Abstract

Frequency mismatch in high-order microring-resonator filters is investigated. We demonstrate that this frequency mismatch is caused mainly by the intrafield distortion of scanning-electron-beam-lithography (SEBL) used in fabrication. The intrafield distortion of an SEBL system is measured, and a simple method is also proposed to correct this distortion. By applying this correction method, the average frequency mismatch in second-order microring-resonator filters was reduced from -8.6GHz to 0.28 GHz.

© 2008 Optical Society of America

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  1. B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Theon, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-511 (1998).
    [CrossRef]
  2. A. Vörckel, M. Mönster, W. Henschel, P. H. Bolivar, and H. Kurz, "Asymmetrically coupled silicon-on-insulator microring resonators for compact add-drop mutiplexers," IEEE Photon. Technol. Lett. 15, 921-923 (2003).
    [CrossRef]
  3. Q. Xu, D. Fattal, and R. G. Beausoleil, "Silicon microring resonators with 1.5-?m radius," Opt. Express 16, 4309 (2008).
    [CrossRef] [PubMed]
  4. J. V. Hryniewicz, Member, IEEE, P. P. Absil, B. E. Little, Member, IEEE, R. A. Wilson, and P.-T. Ho, "Higher-order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000).
    [CrossRef]
  5. Y. Yanagase, S. Suzuki, Y. Kokubun and S. T. Chu, "Box-like filter response and expansion of FSR by a vertically triple coupled microring resonator filter," IEEE J. Lightwave Technol. 20, 1525-1529 (2002).
    [CrossRef]
  6. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J. P. Laine, "Microring resonator channel dropping filters," IEEE J. Lightwave Technol. 15, 998-1005 (1997).
    [CrossRef]
  7. H. I. Smith, T. Barwicz, C. W. Holzwarth, M. A. Popovi??, M. R. Watts, P. T. Rakich, M. Qi, R. Barreto, F. X. Kärtner and E. P. Ippen, "Strategies for fabricating strong-confinement microring filters and circuits," in Optical Fiber Communication Conference (OFC/NFOEC), Technical Digest (CD) (Optical Society of America, 2007), paper OThC2, http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OThC2
  8. T. Barwicz, M. A. Popovi??. P. T. Rakich,M. R. Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, "Microring-resonator-based add-drop filters in SiN: fabrication and analysis," Opt. Express 12, 1437 (2004).
    [CrossRef] [PubMed]
  9. T. Barwicz, M. A. Popovi??, M. R. Watts, P. T. Rakich, E. P. Ippen and H. I. Smith, "Fabrication of Add-Drop Filters Based on Frequency-Matched Microring Resonators," IEEE J. Lightwave Technol. 24, 2207-2218 (2006).
    [CrossRef]
  10. S. Xiao, M. H. Khan, H. Shen, and M. Qi, "Compact silicon microring resonators with ultra-low propagation loss in the C band," Opt. Express 15, 11467 (2007).
    [CrossRef]
  11. M. R. Watts, T. Barwicz, M. A. Popovi??, P. T. Rakich, L. Socci, E. P. Ippen, H. I. Smith, and F.X. Kärtner, "Microring-resonator filter with doubled free-spectral-range by two-point coupling," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper CMP3 http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2005-CMP3
    [PubMed]
  12. C. W. Holzwarth, T. Barwicz, M. A. Popovi??, P. T. Rakich, E. P. Ippen, F. X. Kärtner, and H. I. Smith, "Accurate resonant frequency spacing of microring filters without postfabrication trimming," J. Vac. Sci. Technol. B 24, 3244-3247 (2006).
    [CrossRef]
  13. E. H. Anderson, V. Boegli, M. L. Schattenburg, D. Kern, H. I. Smith, "Metrology of electron-beam lithography systems using holographically produced reference samples," J. Vac. Sci. Technol. B 9, 3606-3610 (1991).
    [CrossRef]
  14. J. G. Goodberlet, J. T. Hastings, and H. I. Smith, "Performance of the Raith 150 electron-beam lithography system," J. Vac. Sci. Technol. B 19, 2499-2502 (2001).
    [CrossRef]

2008 (1)

2007 (1)

S. Xiao, M. H. Khan, H. Shen, and M. Qi, "Compact silicon microring resonators with ultra-low propagation loss in the C band," Opt. Express 15, 11467 (2007).
[CrossRef]

2006 (2)

C. W. Holzwarth, T. Barwicz, M. A. Popovi??, P. T. Rakich, E. P. Ippen, F. X. Kärtner, and H. I. Smith, "Accurate resonant frequency spacing of microring filters without postfabrication trimming," J. Vac. Sci. Technol. B 24, 3244-3247 (2006).
[CrossRef]

T. Barwicz, M. A. Popovi??, M. R. Watts, P. T. Rakich, E. P. Ippen and H. I. Smith, "Fabrication of Add-Drop Filters Based on Frequency-Matched Microring Resonators," IEEE J. Lightwave Technol. 24, 2207-2218 (2006).
[CrossRef]

2004 (1)

2003 (1)

A. Vörckel, M. Mönster, W. Henschel, P. H. Bolivar, and H. Kurz, "Asymmetrically coupled silicon-on-insulator microring resonators for compact add-drop mutiplexers," IEEE Photon. Technol. Lett. 15, 921-923 (2003).
[CrossRef]

2002 (1)

Y. Yanagase, S. Suzuki, Y. Kokubun and S. T. Chu, "Box-like filter response and expansion of FSR by a vertically triple coupled microring resonator filter," IEEE J. Lightwave Technol. 20, 1525-1529 (2002).
[CrossRef]

2001 (1)

J. G. Goodberlet, J. T. Hastings, and H. I. Smith, "Performance of the Raith 150 electron-beam lithography system," J. Vac. Sci. Technol. B 19, 2499-2502 (2001).
[CrossRef]

2000 (1)

J. V. Hryniewicz, Member, IEEE, P. P. Absil, B. E. Little, Member, IEEE, R. A. Wilson, and P.-T. Ho, "Higher-order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000).
[CrossRef]

1998 (1)

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Theon, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-511 (1998).
[CrossRef]

1997 (1)

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

1991 (1)

E. H. Anderson, V. Boegli, M. L. Schattenburg, D. Kern, H. I. Smith, "Metrology of electron-beam lithography systems using holographically produced reference samples," J. Vac. Sci. Technol. B 9, 3606-3610 (1991).
[CrossRef]

Anderson, E. H.

E. H. Anderson, V. Boegli, M. L. Schattenburg, D. Kern, H. I. Smith, "Metrology of electron-beam lithography systems using holographically produced reference samples," J. Vac. Sci. Technol. B 9, 3606-3610 (1991).
[CrossRef]

Barwicz, T.

C. W. Holzwarth, T. Barwicz, M. A. Popovi??, P. T. Rakich, E. P. Ippen, F. X. Kärtner, and H. I. Smith, "Accurate resonant frequency spacing of microring filters without postfabrication trimming," J. Vac. Sci. Technol. B 24, 3244-3247 (2006).
[CrossRef]

T. Barwicz, M. A. Popovi??, M. R. Watts, P. T. Rakich, E. P. Ippen and H. I. Smith, "Fabrication of Add-Drop Filters Based on Frequency-Matched Microring Resonators," IEEE J. Lightwave Technol. 24, 2207-2218 (2006).
[CrossRef]

T. Barwicz, M. A. Popovi??. P. T. Rakich,M. R. Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, "Microring-resonator-based add-drop filters in SiN: fabrication and analysis," Opt. Express 12, 1437 (2004).
[CrossRef] [PubMed]

Beausoleil, R. G.

Boegli, V.

E. H. Anderson, V. Boegli, M. L. Schattenburg, D. Kern, H. I. Smith, "Metrology of electron-beam lithography systems using holographically produced reference samples," J. Vac. Sci. Technol. B 9, 3606-3610 (1991).
[CrossRef]

Bolivar, P. H.

A. Vörckel, M. Mönster, W. Henschel, P. H. Bolivar, and H. Kurz, "Asymmetrically coupled silicon-on-insulator microring resonators for compact add-drop mutiplexers," IEEE Photon. Technol. Lett. 15, 921-923 (2003).
[CrossRef]

Chu, S. T.

Y. Yanagase, S. Suzuki, Y. Kokubun and S. T. Chu, "Box-like filter response and expansion of FSR by a vertically triple coupled microring resonator filter," IEEE J. Lightwave Technol. 20, 1525-1529 (2002).
[CrossRef]

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Theon, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-511 (1998).
[CrossRef]

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

Fattal, D.

Foresi, J.

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

Foresi, J. S.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Theon, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-511 (1998).
[CrossRef]

Goodberlet, J. G.

J. G. Goodberlet, J. T. Hastings, and H. I. Smith, "Performance of the Raith 150 electron-beam lithography system," J. Vac. Sci. Technol. B 19, 2499-2502 (2001).
[CrossRef]

Greene, W.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Theon, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-511 (1998).
[CrossRef]

Hastings, J. T.

J. G. Goodberlet, J. T. Hastings, and H. I. Smith, "Performance of the Raith 150 electron-beam lithography system," J. Vac. Sci. Technol. B 19, 2499-2502 (2001).
[CrossRef]

Haus, H. A.

T. Barwicz, M. A. Popovi??. P. T. Rakich,M. R. Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, "Microring-resonator-based add-drop filters in SiN: fabrication and analysis," Opt. Express 12, 1437 (2004).
[CrossRef] [PubMed]

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Theon, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-511 (1998).
[CrossRef]

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

Henschel, W.

A. Vörckel, M. Mönster, W. Henschel, P. H. Bolivar, and H. Kurz, "Asymmetrically coupled silicon-on-insulator microring resonators for compact add-drop mutiplexers," IEEE Photon. Technol. Lett. 15, 921-923 (2003).
[CrossRef]

Holzwarth, C. W.

C. W. Holzwarth, T. Barwicz, M. A. Popovi??, P. T. Rakich, E. P. Ippen, F. X. Kärtner, and H. I. Smith, "Accurate resonant frequency spacing of microring filters without postfabrication trimming," J. Vac. Sci. Technol. B 24, 3244-3247 (2006).
[CrossRef]

Hryniewicz, J. V.

J. V. Hryniewicz, Member, IEEE, P. P. Absil, B. E. Little, Member, IEEE, R. A. Wilson, and P.-T. Ho, "Higher-order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000).
[CrossRef]

Ippen, E. P.

C. W. Holzwarth, T. Barwicz, M. A. Popovi??, P. T. Rakich, E. P. Ippen, F. X. Kärtner, and H. I. Smith, "Accurate resonant frequency spacing of microring filters without postfabrication trimming," J. Vac. Sci. Technol. B 24, 3244-3247 (2006).
[CrossRef]

T. Barwicz, M. A. Popovi??, M. R. Watts, P. T. Rakich, E. P. Ippen and H. I. Smith, "Fabrication of Add-Drop Filters Based on Frequency-Matched Microring Resonators," IEEE J. Lightwave Technol. 24, 2207-2218 (2006).
[CrossRef]

T. Barwicz, M. A. Popovi??. P. T. Rakich,M. R. Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, "Microring-resonator-based add-drop filters in SiN: fabrication and analysis," Opt. Express 12, 1437 (2004).
[CrossRef] [PubMed]

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Theon, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-511 (1998).
[CrossRef]

Kärtner, F. X.

C. W. Holzwarth, T. Barwicz, M. A. Popovi??, P. T. Rakich, E. P. Ippen, F. X. Kärtner, and H. I. Smith, "Accurate resonant frequency spacing of microring filters without postfabrication trimming," J. Vac. Sci. Technol. B 24, 3244-3247 (2006).
[CrossRef]

Kern, D.

E. H. Anderson, V. Boegli, M. L. Schattenburg, D. Kern, H. I. Smith, "Metrology of electron-beam lithography systems using holographically produced reference samples," J. Vac. Sci. Technol. B 9, 3606-3610 (1991).
[CrossRef]

Khan, M. H.

S. Xiao, M. H. Khan, H. Shen, and M. Qi, "Compact silicon microring resonators with ultra-low propagation loss in the C band," Opt. Express 15, 11467 (2007).
[CrossRef]

Kimerling, L. C.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Theon, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-511 (1998).
[CrossRef]

Kokubun, Y.

Y. Yanagase, S. Suzuki, Y. Kokubun and S. T. Chu, "Box-like filter response and expansion of FSR by a vertically triple coupled microring resonator filter," IEEE J. Lightwave Technol. 20, 1525-1529 (2002).
[CrossRef]

Kurz, H.

A. Vörckel, M. Mönster, W. Henschel, P. H. Bolivar, and H. Kurz, "Asymmetrically coupled silicon-on-insulator microring resonators for compact add-drop mutiplexers," IEEE Photon. Technol. Lett. 15, 921-923 (2003).
[CrossRef]

Laine, J. P.

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

Little, B. E.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Theon, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-511 (1998).
[CrossRef]

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

Mönster, M.

A. Vörckel, M. Mönster, W. Henschel, P. H. Bolivar, and H. Kurz, "Asymmetrically coupled silicon-on-insulator microring resonators for compact add-drop mutiplexers," IEEE Photon. Technol. Lett. 15, 921-923 (2003).
[CrossRef]

Popovi??, M. A.

C. W. Holzwarth, T. Barwicz, M. A. Popovi??, P. T. Rakich, E. P. Ippen, F. X. Kärtner, and H. I. Smith, "Accurate resonant frequency spacing of microring filters without postfabrication trimming," J. Vac. Sci. Technol. B 24, 3244-3247 (2006).
[CrossRef]

T. Barwicz, M. A. Popovi??, M. R. Watts, P. T. Rakich, E. P. Ippen and H. I. Smith, "Fabrication of Add-Drop Filters Based on Frequency-Matched Microring Resonators," IEEE J. Lightwave Technol. 24, 2207-2218 (2006).
[CrossRef]

T. Barwicz, M. A. Popovi??. P. T. Rakich,M. R. Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, "Microring-resonator-based add-drop filters in SiN: fabrication and analysis," Opt. Express 12, 1437 (2004).
[CrossRef] [PubMed]

Qi, M.

S. Xiao, M. H. Khan, H. Shen, and M. Qi, "Compact silicon microring resonators with ultra-low propagation loss in the C band," Opt. Express 15, 11467 (2007).
[CrossRef]

Rakich, P. T.

T. Barwicz, M. A. Popovi??, M. R. Watts, P. T. Rakich, E. P. Ippen and H. I. Smith, "Fabrication of Add-Drop Filters Based on Frequency-Matched Microring Resonators," IEEE J. Lightwave Technol. 24, 2207-2218 (2006).
[CrossRef]

C. W. Holzwarth, T. Barwicz, M. A. Popovi??, P. T. Rakich, E. P. Ippen, F. X. Kärtner, and H. I. Smith, "Accurate resonant frequency spacing of microring filters without postfabrication trimming," J. Vac. Sci. Technol. B 24, 3244-3247 (2006).
[CrossRef]

Rakich,, P. T.

Schattenburg, M. L.

E. H. Anderson, V. Boegli, M. L. Schattenburg, D. Kern, H. I. Smith, "Metrology of electron-beam lithography systems using holographically produced reference samples," J. Vac. Sci. Technol. B 9, 3606-3610 (1991).
[CrossRef]

Shen, H.

S. Xiao, M. H. Khan, H. Shen, and M. Qi, "Compact silicon microring resonators with ultra-low propagation loss in the C band," Opt. Express 15, 11467 (2007).
[CrossRef]

Smith, H. I.

T. Barwicz, M. A. Popovi??, M. R. Watts, P. T. Rakich, E. P. Ippen and H. I. Smith, "Fabrication of Add-Drop Filters Based on Frequency-Matched Microring Resonators," IEEE J. Lightwave Technol. 24, 2207-2218 (2006).
[CrossRef]

C. W. Holzwarth, T. Barwicz, M. A. Popovi??, P. T. Rakich, E. P. Ippen, F. X. Kärtner, and H. I. Smith, "Accurate resonant frequency spacing of microring filters without postfabrication trimming," J. Vac. Sci. Technol. B 24, 3244-3247 (2006).
[CrossRef]

T. Barwicz, M. A. Popovi??. P. T. Rakich,M. R. Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, "Microring-resonator-based add-drop filters in SiN: fabrication and analysis," Opt. Express 12, 1437 (2004).
[CrossRef] [PubMed]

J. G. Goodberlet, J. T. Hastings, and H. I. Smith, "Performance of the Raith 150 electron-beam lithography system," J. Vac. Sci. Technol. B 19, 2499-2502 (2001).
[CrossRef]

E. H. Anderson, V. Boegli, M. L. Schattenburg, D. Kern, H. I. Smith, "Metrology of electron-beam lithography systems using holographically produced reference samples," J. Vac. Sci. Technol. B 9, 3606-3610 (1991).
[CrossRef]

Steinmeyer, G.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Theon, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-511 (1998).
[CrossRef]

Suzuki, S.

Y. Yanagase, S. Suzuki, Y. Kokubun and S. T. Chu, "Box-like filter response and expansion of FSR by a vertically triple coupled microring resonator filter," IEEE J. Lightwave Technol. 20, 1525-1529 (2002).
[CrossRef]

Theon, E. R.

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Theon, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-511 (1998).
[CrossRef]

Vörckel, A.

A. Vörckel, M. Mönster, W. Henschel, P. H. Bolivar, and H. Kurz, "Asymmetrically coupled silicon-on-insulator microring resonators for compact add-drop mutiplexers," IEEE Photon. Technol. Lett. 15, 921-923 (2003).
[CrossRef]

Watts, M. R.

T. Barwicz, M. A. Popovi??, M. R. Watts, P. T. Rakich, E. P. Ippen and H. I. Smith, "Fabrication of Add-Drop Filters Based on Frequency-Matched Microring Resonators," IEEE J. Lightwave Technol. 24, 2207-2218 (2006).
[CrossRef]

T. Barwicz, M. A. Popovi??. P. T. Rakich,M. R. Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, "Microring-resonator-based add-drop filters in SiN: fabrication and analysis," Opt. Express 12, 1437 (2004).
[CrossRef] [PubMed]

Xiao, S.

S. Xiao, M. H. Khan, H. Shen, and M. Qi, "Compact silicon microring resonators with ultra-low propagation loss in the C band," Opt. Express 15, 11467 (2007).
[CrossRef]

Xu, Q.

Yanagase, Y.

Y. Yanagase, S. Suzuki, Y. Kokubun and S. T. Chu, "Box-like filter response and expansion of FSR by a vertically triple coupled microring resonator filter," IEEE J. Lightwave Technol. 20, 1525-1529 (2002).
[CrossRef]

IEEE J. Lightwave Technol. (3)

Y. Yanagase, S. Suzuki, Y. Kokubun and S. T. Chu, "Box-like filter response and expansion of FSR by a vertically triple coupled microring resonator filter," IEEE J. Lightwave Technol. 20, 1525-1529 (2002).
[CrossRef]

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

T. Barwicz, M. A. Popovi??, M. R. Watts, P. T. Rakich, E. P. Ippen and H. I. Smith, "Fabrication of Add-Drop Filters Based on Frequency-Matched Microring Resonators," IEEE J. Lightwave Technol. 24, 2207-2218 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

J. V. Hryniewicz, Member, IEEE, P. P. Absil, B. E. Little, Member, IEEE, R. A. Wilson, and P.-T. Ho, "Higher-order filter response in coupled microring resonators," IEEE Photon. Technol. Lett. 12, 320-322 (2000).
[CrossRef]

B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Theon, S. T. Chu, H. A. Haus, E. P. Ippen, L. C. Kimerling, and W. Greene, "Ultra-compact Si-SiO2 microring resonator optical channel dropping filters," IEEE Photon. Technol. Lett. 10, 549-511 (1998).
[CrossRef]

A. Vörckel, M. Mönster, W. Henschel, P. H. Bolivar, and H. Kurz, "Asymmetrically coupled silicon-on-insulator microring resonators for compact add-drop mutiplexers," IEEE Photon. Technol. Lett. 15, 921-923 (2003).
[CrossRef]

J. Vac. Sci. Technol. B (3)

C. W. Holzwarth, T. Barwicz, M. A. Popovi??, P. T. Rakich, E. P. Ippen, F. X. Kärtner, and H. I. Smith, "Accurate resonant frequency spacing of microring filters without postfabrication trimming," J. Vac. Sci. Technol. B 24, 3244-3247 (2006).
[CrossRef]

E. H. Anderson, V. Boegli, M. L. Schattenburg, D. Kern, H. I. Smith, "Metrology of electron-beam lithography systems using holographically produced reference samples," J. Vac. Sci. Technol. B 9, 3606-3610 (1991).
[CrossRef]

J. G. Goodberlet, J. T. Hastings, and H. I. Smith, "Performance of the Raith 150 electron-beam lithography system," J. Vac. Sci. Technol. B 19, 2499-2502 (2001).
[CrossRef]

Opt. Express (3)

Other (2)

M. R. Watts, T. Barwicz, M. A. Popovi??, P. T. Rakich, L. Socci, E. P. Ippen, H. I. Smith, and F.X. Kärtner, "Microring-resonator filter with doubled free-spectral-range by two-point coupling," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science and Photonic Applications Systems Technologies, Technical Digest (CD) (Optical Society of America, 2005), paper CMP3 http://www.opticsinfobase.org/abstract.cfm?URI=CLEO-2005-CMP3
[PubMed]

H. I. Smith, T. Barwicz, C. W. Holzwarth, M. A. Popovi??, M. R. Watts, P. T. Rakich, M. Qi, R. Barreto, F. X. Kärtner and E. P. Ippen, "Strategies for fabricating strong-confinement microring filters and circuits," in Optical Fiber Communication Conference (OFC/NFOEC), Technical Digest (CD) (Optical Society of America, 2007), paper OThC2, http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2007-OThC2

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Figures (7)

Fig. 1.
Fig. 1.

(a). Diagram of a second-order microring-resonator filter, κ 0,1 represent the coupling coefficients and f 0,1 represent the resonant frequencies. (b) Illustration of impact of frequency mismatch on the through-port response for a second-order filter (simulation). The simulation was done by conventional Transfer-Matrix-Method using the following parameters: κ 0=0.0788, κ 1=0.00187, f 1=191THz (1569.5nm), f 2=f 1 +Δf.

Fig. 2.
Fig. 2.

(a). Illustration of intrafield distortion in SEBL. (b) Illustration of how intrafield distortion is determined from the phase difference between the ideal grid signal (blue) and the actual measured signal (red).

Fig. 3.
Fig. 3.

Intrafield distortion in (a) x and (b) y direction in a 100µm×100µm writing field of a Raith 150 SEBL system. The two dimensional quasi-periodic character of the distortion (i.e. the quasi-periodic peaks and valleys in the above distortion maps) is probably an indicator of digital-analog converter imperfection of the system.

Fig. 4.
Fig. 4.

(a). Diagram of waveguides cross-section. (b) Scanning-electron micrograph of the fabricated second-order microring filter, and details in bus-ring and ring-ring coupling regions.

Fig. 5.
Fig. 5.

Frequency mismatch between the two rings of second-order microring filters at various positions in the SEBL writing field: (a) the positions of the center of the second-order filter are at y=0 and various values of x, from x=-24 µm to x=+24 µm, and (b) the positions of the center of the second-order filter are at x=0 and various values of y from y=-24 µm to y=+24 µm. The inset diagrams illustrate the orientations of the filters in the two cases. The continuous lines are the simulation results. The red dots are measured frequency mismatch without intrafield-distortion correction, and the black squares are with correction.

Fig. 6.
Fig. 6.

Through-port (solid) and drop-port (dash) responses of a second-order filter (centering at (12µm, 0) in the writing field) with (blue) and without (red) intrafield-distortion correction.

Fig. 7.
Fig. 7.

Statistics of frequency mismatch of a number of second-order filters at several positions in the SEBL writing field, where µ is the average frequency mismatch, and σ is the standard deviation of frequency mismatch: (a) without distortion correction and (b) with distortion correction. Note that the correction results in a reduction of µ from -8.6GHz to 0.28GHz.

Equations (3)

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O B ¯ = x ̂ Δ x + y ̂ Δ y = x ̂ ( x B x 0 ) + y ̂ ( y B y 0 )
{ x B = x 0 + Δ x = a 0 + a 1 x 0 + a 2 y 0 + a 3 x 0 2 + a 4 x 0 y 0 + a 5 y 0 2 + = f ( x 0 , y 0 ) y B = y 0 + Δ y = b 0 + b 1 x 0 + b 2 y 0 + b 3 x 0 2 + b 4 x 0 y 0 + b 5 y 0 2 + = g ( x 0 , y 0 )
x 0 = f ( x 1 , y 1 ) , y 0 = g ( x 1 , y 1 )

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