "Field modeling of circular microresonators by film mode matching," IEEE J. Sel. Top. Quantum Electron. 11(1), 217-223 (2005).
[CrossRef]

M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, "Low-loss quasi-planar ridge waveguides formed on thin silicon-on-insulator," Appl. Phys. Lett. 87(23), 231108-231110 (2005).
[CrossRef]

1994 (1)

A. S. Sudbo, "Improved formulation of the film mode matching method for mode field calculations in dielectric waveguides," J. Opt. A, Pure Appl. Opt. 3, 381-388 (1994).

1983 (1)

1981 (1)

A. A. Oliner, S.-T. Peng, T.-I. Hsu, and A. Sanchez, "Guidance and Leakage Properties of a Class of Open Dielectric Waveguides: Part II-New Physical Effects," IEEE Trans. Microwave Theory Tech. 29(9), 855-869 (1981).
[CrossRef]

Ctyroký, J.

L. Prkna, M. Hubálek, and J. Ctyroký, "Field modeling of circular microresonators by film mode matching," IEEE J. Sel. Top. Quantum Electron. 11(1), 217-223 (2005).
[CrossRef]

Fathpour, S.

Hsu, T.-I.

A. A. Oliner, S.-T. Peng, T.-I. Hsu, and A. Sanchez, "Guidance and Leakage Properties of a Class of Open Dielectric Waveguides: Part II-New Physical Effects," IEEE Trans. Microwave Theory Tech. 29(9), 855-869 (1981).
[CrossRef]

Hubálek, M.

L. Prkna, M. Hubálek, and J. Ctyroký, "Field modeling of circular microresonators by film mode matching," IEEE J. Sel. Top. Quantum Electron. 11(1), 217-223 (2005).
[CrossRef]

Jalali, B.

Koch, T.

M. Webster, R. Pafchek, A. Mitchell, and T. Koch, "Width dependence of inherent TM-mode lateral leakage loss in silicon-on-insulator ridge waveguides," IEEE Photon. Technol. Lett. 19(6), 429-431 (2007).
[CrossRef]

Koch, T. L.

T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, "Rigorous Modeling of Lateral Leakage Loss in SOI Thin-Ridge Waveguides and Couplers," IEEE Photon. Technol. Lett. 21(7), 486 (2009).
[CrossRef]

M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, "Low-loss quasi-planar ridge waveguides formed on thin silicon-on-insulator," Appl. Phys. Lett. 87(23), 231108-231110 (2005).
[CrossRef]

Mitchell, A.

T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, "Rigorous Modeling of Lateral Leakage Loss in SOI Thin-Ridge Waveguides and Couplers," IEEE Photon. Technol. Lett. 21(7), 486 (2009).
[CrossRef]

M. Webster, R. Pafchek, A. Mitchell, and T. Koch, "Width dependence of inherent TM-mode lateral leakage loss in silicon-on-insulator ridge waveguides," IEEE Photon. Technol. Lett. 19(6), 429-431 (2007).
[CrossRef]

Nguyen, T. G.

T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, "Rigorous Modeling of Lateral Leakage Loss in SOI Thin-Ridge Waveguides and Couplers," IEEE Photon. Technol. Lett. 21(7), 486 (2009).
[CrossRef]

Ogusu, K.

Oliner, A. A.

A. A. Oliner, S.-T. Peng, T.-I. Hsu, and A. Sanchez, "Guidance and Leakage Properties of a Class of Open Dielectric Waveguides: Part II-New Physical Effects," IEEE Trans. Microwave Theory Tech. 29(9), 855-869 (1981).
[CrossRef]

Pafchek, R.

M. Webster, R. Pafchek, A. Mitchell, and T. Koch, "Width dependence of inherent TM-mode lateral leakage loss in silicon-on-insulator ridge waveguides," IEEE Photon. Technol. Lett. 19(6), 429-431 (2007).
[CrossRef]

Pafchek, R. M.

M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, "Low-loss quasi-planar ridge waveguides formed on thin silicon-on-insulator," Appl. Phys. Lett. 87(23), 231108-231110 (2005).
[CrossRef]

Peng, S.-T.

A. A. Oliner, S.-T. Peng, T.-I. Hsu, and A. Sanchez, "Guidance and Leakage Properties of a Class of Open Dielectric Waveguides: Part II-New Physical Effects," IEEE Trans. Microwave Theory Tech. 29(9), 855-869 (1981).
[CrossRef]

Prkna, L.

L. Prkna, M. Hubálek, and J. Ctyroký, "Field modeling of circular microresonators by film mode matching," IEEE J. Sel. Top. Quantum Electron. 11(1), 217-223 (2005).
[CrossRef]

Sanchez, A.

A. A. Oliner, S.-T. Peng, T.-I. Hsu, and A. Sanchez, "Guidance and Leakage Properties of a Class of Open Dielectric Waveguides: Part II-New Physical Effects," IEEE Trans. Microwave Theory Tech. 29(9), 855-869 (1981).
[CrossRef]

Sudbo, A. S.

A. S. Sudbo, "Improved formulation of the film mode matching method for mode field calculations in dielectric waveguides," J. Opt. A, Pure Appl. Opt. 3, 381-388 (1994).

Sukumaran, G.

M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, "Low-loss quasi-planar ridge waveguides formed on thin silicon-on-insulator," Appl. Phys. Lett. 87(23), 231108-231110 (2005).
[CrossRef]

Tummidi, R. S.

T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, "Rigorous Modeling of Lateral Leakage Loss in SOI Thin-Ridge Waveguides and Couplers," IEEE Photon. Technol. Lett. 21(7), 486 (2009).
[CrossRef]

Webster, M.

M. Webster, R. Pafchek, A. Mitchell, and T. Koch, "Width dependence of inherent TM-mode lateral leakage loss in silicon-on-insulator ridge waveguides," IEEE Photon. Technol. Lett. 19(6), 429-431 (2007).
[CrossRef]

Webster, M. A.

M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, "Low-loss quasi-planar ridge waveguides formed on thin silicon-on-insulator," Appl. Phys. Lett. 87(23), 231108-231110 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

M. A. Webster, R. M. Pafchek, G. Sukumaran, and T. L. Koch, "Low-loss quasi-planar ridge waveguides formed on thin silicon-on-insulator," Appl. Phys. Lett. 87(23), 231108-231110 (2005).
[CrossRef]

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

L. Prkna, M. Hubálek, and J. Ctyroký, "Field modeling of circular microresonators by film mode matching," IEEE J. Sel. Top. Quantum Electron. 11(1), 217-223 (2005).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

M. Webster, R. Pafchek, A. Mitchell, and T. Koch, "Width dependence of inherent TM-mode lateral leakage loss in silicon-on-insulator ridge waveguides," IEEE Photon. Technol. Lett. 19(6), 429-431 (2007).
[CrossRef]

T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, "Rigorous Modeling of Lateral Leakage Loss in SOI Thin-Ridge Waveguides and Couplers," IEEE Photon. Technol. Lett. 21(7), 486 (2009).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

A. A. Oliner, S.-T. Peng, T.-I. Hsu, and A. Sanchez, "Guidance and Leakage Properties of a Class of Open Dielectric Waveguides: Part II-New Physical Effects," IEEE Trans. Microwave Theory Tech. 29(9), 855-869 (1981).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. A, Pure Appl. Opt. (1)

A. S. Sudbo, "Improved formulation of the film mode matching method for mode field calculations in dielectric waveguides," J. Opt. A, Pure Appl. Opt. 3, 381-388 (1994).

J. Opt. Soc. Am. (1)

Other (7)

T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, "Lateral leakage in TM-like whispering gallery mode of thin-ridge silicon-on-insulator disk resonators," Opt. Lett. 34(7), 980-982 (2009). URL http://ol.osa.org/abstract.cfm?URI=ol-34-7-980.
[CrossRef] [PubMed]

T. G. Nguyen, R. S. Tummidi, T. L. Koch, and A. Mitchell, "Thin-Ridge SOI Disk and Ring Resonators with "Magic Radius" and "Magic Width" Phenomena," in IEEE/OSA Conference on Lasers and Electro-Optics (CLEO) 2009 (Baltimore, MD, 2009).

R. S. Tummidi, T. Nguyen, A. Mitchell, and T. L. Koch, "Anomalous Losses in Curved Waveguides and Directional Couplers at "Magic Widths"," in 21st Annual Meeting of the IEEE Lasers and Electro-Optics Society, pp.521-522, (2008).

J. Jin, The finite element method in electromagnetics, 2nd ed. (Wiley-IEEE press, 2002).

Comsol, Inc. URL http://www.comsol.com.

T. L. Koch, R. M. Pafchek, and M. A. Webster, "Fabrication of Optical Waveguides," US Patent App. 20060098928, (2006).

R. Pafchek, R. Tummidi, J. Li, M. A. Webster, E. Chen, and T. L. Koch, "Low-loss silicon-on-insulator shallow ridge TE and TM waveguides formed using thermal oxidation," Appl. Opt. 48(5), 958-963 (2009). URL http://ao.osa.org/abstract.cfm?URI=ao-48-5-958.
[CrossRef] [PubMed]

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Figures (9)

Fig. 1.
Fig. 1.

(a) Cross section, and (b) plan view and mode coupling diagram of a SOI thin-ridge ring resonator. Waveguide dimensions and material refractive indices are shown.

Fig. 2.
Fig. 2.

Simulated propagation loss of the TM-like guided mode of a thin-ridge SOI bent waveguide (obtained by preventing the secant TE waves from re-entering the waveguide section) (a) as a function of waveguide width for different bend radii and (b) as a function of the bend radius when the waveguide width is fixed at 1.43 μm.

Fig. 3.
Fig. 3.

Simulation domain used to model rings with R = 100μm in FEM (not to scale).

Fig. 4.
Fig. 4.

Propagation loss of the fundamental TM-like mode of a ring resonator as a function of the ring radius. The waveguide width is w = 1.43 μm.

Fig. 5.
Fig. 5.

Propagation loss of the fundamental TM-like mode of a ring resonator as a function of the waveguide width for different ring radii.

Fig. 6.
Fig. 6.

Propagation loss of the fundamental TM-like mode of a ring resonator as a function of the waveguide width and ring radius: (a) nominal radius 200 μm and (b) nominal radius 400 μm.

Fig. 7.
Fig. 7.

Electric field distributions of the fundamental TM-like mode of a ring resonator with a waveguide width of 1.35μm and radius of (a) 199.62 μm (high loss) and (b) 198.95 μm (low loss).

Fig. 8.
Fig. 8.

Electric field distributions of the fundamental TM-like mode of a ring resonator with bending radius of (a) 199.84 μm and (b) 200.46 μm. The waveguide width is 1.43 μm.

Fig. 9.
Fig. 9.

Wavelength dependent loss of the TM-like mode in thin-ridge SOI ring resonators with waveguide with of (a) 1.43 μm and (b) 1.35 μm.

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