Abstract

The spectral characteristics of a ring resonator made of Si photonic wires are modeled using mode expansion of supermodes of the directional coupler. The influence of the coupling coefficient, loss factor and waveguide dispersion on the spectral features are analyzed in detail. The model is then compared with the experimental data of a ring resonator designed for sensing purposes. The model that includes a wavelength dependence on coupling length reproduces the large variations of the envelope of the experimental spectrum, when coupling coefficient cover its full range from 0 to 1. Fitting parameters explain the details of the experimental spectrum and contribute to the sensor optimization, as well as illustrating general guidelines for ring resonator design.

© 2009 IEEE

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  1. L. F. Stokes, M. Chodorow, H. J. Shaw, "All-single-mode fiber resonator," Opt. Lett. 7, 288-90 (1982) 1982.
  2. A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, B. B. Goldberg, "Optical sensing of biomolecules using microring resonators," IEEE J. Sel. Topics Quantum Electron. 12, 148-55 (2006).
  3. B. Bortnik, Y.-C. Hung, H. Tazawa, B.-J. Seo, J. Luo, A. K.-Y. Jen, W. H. Steier, H. R. Fetterman, "Electrooptic polymer ring resonator modulation up to 165 GHz," IEEE J. Sel. Topics Quantum Electron. 13, 104-109 (2007).
  4. D. Rafizadeh, J. P. Zhang, R. C. Tiberio, S. T. Ho, "Propagation loss measurements in semiconductor microcavity ring and disk resonators," J. Lightw. Technol. 16, 1308 (1998) 1998.
  5. K. M. De Vos, I. Bartolozzi, P. Bienstman, R. Baets, E. Schacht, "Optical biosensor based on silicon-on-insulator microring cavities for specific protein binding detection," Proc. SPIE 6447 Nanoscale Imaging, Spectrosc., Sens., Actuation for Biomed. Appl. IV (2007).
  6. D.-X. Xu, S. Janz, P. Cheben, "Design of polarization-insensitive ring resonators in SOI stress engineering and MMI couplers," IEEE Photon. Technol. Lett. 18, 343-345 (2006).
  7. D. Po, S. F. Preble, M. Lipson, "All-optical compact silicon comb switch," Opt. Express 15, 9600-9605 (2007).
  8. T.-J. Wang, C.-H. Chu, C.-Y. Lin, "Electro-optically tunable microring resonators on lithium niobate," Opt. Lett. 32, 2777-2779 (2007).
  9. M. S. Nawrocka, T. Liu, X. Wang, R. R. Panepucci, "Tunable silicon microring resonator with wide free spectral range," Appl. Phys. Lett. 89, 071110 (2006).
  10. Z. Lu, "Efficient fiber-to-waveguide coupling through the vertical leakage from a microring," Opt. Lett. 32, 2861-3 (2007).
  11. D. G. Rabus, Integrated Ring Resonnators: The Compedium (Springer-Verlag, 2007).
  12. J. Heebner, R. Grover, T. Ibrahim, Titre Optical Microresonators: Theory, Fabrication, and Applications (Springer, 2008).
  13. http://www.biacore.com.
  14. A. Densmore, D.-X. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delâge, B. Lamontagne, J. H. Schmid, E. Post, "A silicon-on-insulator photonic wire based evanescent field sensor," IEEE Photon. Technol. Lett. 18, 2520-2522 (2006).
  15. R. Baets, "Progress in high index contrast integrated optics," Proc. ECIO 2007 (2007).
  16. K. Okamoto, Fundamental of Optical Waveguides (Academic, 2005).
  17. H. S. Lee, C. H. Choi, B. H. O, D. G. Park, B. G. Kang, S. H. Kim, S. G. Lee, E. H. Lee, "A nonunitary transfer matrix method for practical analysis of racetrack microresonator waveguide," IEEE Photon. Technol. Lett. 16, 1086-1088 (2004).
  18. G. Cusmai, F. Morichetti, P. Rosotti, R. Costa, A. Melloni, "Circuit-oriented modeling of ring-resonators," Opt. Quantum Electron. 37, 343-358 (2005).
  19. D.-X. Xu, A. Densmore, A. Delâge, P. Waldron, R. McKinnon, S. Janz, J. Lapointe, G. Lopinski, T. Mischki, E. Post, P. Cheben, J. H. Schmid, B. Lamontagne, "Folded cavity SOI microring sensors for high sensitivity and real time measurement of biomolecular binding," Opt. Exp. 16, 15137-15148 (2008).
  20. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in FORTRAN (Cambridge Univ. Press, 1992).
  21. http://www.photond.com/.
  22. F. Xia, L. Sekaric, Y. A. Vlasov, "Mode conversion losses in silicon-on-insulator photonic wire based racetrack resonators," Opt. Express 14, 3872-86 (2006).
  23. F. Morichetti, A. Melloni, M. Martinelli, "Effects of polarization rotation in optical ring-resonator-based devices," J. Lightw. Technol. 24, 573-584 (2006).
  24. S. Xiao, M. H. Khan, H. Shen, M. Qi, "Modeling and measurement of losses in silicon-on-insulator resonators and bends," Opt. Express 15, 10553-61 (2007).
  25. V. Van, P. P. Absil, J. V. Hryniewicz, P.-T. Ho, "Propagation loss in single-mode GaAs-AlGaAs microring resonators: Measurement and model," J. Lightw. Technol. 19, 1734-9 (2001).
  26. P. K. Tien, "Light waves in thin films and integrated optics," Appl. Opt. 10, 2395-2419 (1971).
  27. K. R. Hiremath, M. Hammer, "Modeling of tuning of microresonator filters by perturbational evaluation of cavity mode phase shifts," J. Lightw. Technol. 25, 3760-5 (2007).
  28. Y. Vlasov, S. McNab, "Losses in single-mode silicon-on-insulator strip waveguides and bends," Opt. Express 12, 1622-1631 (2004).
  29. K. K. Lee, D. R. Lim, L. C. Kimerling, "Fabrication of ultralow-loss Si/SiO waveguides by roughness reduction," Opt. Lett. 26, 1888 (2001).
  30. K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, R. Baets, "Silicon-on-insulator microring resonator for sensitive and label-free biosensing," Opt. Express 15, 7610-5 (2007).

2008 (1)

D.-X. Xu, A. Densmore, A. Delâge, P. Waldron, R. McKinnon, S. Janz, J. Lapointe, G. Lopinski, T. Mischki, E. Post, P. Cheben, J. H. Schmid, B. Lamontagne, "Folded cavity SOI microring sensors for high sensitivity and real time measurement of biomolecular binding," Opt. Exp. 16, 15137-15148 (2008).

2007 (7)

S. Xiao, M. H. Khan, H. Shen, M. Qi, "Modeling and measurement of losses in silicon-on-insulator resonators and bends," Opt. Express 15, 10553-61 (2007).

K. R. Hiremath, M. Hammer, "Modeling of tuning of microresonator filters by perturbational evaluation of cavity mode phase shifts," J. Lightw. Technol. 25, 3760-5 (2007).

B. Bortnik, Y.-C. Hung, H. Tazawa, B.-J. Seo, J. Luo, A. K.-Y. Jen, W. H. Steier, H. R. Fetterman, "Electrooptic polymer ring resonator modulation up to 165 GHz," IEEE J. Sel. Topics Quantum Electron. 13, 104-109 (2007).

D. Po, S. F. Preble, M. Lipson, "All-optical compact silicon comb switch," Opt. Express 15, 9600-9605 (2007).

T.-J. Wang, C.-H. Chu, C.-Y. Lin, "Electro-optically tunable microring resonators on lithium niobate," Opt. Lett. 32, 2777-2779 (2007).

Z. Lu, "Efficient fiber-to-waveguide coupling through the vertical leakage from a microring," Opt. Lett. 32, 2861-3 (2007).

K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, R. Baets, "Silicon-on-insulator microring resonator for sensitive and label-free biosensing," Opt. Express 15, 7610-5 (2007).

2006 (6)

A. Densmore, D.-X. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delâge, B. Lamontagne, J. H. Schmid, E. Post, "A silicon-on-insulator photonic wire based evanescent field sensor," IEEE Photon. Technol. Lett. 18, 2520-2522 (2006).

M. S. Nawrocka, T. Liu, X. Wang, R. R. Panepucci, "Tunable silicon microring resonator with wide free spectral range," Appl. Phys. Lett. 89, 071110 (2006).

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, B. B. Goldberg, "Optical sensing of biomolecules using microring resonators," IEEE J. Sel. Topics Quantum Electron. 12, 148-55 (2006).

F. Xia, L. Sekaric, Y. A. Vlasov, "Mode conversion losses in silicon-on-insulator photonic wire based racetrack resonators," Opt. Express 14, 3872-86 (2006).

F. Morichetti, A. Melloni, M. Martinelli, "Effects of polarization rotation in optical ring-resonator-based devices," J. Lightw. Technol. 24, 573-584 (2006).

D.-X. Xu, S. Janz, P. Cheben, "Design of polarization-insensitive ring resonators in SOI stress engineering and MMI couplers," IEEE Photon. Technol. Lett. 18, 343-345 (2006).

2005 (1)

G. Cusmai, F. Morichetti, P. Rosotti, R. Costa, A. Melloni, "Circuit-oriented modeling of ring-resonators," Opt. Quantum Electron. 37, 343-358 (2005).

2004 (2)

Y. Vlasov, S. McNab, "Losses in single-mode silicon-on-insulator strip waveguides and bends," Opt. Express 12, 1622-1631 (2004).

H. S. Lee, C. H. Choi, B. H. O, D. G. Park, B. G. Kang, S. H. Kim, S. G. Lee, E. H. Lee, "A nonunitary transfer matrix method for practical analysis of racetrack microresonator waveguide," IEEE Photon. Technol. Lett. 16, 1086-1088 (2004).

2001 (2)

K. K. Lee, D. R. Lim, L. C. Kimerling, "Fabrication of ultralow-loss Si/SiO waveguides by roughness reduction," Opt. Lett. 26, 1888 (2001).

V. Van, P. P. Absil, J. V. Hryniewicz, P.-T. Ho, "Propagation loss in single-mode GaAs-AlGaAs microring resonators: Measurement and model," J. Lightw. Technol. 19, 1734-9 (2001).

1998 (1)

D. Rafizadeh, J. P. Zhang, R. C. Tiberio, S. T. Ho, "Propagation loss measurements in semiconductor microcavity ring and disk resonators," J. Lightw. Technol. 16, 1308 (1998) 1998.

1982 (1)

1971 (1)

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. S. Nawrocka, T. Liu, X. Wang, R. R. Panepucci, "Tunable silicon microring resonator with wide free spectral range," Appl. Phys. Lett. 89, 071110 (2006).

IEEE Photon. Technol. Lett. (1)

D.-X. Xu, S. Janz, P. Cheben, "Design of polarization-insensitive ring resonators in SOI stress engineering and MMI couplers," IEEE Photon. Technol. Lett. 18, 343-345 (2006).

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

A. Yalçin, K. C. Popat, J. C. Aldridge, T. A. Desai, J. Hryniewicz, N. Chbouki, B. E. Little, O. King, V. Van, S. Chu, D. Gill, M. Anthes-Washburn, M. S. Ünlü, B. B. Goldberg, "Optical sensing of biomolecules using microring resonators," IEEE J. Sel. Topics Quantum Electron. 12, 148-55 (2006).

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

B. Bortnik, Y.-C. Hung, H. Tazawa, B.-J. Seo, J. Luo, A. K.-Y. Jen, W. H. Steier, H. R. Fetterman, "Electrooptic polymer ring resonator modulation up to 165 GHz," IEEE J. Sel. Topics Quantum Electron. 13, 104-109 (2007).

IEEE Photon. Technol. Lett. (2)

A. Densmore, D.-X. Xu, P. Waldron, S. Janz, P. Cheben, J. Lapointe, A. Delâge, B. Lamontagne, J. H. Schmid, E. Post, "A silicon-on-insulator photonic wire based evanescent field sensor," IEEE Photon. Technol. Lett. 18, 2520-2522 (2006).

H. S. Lee, C. H. Choi, B. H. O, D. G. Park, B. G. Kang, S. H. Kim, S. G. Lee, E. H. Lee, "A nonunitary transfer matrix method for practical analysis of racetrack microresonator waveguide," IEEE Photon. Technol. Lett. 16, 1086-1088 (2004).

J. Lightw. Technol. (2)

V. Van, P. P. Absil, J. V. Hryniewicz, P.-T. Ho, "Propagation loss in single-mode GaAs-AlGaAs microring resonators: Measurement and model," J. Lightw. Technol. 19, 1734-9 (2001).

F. Morichetti, A. Melloni, M. Martinelli, "Effects of polarization rotation in optical ring-resonator-based devices," J. Lightw. Technol. 24, 573-584 (2006).

J. Lightw. Technol. (1)

D. Rafizadeh, J. P. Zhang, R. C. Tiberio, S. T. Ho, "Propagation loss measurements in semiconductor microcavity ring and disk resonators," J. Lightw. Technol. 16, 1308 (1998) 1998.

J. Lightw. Technol. (1)

K. R. Hiremath, M. Hammer, "Modeling of tuning of microresonator filters by perturbational evaluation of cavity mode phase shifts," J. Lightw. Technol. 25, 3760-5 (2007).

Opt. Exp. (1)

D.-X. Xu, A. Densmore, A. Delâge, P. Waldron, R. McKinnon, S. Janz, J. Lapointe, G. Lopinski, T. Mischki, E. Post, P. Cheben, J. H. Schmid, B. Lamontagne, "Folded cavity SOI microring sensors for high sensitivity and real time measurement of biomolecular binding," Opt. Exp. 16, 15137-15148 (2008).

Opt. Express (2)

F. Xia, L. Sekaric, Y. A. Vlasov, "Mode conversion losses in silicon-on-insulator photonic wire based racetrack resonators," Opt. Express 14, 3872-86 (2006).

K. De Vos, I. Bartolozzi, E. Schacht, P. Bienstman, R. Baets, "Silicon-on-insulator microring resonator for sensitive and label-free biosensing," Opt. Express 15, 7610-5 (2007).

Opt. Lett. (1)

K. K. Lee, D. R. Lim, L. C. Kimerling, "Fabrication of ultralow-loss Si/SiO waveguides by roughness reduction," Opt. Lett. 26, 1888 (2001).

Opt. Express (3)

Opt. Lett. (3)

Opt. Quantum Electron. (1)

G. Cusmai, F. Morichetti, P. Rosotti, R. Costa, A. Melloni, "Circuit-oriented modeling of ring-resonators," Opt. Quantum Electron. 37, 343-358 (2005).

Other (8)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in FORTRAN (Cambridge Univ. Press, 1992).

http://www.photond.com/.

R. Baets, "Progress in high index contrast integrated optics," Proc. ECIO 2007 (2007).

K. Okamoto, Fundamental of Optical Waveguides (Academic, 2005).

D. G. Rabus, Integrated Ring Resonnators: The Compedium (Springer-Verlag, 2007).

J. Heebner, R. Grover, T. Ibrahim, Titre Optical Microresonators: Theory, Fabrication, and Applications (Springer, 2008).

http://www.biacore.com.

K. M. De Vos, I. Bartolozzi, P. Bienstman, R. Baets, E. Schacht, "Optical biosensor based on silicon-on-insulator microring cavities for specific protein binding detection," Proc. SPIE 6447 Nanoscale Imaging, Spectrosc., Sens., Actuation for Biomed. Appl. IV (2007).

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