Abstract

Coupling-induced resonance frequency shifts (CIFS) are theoretically described, and are found to be an important fundamental source of resonance frequency mismatch between coupled optical cavities that would be degenerate in isolation. Their deleterious effect on high-order resonant filter responses and complete correction by pre-distortion are described. Analysis of the physical effects contributing to CIFS shows that a positive index perturbation may bring about a resonance shift of either sign. Higher-order CIFS effects, the scaling of CIFS-caused impairment with finesse, FSR and index contrast, and the tolerability of frequency mismatch in telecom-grade filters are addressed. The results also suggest possible designs and applications for CIFS-free coupled-resonator systems.

© 2006 Optical Society of America

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  1. B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, “Microring resonator channel dropping filters,” J. Lightwave Technol. 15, 998–1005 (1997).
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  3. P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs microring resonators,” Opt. Lett. 25, 554–556 (2000).
    [CrossRef]
  4. B. Liu, A. Shakouri, and J. E. Bowers, “Passive microring-resonator-coupled lasers,” Appl. Phys. Lett. 79, 3561–3563 (2001).
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    [CrossRef]
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  10. M. J. Khan, C. Manolatou, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Mode-coupling analysis of multipole symmetric resonant add/drop filters,” IEEE J. Quantum Electron. 35, 1451–1460 (1999).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  23. M. J. Khan, M. Lim, C. Joyner, T. Murphy, H. A. Haus, and H. I. Smith, “Integrated Bragg grating structures,” in Digest of the LEOS Summer Topical Meeting on WDM Components (Copper Mountain, CO, 2001).
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  27. B. E. Little, J.-P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. 22, 4–6 (1997).
    [CrossRef] [PubMed]
  28. M. M. Lee and M. C. Wu, “MEMS-actuated microdisk resonators with variable power coupling ratios,” IEEE Photon. Technol. Lett. 17, 1034–1036 (2005).
    [CrossRef]

2005 (1)

M. M. Lee and M. C. Wu, “MEMS-actuated microdisk resonators with variable power coupling ratios,” IEEE Photon. Technol. Lett. 17, 1034–1036 (2005).
[CrossRef]

2004 (1)

2003 (2)

J. Scheuer and A. Yariv, “Two-dimensional optical ring resonators based on radial Bragg resonance,” Opt. Lett. 28, 1528–1530 (2003).
[CrossRef] [PubMed]

M. Lončar, T. Yoshie, Y. Qiu, P. Gogna, and A. Scherer, “Low-threshold photonic crystal laser,” in Proc. SPIE 5000, 16–26 (2003).
[CrossRef]

2002 (2)

2001 (2)

S. Blair and Y. Chen, “Resonant-enhanced evanescent-wave fluorescence biosensing with cylindrical optical cavities,” Appl. Opt. 40, 570–582 (2001).
[CrossRef]

B. Liu, A. Shakouri, and J. E. Bowers, “Passive microring-resonator-coupled lasers,” Appl. Phys. Lett. 79, 3561–3563 (2001).
[CrossRef]

2000 (2)

P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs microring resonators,” Opt. Lett. 25, 554–556 (2000).
[CrossRef]

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36, 321–322 (2000).
[CrossRef]

1999 (3)

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

M. J. Khan, C. Manolatou, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Mode-coupling analysis of multipole symmetric resonant add/drop filters,” IEEE J. Quantum Electron. 35, 1451–1460 (1999).
[CrossRef]

1997 (2)

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

B. E. Little, J.-P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. 22, 4–6 (1997).
[CrossRef] [PubMed]

1995 (1)

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photonics Technol. Lett. 7, 1447–1449 (1995).
[CrossRef]

1991 (1)

H. A. Haus and W.-P. Huang, “Coupled-mode theory,” in Proc. IEEE 79, 1505–1518 (1991).

1989 (1)

Absil, P. P.

Barwicz, T.

T. Barwicz, M. A. Popović, P. T. Rakich, M. R Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, “Microring-resonator-based add-rop filters in SiN: fabrication and analysis,” Opt. Express 12, 1437–1442 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1437.
[CrossRef] [PubMed]

C. Manolatou, M. A. Popović, P. T. Rakich, T. Barwicz, H. A. Haus, and E. P. Ippen, “Spectral anomalies due to coupling-induced frequency shifts in dielectric coupled-resonator filters,” in Proceedings of Optical Fiber Communication Conference on CD-ROM (Los Angeles, CA February2004), TuD5.

M. A. Popović, M. R. Watts, T. Barwicz, P. T. Rakich, L. Socci, E. P. Ippen, F. X. Kärtner, and H. I. Smith, “High-index-contrast, wide-FSR microring-resonator filter design and realization with frequency-shift compensation,” in Proc. Optical Fiber Comm. Conf. (Optical Society of America, Washington, DC,2005).

T. Barwicz, M. A. Popović, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” submitted to J. Lightwave Technol.

Benson, T. M.

Berk, A. D.

A. D. Berk, “Variational principles for electromagnetic resonators and waveguides,” IRE Trans. Antennas Propag., April 1956, pp. 104–111.

Blair, S.

Boriskina, S. V.

Bowers, J. E.

B. Liu, A. Shakouri, and J. E. Bowers, “Passive microring-resonator-coupled lasers,” Appl. Phys. Lett. 79, 3561–3563 (2001).
[CrossRef]

Chen, Y.

Cho, P. S.

Chu, S. T.

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

B. E. Little, J.-P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. 22, 4–6 (1997).
[CrossRef] [PubMed]

H. A. Haus, B. E. Little, M. A. Popović, S. T. Chu, M. R. Watts, and C. Manolatou, “Optical resonators and filters,” in Optical Microcavities, K. Vahala, ed. (World Scientific, Singapore, 2004).

Fan, S.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

M. J. Khan, C. Manolatou, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Mode-coupling analysis of multipole symmetric resonant add/drop filters,” IEEE J. Quantum Electron. 35, 1451–1460 (1999).
[CrossRef]

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

Foresi, J.

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

Gogna, P.

M. Lončar, T. Yoshie, Y. Qiu, P. Gogna, and A. Scherer, “Low-threshold photonic crystal laser,” in Proc. SPIE 5000, 16–26 (2003).
[CrossRef]

Haus, H. A.

T. Barwicz, M. A. Popović, P. T. Rakich, M. R Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, “Microring-resonator-based add-rop filters in SiN: fabrication and analysis,” Opt. Express 12, 1437–1442 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1437.
[CrossRef] [PubMed]

M. J. Khan, C. Manolatou, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Mode-coupling analysis of multipole symmetric resonant add/drop filters,” IEEE J. Quantum Electron. 35, 1451–1460 (1999).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

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

H. A. Haus and W.-P. Huang, “Coupled-mode theory,” in Proc. IEEE 79, 1505–1518 (1991).

H. A. Haus, W. P. Huang, and A. W. Snyder, “Coupled-mode formulations,” Opt. Lett. 14, 1222–1224 (1989).
[CrossRef] [PubMed]

M. J. Khan, M. Lim, C. Joyner, T. Murphy, H. A. Haus, and H. I. Smith, “Integrated Bragg grating structures,” in Digest of the LEOS Summer Topical Meeting on WDM Components (Copper Mountain, CO, 2001).

H. A. Haus, Waves and fields in optoelectronics (Prentice-Hall, Englewood Cliffs, NJ, 1984).

C. Manolatou, M. A. Popović, P. T. Rakich, T. Barwicz, H. A. Haus, and E. P. Ippen, “Spectral anomalies due to coupling-induced frequency shifts in dielectric coupled-resonator filters,” in Proceedings of Optical Fiber Communication Conference on CD-ROM (Los Angeles, CA February2004), TuD5.

H. A. Haus, “Microwaves and Photonics,” in OSA TOPS 23 Symposium on Electro-Optics: Present and Future, H. A. Haus, (Optical Society of America, Washington, DC, 1998), pp. 2–8.

H. A. Haus, B. E. Little, M. A. Popović, S. T. Chu, M. R. Watts, and C. Manolatou, “Optical resonators and filters,” in Optical Microcavities, K. Vahala, ed. (World Scientific, Singapore, 2004).

Ho, P.-T.

Hryniewicz, J. V.

Huang, W. P.

Huang, W.-P.

H. A. Haus and W.-P. Huang, “Coupled-mode theory,” in Proc. IEEE 79, 1505–1518 (1991).

Ippen, E. P.

T. Barwicz, M. A. Popović, P. T. Rakich, M. R Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, “Microring-resonator-based add-rop filters in SiN: fabrication and analysis,” Opt. Express 12, 1437–1442 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1437.
[CrossRef] [PubMed]

C. Manolatou, M. A. Popović, P. T. Rakich, T. Barwicz, H. A. Haus, and E. P. Ippen, “Spectral anomalies due to coupling-induced frequency shifts in dielectric coupled-resonator filters,” in Proceedings of Optical Fiber Communication Conference on CD-ROM (Los Angeles, CA February2004), TuD5.

M. A. Popović, M. R. Watts, T. Barwicz, P. T. Rakich, L. Socci, E. P. Ippen, F. X. Kärtner, and H. I. Smith, “High-index-contrast, wide-FSR microring-resonator filter design and realization with frequency-shift compensation,” in Proc. Optical Fiber Comm. Conf. (Optical Society of America, Washington, DC,2005).

T. Barwicz, M. A. Popović, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” submitted to J. Lightwave Technol.

Joannopoulos, J. D.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

M. J. Khan, C. Manolatou, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Mode-coupling analysis of multipole symmetric resonant add/drop filters,” IEEE J. Quantum Electron. 35, 1451–1460 (1999).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

Joneckis, L. G.

Joyner, C.

M. J. Khan, M. Lim, C. Joyner, T. Murphy, H. A. Haus, and H. I. Smith, “Integrated Bragg grating structures,” in Digest of the LEOS Summer Topical Meeting on WDM Components (Copper Mountain, CO, 2001).

Kärtner, F. X.

M. A. Popović, M. R. Watts, T. Barwicz, P. T. Rakich, L. Socci, E. P. Ippen, F. X. Kärtner, and H. I. Smith, “High-index-contrast, wide-FSR microring-resonator filter design and realization with frequency-shift compensation,” in Proc. Optical Fiber Comm. Conf. (Optical Society of America, Washington, DC,2005).

Khan, M. J.

M. J. Khan, C. Manolatou, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Mode-coupling analysis of multipole symmetric resonant add/drop filters,” IEEE J. Quantum Electron. 35, 1451–1460 (1999).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

M. J. Khan, M. Lim, C. Joyner, T. Murphy, H. A. Haus, and H. I. Smith, “Integrated Bragg grating structures,” in Digest of the LEOS Summer Topical Meeting on WDM Components (Copper Mountain, CO, 2001).

Laine, J.-P.

B. E. Little, J.-P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. 22, 4–6 (1997).
[CrossRef] [PubMed]

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

Lee, M. M.

M. M. Lee and M. C. Wu, “MEMS-actuated microdisk resonators with variable power coupling ratios,” IEEE Photon. Technol. Lett. 17, 1034–1036 (2005).
[CrossRef]

Lim, M.

M. J. Khan, M. Lim, C. Joyner, T. Murphy, H. A. Haus, and H. I. Smith, “Integrated Bragg grating structures,” in Digest of the LEOS Summer Topical Meeting on WDM Components (Copper Mountain, CO, 2001).

Little, B. E.

P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R A. Wilson, L. G. Joneckis, and P.-T. Ho, “Wavelength conversion in GaAs microring resonators,” Opt. Lett. 25, 554–556 (2000).
[CrossRef]

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

B. E. Little, J.-P. Laine, and S. T. Chu, “Surface-roughness-induced contradirectional coupling in ring and disk resonators,” Opt. Lett. 22, 4–6 (1997).
[CrossRef] [PubMed]

H. A. Haus, B. E. Little, M. A. Popović, S. T. Chu, M. R. Watts, and C. Manolatou, “Optical resonators and filters,” in Optical Microcavities, K. Vahala, ed. (World Scientific, Singapore, 2004).

Liu, B.

B. Liu, A. Shakouri, and J. E. Bowers, “Passive microring-resonator-coupled lasers,” Appl. Phys. Lett. 79, 3561–3563 (2001).
[CrossRef]

Loncar, M.

M. Lončar, T. Yoshie, Y. Qiu, P. Gogna, and A. Scherer, “Low-threshold photonic crystal laser,” in Proc. SPIE 5000, 16–26 (2003).
[CrossRef]

Madsen, C. K.

C. K. Madsen and J. H. Zhao, Optical filter design and analysis: a signal processing approach (Wiley, 1999).

Manolatou, C.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

M. J. Khan, C. Manolatou, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Mode-coupling analysis of multipole symmetric resonant add/drop filters,” IEEE J. Quantum Electron. 35, 1451–1460 (1999).
[CrossRef]

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

C. Manolatou, M. A. Popović, P. T. Rakich, T. Barwicz, H. A. Haus, and E. P. Ippen, “Spectral anomalies due to coupling-induced frequency shifts in dielectric coupled-resonator filters,” in Proceedings of Optical Fiber Communication Conference on CD-ROM (Los Angeles, CA February2004), TuD5.

H. A. Haus, B. E. Little, M. A. Popović, S. T. Chu, M. R. Watts, and C. Manolatou, “Optical resonators and filters,” in Optical Microcavities, K. Vahala, ed. (World Scientific, Singapore, 2004).

Martinelli, M.

Melloni, A.

Murphy, T.

M. J. Khan, M. Lim, C. Joyner, T. Murphy, H. A. Haus, and H. I. Smith, “Integrated Bragg grating structures,” in Digest of the LEOS Summer Topical Meeting on WDM Components (Copper Mountain, CO, 2001).

Nosich, A. I.

Orta, R.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photonics Technol. Lett. 7, 1447–1449 (1995).
[CrossRef]

Popovic, M.

M. Popović, “Complex-frequency leaky mode computations using PML boundary layers for dielectric resonant structures,” in Proceedings of Integrated Photonics Research (Washington, DC, June 17, 2003).

Popovic, M. A.

T. Barwicz, M. A. Popović, P. T. Rakich, M. R Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, “Microring-resonator-based add-rop filters in SiN: fabrication and analysis,” Opt. Express 12, 1437–1442 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1437.
[CrossRef] [PubMed]

C. Manolatou, M. A. Popović, P. T. Rakich, T. Barwicz, H. A. Haus, and E. P. Ippen, “Spectral anomalies due to coupling-induced frequency shifts in dielectric coupled-resonator filters,” in Proceedings of Optical Fiber Communication Conference on CD-ROM (Los Angeles, CA February2004), TuD5.

T. Barwicz, M. A. Popović, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” submitted to J. Lightwave Technol.

M. A. Popović, M. R. Watts, T. Barwicz, P. T. Rakich, L. Socci, E. P. Ippen, F. X. Kärtner, and H. I. Smith, “High-index-contrast, wide-FSR microring-resonator filter design and realization with frequency-shift compensation,” in Proc. Optical Fiber Comm. Conf. (Optical Society of America, Washington, DC,2005).

H. A. Haus, B. E. Little, M. A. Popović, S. T. Chu, M. R. Watts, and C. Manolatou, “Optical resonators and filters,” in Optical Microcavities, K. Vahala, ed. (World Scientific, Singapore, 2004).

Qiu, Y.

M. Lončar, T. Yoshie, Y. Qiu, P. Gogna, and A. Scherer, “Low-threshold photonic crystal laser,” in Proc. SPIE 5000, 16–26 (2003).
[CrossRef]

Rakich, P. T.

T. Barwicz, M. A. Popović, P. T. Rakich, M. R Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, “Microring-resonator-based add-rop filters in SiN: fabrication and analysis,” Opt. Express 12, 1437–1442 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1437.
[CrossRef] [PubMed]

C. Manolatou, M. A. Popović, P. T. Rakich, T. Barwicz, H. A. Haus, and E. P. Ippen, “Spectral anomalies due to coupling-induced frequency shifts in dielectric coupled-resonator filters,” in Proceedings of Optical Fiber Communication Conference on CD-ROM (Los Angeles, CA February2004), TuD5.

M. A. Popović, M. R. Watts, T. Barwicz, P. T. Rakich, L. Socci, E. P. Ippen, F. X. Kärtner, and H. I. Smith, “High-index-contrast, wide-FSR microring-resonator filter design and realization with frequency-shift compensation,” in Proc. Optical Fiber Comm. Conf. (Optical Society of America, Washington, DC,2005).

T. Barwicz, M. A. Popović, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” submitted to J. Lightwave Technol.

Savi, P.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photonics Technol. Lett. 7, 1447–1449 (1995).
[CrossRef]

Scherer, A.

M. Lončar, T. Yoshie, Y. Qiu, P. Gogna, and A. Scherer, “Low-threshold photonic crystal laser,” in Proc. SPIE 5000, 16–26 (2003).
[CrossRef]

Scheuer, J.

Sewell, P.

Shakouri, A.

B. Liu, A. Shakouri, and J. E. Bowers, “Passive microring-resonator-coupled lasers,” Appl. Phys. Lett. 79, 3561–3563 (2001).
[CrossRef]

Smith, H. I.

T. Barwicz, M. A. Popović, P. T. Rakich, M. R Watts, H. A. Haus, E. P. Ippen, and H. I. Smith, “Microring-resonator-based add-rop filters in SiN: fabrication and analysis,” Opt. Express 12, 1437–1442 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-7-1437.
[CrossRef] [PubMed]

M. A. Popović, M. R. Watts, T. Barwicz, P. T. Rakich, L. Socci, E. P. Ippen, F. X. Kärtner, and H. I. Smith, “High-index-contrast, wide-FSR microring-resonator filter design and realization with frequency-shift compensation,” in Proc. Optical Fiber Comm. Conf. (Optical Society of America, Washington, DC,2005).

M. J. Khan, M. Lim, C. Joyner, T. Murphy, H. A. Haus, and H. I. Smith, “Integrated Bragg grating structures,” in Digest of the LEOS Summer Topical Meeting on WDM Components (Copper Mountain, CO, 2001).

T. Barwicz, M. A. Popović, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” submitted to J. Lightwave Technol.

Snyder, A. W.

Socci, L.

M. A. Popović, M. R. Watts, T. Barwicz, P. T. Rakich, L. Socci, E. P. Ippen, F. X. Kärtner, and H. I. Smith, “High-index-contrast, wide-FSR microring-resonator filter design and realization with frequency-shift compensation,” in Proc. Optical Fiber Comm. Conf. (Optical Society of America, Washington, DC,2005).

Tascone, R.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photonics Technol. Lett. 7, 1447–1449 (1995).
[CrossRef]

Trinchero, D.

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photonics Technol. Lett. 7, 1447–1449 (1995).
[CrossRef]

Villeneuve, P. R.

M. J. Khan, C. Manolatou, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Mode-coupling analysis of multipole symmetric resonant add/drop filters,” IEEE J. Quantum Electron. 35, 1451–1460 (1999).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

Watts, M. R

Watts, M. R.

M. A. Popović, M. R. Watts, T. Barwicz, P. T. Rakich, L. Socci, E. P. Ippen, F. X. Kärtner, and H. I. Smith, “High-index-contrast, wide-FSR microring-resonator filter design and realization with frequency-shift compensation,” in Proc. Optical Fiber Comm. Conf. (Optical Society of America, Washington, DC,2005).

T. Barwicz, M. A. Popović, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” submitted to J. Lightwave Technol.

H. A. Haus, B. E. Little, M. A. Popović, S. T. Chu, M. R. Watts, and C. Manolatou, “Optical resonators and filters,” in Optical Microcavities, K. Vahala, ed. (World Scientific, Singapore, 2004).

Wilson, R A.

Wu, M. C.

M. M. Lee and M. C. Wu, “MEMS-actuated microdisk resonators with variable power coupling ratios,” IEEE Photon. Technol. Lett. 17, 1034–1036 (2005).
[CrossRef]

Yariv, A.

J. Scheuer and A. Yariv, “Two-dimensional optical ring resonators based on radial Bragg resonance,” Opt. Lett. 28, 1528–1530 (2003).
[CrossRef] [PubMed]

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36, 321–322 (2000).
[CrossRef]

Yoshie, T.

M. Lončar, T. Yoshie, Y. Qiu, P. Gogna, and A. Scherer, “Low-threshold photonic crystal laser,” in Proc. SPIE 5000, 16–26 (2003).
[CrossRef]

Zhao, J. H.

C. K. Madsen and J. H. Zhao, Optical filter design and analysis: a signal processing approach (Wiley, 1999).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

B. Liu, A. Shakouri, and J. E. Bowers, “Passive microring-resonator-coupled lasers,” Appl. Phys. Lett. 79, 3561–3563 (2001).
[CrossRef]

Electron. Lett. (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36, 321–322 (2000).
[CrossRef]

IEEE J. Quantum Electron. (2)

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1331 (1999).
[CrossRef]

M. J. Khan, C. Manolatou, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Mode-coupling analysis of multipole symmetric resonant add/drop filters,” IEEE J. Quantum Electron. 35, 1451–1460 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. M. Lee and M. C. Wu, “MEMS-actuated microdisk resonators with variable power coupling ratios,” IEEE Photon. Technol. Lett. 17, 1034–1036 (2005).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

R. Orta, P. Savi, R. Tascone, and D. Trinchero, “Synthesis of multiple-ring-resonator filters for optical systems,” IEEE Photonics Technol. Lett. 7, 1447–1449 (1995).
[CrossRef]

in Proc. SPIE (1)

M. Lončar, T. Yoshie, Y. Qiu, P. Gogna, and A. Scherer, “Low-threshold photonic crystal laser,” in Proc. SPIE 5000, 16–26 (2003).
[CrossRef]

J. Lightwave Technol. (3)

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. B (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59, 15882–15892 (1999).
[CrossRef]

Other (11)

H. A. Haus, B. E. Little, M. A. Popović, S. T. Chu, M. R. Watts, and C. Manolatou, “Optical resonators and filters,” in Optical Microcavities, K. Vahala, ed. (World Scientific, Singapore, 2004).

H. A. Haus, “Microwaves and Photonics,” in OSA TOPS 23 Symposium on Electro-Optics: Present and Future, H. A. Haus, (Optical Society of America, Washington, DC, 1998), pp. 2–8.

C. K. Madsen and J. H. Zhao, Optical filter design and analysis: a signal processing approach (Wiley, 1999).

C. Manolatou, M. A. Popović, P. T. Rakich, T. Barwicz, H. A. Haus, and E. P. Ippen, “Spectral anomalies due to coupling-induced frequency shifts in dielectric coupled-resonator filters,” in Proceedings of Optical Fiber Communication Conference on CD-ROM (Los Angeles, CA February2004), TuD5.

M. A. Popović, M. R. Watts, T. Barwicz, P. T. Rakich, L. Socci, E. P. Ippen, F. X. Kärtner, and H. I. Smith, “High-index-contrast, wide-FSR microring-resonator filter design and realization with frequency-shift compensation,” in Proc. Optical Fiber Comm. Conf. (Optical Society of America, Washington, DC,2005).

H. A. Haus, Waves and fields in optoelectronics (Prentice-Hall, Englewood Cliffs, NJ, 1984).

H. A. Haus and W.-P. Huang, “Coupled-mode theory,” in Proc. IEEE 79, 1505–1518 (1991).

T. Barwicz, M. A. Popović, M. R. Watts, P. T. Rakich, E. P. Ippen, and H. I. Smith, “Fabrication of add-drop filters based on frequency-matched microring resonators,” submitted to J. Lightwave Technol.

M. Popović, “Complex-frequency leaky mode computations using PML boundary layers for dielectric resonant structures,” in Proceedings of Integrated Photonics Research (Washington, DC, June 17, 2003).

A. D. Berk, “Variational principles for electromagnetic resonators and waveguides,” IRE Trans. Antennas Propag., April 1956, pp. 104–111.

M. J. Khan, M. Lim, C. Joyner, T. Murphy, H. A. Haus, and H. I. Smith, “Integrated Bragg grating structures,” in Digest of the LEOS Summer Topical Meeting on WDM Components (Copper Mountain, CO, 2001).

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Figures (7)

Fig. 1.
Fig. 1.

(a) Coupled-dielectric-resonator system in infinite perfect-conductor waveguide, with analytic mode solutions [17]; (b) TM10 supermode frequency splitting and CIFS vs.resonator spacing.

Fig. 2.
Fig. 2.

CIFS impairment of 3-cavity microring filter: (a) simulated structure using identical rings (dimensions shown); (b) ideal (synthesized) and simulated (complete-structure FDTD and model) frequency response showing apparent cavity mismatch due to CIFS.

Fig. 3.
Fig. 3.

Diagram of CIFS resonance mismatch and its correction: isolated resonator (a) attains CIFS when part of a coupled structure (b); the combination of nominally degenerate resonators in a coupled-cavity filter (c) results in effectively mismatched resonators and a distorted response (Fig. 2), which can be corrected by pre-distorting the resonators by the expected CIFS

Fig. 4.
Fig. 4.

CIFS in a single-ring cavity due to side-coupled bus waveguides: (a) mode-solver-simulated structure; (b) CIFS for TE, TM resonances and for two bus widths, vs. gap spacing. Phasor-amplitude plots (c), (d) of the standing-wave-mode resonant field show a partial standing wave in the coupling region and, respectively, a symmetric-like and antisymmetric-like supermode formed with the waveguide continuum corresponding to negative- and positive-frequency CIFS.

Fig. 5.
Fig. 5.

CIFS due to coupled bus waveguides in a square standing-wave cavity: (a) CIFS vs. gap spacing and waveguide width, and mode-solver simulated structure. Mode phasor magnitude plots show (b) symmetric and (c) anti-symmetric coupling, respectively, with a partial standing wave established in the waveguide, for negative- and positive-frequency CIFS. Case (b) shows significant mode shape modification caused by coupling.

Fig. 6.
Fig. 6.

(a) Lumped point-interaction model of coupling of traveling-wave resonator and access waveguide. FDTD simulation of the coupled structure with respect to ports 1-4, and of the two waveguides individually, leads to lumped point-interaction matrix U, describing the effect of the coupling on port-to-port scattering matrix element (b) phase, and (c) power coupling.

Fig. 7.
Fig. 7.

FDTD simulation of 3-cavity microring filter, with cavity resonance frequencies pre-compensated by design for CIFS: (a) simulated structure with lower-core-index middle ring; (b) FDTD simulation and model of the filter showing recovered ideal frequency responses.

Equations (15)

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

d dt a = j ω ¯ ¯ a j μ ¯ ¯ a
ω s , a = ω 1 μ 11 + ω 2 μ 22 2 ( ( ω 1 μ 11 ) ( ω 2 μ 22 ) 2 ) 2 + μ 12 μ 21 .
d dt a = j ω ̿ a j W ̿ 1 M ̿ . a = j ω ̿ a j μ ̿ a
δ ω 1 = μ 11 = M 11 W 12 W 22 M 21 W 11 W 12 W 22 W 21 .
ω 2 = V E × μ ̿ 1 × E dv V E . ̿ . E dv
Δ f CIFS Δ f FSR Δ f CIFS n g L c Δ ϕ 2 π .
U ̿ u 11 e 11 u 12 e 12 u 21 e 21 u 22 e 22 = e o 1 κ e 1 i κ e 2 i κ e 2 1 κ e 1
ϕ 11 + ϕ 22 = ϕ 21 + ϕ 12 ± π
δ β 1 = K 11 P 12 P 22 K 21 P 11 P 12 P 22 P 21
Δ θ 1 = β 1 z + δ β 1 z + [ δz arg { cos ( β o z ) + j δ β o sin ( β o z ) } ]
CBR cavity cavity BW FSR fixed coupling geometry = 1 finesse
CBR ϕ 11 κ = 1 L eff α R eff fixed BW , FSR
× ε ̿ 1 × H = ω 2 μ ̿ H
W mn ω n ω m V ˜ H m T μ ̿ H n d v ˜
M mn ω n 2 V ˜ D m T Δ ε n ¯ ¯ 1 D n d v ˜

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