Abstract

We present a simple and fast technique for the design of ring resonator-based optical filters. The technique is based on tapering the ring scattering parameters to achieve the optimal filter response. A perturbation method is developed for the linearization of the resulting design problem. The design problem is then formulated as an optimization problem. The optimal filter design is achieved by solving a constrained linear least square problem. This optimization problem can be solved efficiently to get the global optimal design. Our technique has been verified using different proposed targeted filter responses.

© 2011 IEEE

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  1. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.-P. Laine, "Microring resonator channel dropping filters," J. Lightw. Technol. 15, 998-1005 (1997).
  2. F. C. Blom, D. R. Van Dijk, H. J. W. M. Hoesktra, A. Driessen, T. J. A. Popma, "Experimental study of integrated-optics microcavity resonators: Toward an all-optical switching device," Appl. Phys. Lett. 71, 747-749 (1997).
  3. B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, W. Greene, "Ultra-compact Si/SiO$_2$ microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).
  4. Y. Yanagase, S. Suzuki, T. Kokubun, S. T. Chu, "Vertical triple series-coupled microring resonator filter for passband flattening and expansion of free spectral range," Jpn. J. Appl. Phys. 41, L141-L143 (2002).
  5. C. Ozturk, A. Huntington, A. Aydinli, Y. T. Byun, N. Dagli, "Filtering characteristics of hybrid integrated polymer and compound semiconductor waveguides," J. Lightw. Technol. 20, 1530-1536 (2002).
  6. C. K. Madsen, J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, 1999).
  7. T. Barwicz, M. A. Popovic, M. R. Watts, P. T. Rakich, E. P. Ippen, H. I. Smith, "Fabrication of add-drop filters based on frequency matched microring resonators," J. Lightw. Technol. 24, 2207-2218 (2006).
  8. F. Xia, M. Rooks, L. Sekaric, Y. Vlasov, "Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects," Opt. Exp. 15, 11934-11941 (2007).
  9. B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).
  10. O. Schwelb, "Transmission, group delay, and dispersion in single-ring optical resonators and add/drop filters—A tutorial overview," J. Lightw. Technol. 22, 1380-1394 (2004).
  11. A. Melloni, M. Martinelli, "Synthesis of direct-coupled-resonators bandpass filters for WDM systems," J. Lightw. Technol. 20, 296-303 (2002).
  12. A. Melloni, "Synthesis of a parallel-coupled ring-resonator filter," Opt. Lett. 26, 917-919 (2001).
  13. P. Chak, J. E. Sipe, "Minimizing finite-size effects in artificial resonance tunneling structures," Opt. Lett. 31, 2568-2570 (2006).
  14. E. Dowling, D. MacFarlane, "Lightwave lattice filters for optically multiplexed communication systems," J. Lightw. Technol. 12, 471-486 (1994).
  15. C. K. Madsen, "General IIR optical filter design for WDM applications using all-pass filters," J. Lightw. Technol. 18, 860-868 (2000).
  16. R. Orta, P. Savi, R. Tascone, D. Trinchero, "Synthesis of multiple ring-resonator filters for optical systems," IEEE Photon. Technol. Lett. 7, 1447-1449 (1995).
  17. J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, A. Yariv, "Matrix analysis of microring coupled-resonator optical waveguides," Opt. Exp. 12, 90-103 (2004).
  18. B. E. Little, S. T. Chu, J. V. Hryniewicz, P. P. Absil, "Filter synthesis for periodically coupled microring resonators," Opt. Lett. 25, 344-346 (2000).
  19. C. Ferrari, F. Morichetti, A. Melloni, "Disorder in coupled-resonator optical waveguides," J. Opt. Soc. Amer. B 26, 858-866 (2009).
  20. G. Matthaei, E. Jones, L. Young, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (Artech House, 1980).
  21. S. Cohn, "Direct-coupled-resonator filters," Proc. IRE 45, 187-196 (1957).
  22. L. Young, "Direct-coupled cavity filters for wide and narrow bandwidths," IEEE Trans. Microw. Theory Tech. MTT-11, 162-178 (1963).
  23. L. N. Binh, N. Q. Ngo, S. F. Luk, "Graphical representation and analysis of the Z-shaped double-coupler optical resonator," J. Lightw. Technol. 11, 1782-1792 (1993).
  24. C. J. Kaalund, G.-D. Peng, "Pole-zero diagram approach to the design of ring resonator-based filters for photonic applications," J. Lightw. Technol. 22, 1548-1559 (2004).
  25. S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge Univ. Press, 2004).
  26. H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  27. MATLAB 7.1 (2005).

2009 (1)

C. Ferrari, F. Morichetti, A. Melloni, "Disorder in coupled-resonator optical waveguides," J. Opt. Soc. Amer. B 26, 858-866 (2009).

2007 (1)

F. Xia, M. Rooks, L. Sekaric, Y. Vlasov, "Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects," Opt. Exp. 15, 11934-11941 (2007).

2006 (2)

T. Barwicz, M. A. Popovic, M. R. Watts, P. T. Rakich, E. P. Ippen, H. I. Smith, "Fabrication of add-drop filters based on frequency matched microring resonators," J. Lightw. Technol. 24, 2207-2218 (2006).

P. Chak, J. E. Sipe, "Minimizing finite-size effects in artificial resonance tunneling structures," Opt. Lett. 31, 2568-2570 (2006).

2004 (4)

C. J. Kaalund, G.-D. Peng, "Pole-zero diagram approach to the design of ring resonator-based filters for photonic applications," J. Lightw. Technol. 22, 1548-1559 (2004).

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, A. Yariv, "Matrix analysis of microring coupled-resonator optical waveguides," Opt. Exp. 12, 90-103 (2004).

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).

O. Schwelb, "Transmission, group delay, and dispersion in single-ring optical resonators and add/drop filters—A tutorial overview," J. Lightw. Technol. 22, 1380-1394 (2004).

2002 (3)

A. Melloni, M. Martinelli, "Synthesis of direct-coupled-resonators bandpass filters for WDM systems," J. Lightw. Technol. 20, 296-303 (2002).

Y. Yanagase, S. Suzuki, T. Kokubun, S. T. Chu, "Vertical triple series-coupled microring resonator filter for passband flattening and expansion of free spectral range," Jpn. J. Appl. Phys. 41, L141-L143 (2002).

C. Ozturk, A. Huntington, A. Aydinli, Y. T. Byun, N. Dagli, "Filtering characteristics of hybrid integrated polymer and compound semiconductor waveguides," J. Lightw. Technol. 20, 1530-1536 (2002).

2001 (1)

2000 (2)

B. E. Little, S. T. Chu, J. V. Hryniewicz, P. P. Absil, "Filter synthesis for periodically coupled microring resonators," Opt. Lett. 25, 344-346 (2000).

C. K. Madsen, "General IIR optical filter design for WDM applications using all-pass filters," J. Lightw. Technol. 18, 860-868 (2000).

1998 (1)

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, W. Greene, "Ultra-compact Si/SiO$_2$ microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).

1997 (2)

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.-P. Laine, "Microring resonator channel dropping filters," J. Lightw. Technol. 15, 998-1005 (1997).

F. C. Blom, D. R. Van Dijk, H. J. W. M. Hoesktra, A. Driessen, T. J. A. Popma, "Experimental study of integrated-optics microcavity resonators: Toward an all-optical switching device," Appl. Phys. Lett. 71, 747-749 (1997).

1995 (1)

R. Orta, P. Savi, R. Tascone, D. Trinchero, "Synthesis of multiple ring-resonator filters for optical systems," IEEE Photon. Technol. Lett. 7, 1447-1449 (1995).

1994 (1)

E. Dowling, D. MacFarlane, "Lightwave lattice filters for optically multiplexed communication systems," J. Lightw. Technol. 12, 471-486 (1994).

1993 (1)

L. N. Binh, N. Q. Ngo, S. F. Luk, "Graphical representation and analysis of the Z-shaped double-coupler optical resonator," J. Lightw. Technol. 11, 1782-1792 (1993).

1963 (1)

L. Young, "Direct-coupled cavity filters for wide and narrow bandwidths," IEEE Trans. Microw. Theory Tech. MTT-11, 162-178 (1963).

1957 (1)

S. Cohn, "Direct-coupled-resonator filters," Proc. IRE 45, 187-196 (1957).

Appl. Phys. Lett. (1)

F. C. Blom, D. R. Van Dijk, H. J. W. M. Hoesktra, A. Driessen, T. J. A. Popma, "Experimental study of integrated-optics microcavity resonators: Toward an all-optical switching device," Appl. Phys. Lett. 71, 747-749 (1997).

IEEE Photon. Technol. Lett. (3)

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, W. Greene, "Ultra-compact Si/SiO$_2$ microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-551 (1998).

B. E. Little, S. T. Chu, P. P. Absil, J. V. Hryniewicz, F. G. Johnson, F. Seiferth, D. Gill, V. Van, O. King, M. Trakalo, "Very high-order microring resonator filters for WDM applications," IEEE Photon. Technol. Lett. 16, 2263-2265 (2004).

R. Orta, P. Savi, R. Tascone, D. Trinchero, "Synthesis of multiple ring-resonator filters for optical systems," IEEE Photon. Technol. Lett. 7, 1447-1449 (1995).

IEEE Trans. Microw. Theory Tech. (1)

L. Young, "Direct-coupled cavity filters for wide and narrow bandwidths," IEEE Trans. Microw. Theory Tech. MTT-11, 162-178 (1963).

J. Lightw. Technol. (9)

L. N. Binh, N. Q. Ngo, S. F. Luk, "Graphical representation and analysis of the Z-shaped double-coupler optical resonator," J. Lightw. Technol. 11, 1782-1792 (1993).

C. J. Kaalund, G.-D. Peng, "Pole-zero diagram approach to the design of ring resonator-based filters for photonic applications," J. Lightw. Technol. 22, 1548-1559 (2004).

T. Barwicz, M. A. Popovic, M. R. Watts, P. T. Rakich, E. P. Ippen, H. I. Smith, "Fabrication of add-drop filters based on frequency matched microring resonators," J. Lightw. Technol. 24, 2207-2218 (2006).

B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, J.-P. Laine, "Microring resonator channel dropping filters," J. Lightw. Technol. 15, 998-1005 (1997).

O. Schwelb, "Transmission, group delay, and dispersion in single-ring optical resonators and add/drop filters—A tutorial overview," J. Lightw. Technol. 22, 1380-1394 (2004).

A. Melloni, M. Martinelli, "Synthesis of direct-coupled-resonators bandpass filters for WDM systems," J. Lightw. Technol. 20, 296-303 (2002).

C. Ozturk, A. Huntington, A. Aydinli, Y. T. Byun, N. Dagli, "Filtering characteristics of hybrid integrated polymer and compound semiconductor waveguides," J. Lightw. Technol. 20, 1530-1536 (2002).

E. Dowling, D. MacFarlane, "Lightwave lattice filters for optically multiplexed communication systems," J. Lightw. Technol. 12, 471-486 (1994).

C. K. Madsen, "General IIR optical filter design for WDM applications using all-pass filters," J. Lightw. Technol. 18, 860-868 (2000).

J. Opt. Soc. Amer. B (1)

C. Ferrari, F. Morichetti, A. Melloni, "Disorder in coupled-resonator optical waveguides," J. Opt. Soc. Amer. B 26, 858-866 (2009).

Jpn. J. Appl. Phys. (1)

Y. Yanagase, S. Suzuki, T. Kokubun, S. T. Chu, "Vertical triple series-coupled microring resonator filter for passband flattening and expansion of free spectral range," Jpn. J. Appl. Phys. 41, L141-L143 (2002).

Opt. Exp. (2)

F. Xia, M. Rooks, L. Sekaric, Y. Vlasov, "Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects," Opt. Exp. 15, 11934-11941 (2007).

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, A. Yariv, "Matrix analysis of microring coupled-resonator optical waveguides," Opt. Exp. 12, 90-103 (2004).

Opt. Lett. (3)

Proc. IRE (1)

S. Cohn, "Direct-coupled-resonator filters," Proc. IRE 45, 187-196 (1957).

Other (5)

S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge Univ. Press, 2004).

H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

MATLAB 7.1 (2005).

C. K. Madsen, J. H. Zhao, Optical Filter Design and Analysis: A Signal Processing Approach (Wiley, 1999).

G. Matthaei, E. Jones, L. Young, Microwave Filters, Impedance-Matching Networks, and Coupling Structures (Artech House, 1980).

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