Abstract

Ring resonators are waveguide realizations of Fabry-Perot resonators which can be readily integrated in array geometries to implement many useful functions. Its nonlinear phase response can be readily incorporated into a Mach-Zehnder interferometer to produce specific intensity output function. We present two generalized array configurations of ring-coupled MZI and discuss their characteristics in terms of the amplitude and phase response of the ring arrays as well as the transmission output of the MZIs. The two types of array have distinct transfer functions and effective phase shifts, and can be tailored to phase-engineer a wide-range of MZI transmission functions.

© 2005 Optical Society of America

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References

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  1. John E. Heebner, Robert W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt Lett. 24, 847–849, June 1999.
    [CrossRef]
  2. Li Chun-Fei, Bananej Alireza, “Finesse-enhanced ring resonator coupled Mach-Zehnder Interferometer all-optical switches,” Chin. Phys. Lett. 21, 90–93 (2004).
    [CrossRef]
  3. L. Liao, D. Samara-Rubio, M. Morse, Ansheng Liu, D. Hodge, D. Rubin, U. D. Keil, T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express. 13, 3130–3135 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3129.
    [CrossRef]
  4. R. W. Boyd, J. E. Heebner, “Sensitive disk resonator photonic biosensor,” Appl. Opt. 40, 5742–5747 (2001).
    [CrossRef]
  5. C.-Y. Chao, L. J. Guo,“A new interferometric sensor with ring-feedback MZI”, in Proceedings of IEEE on Sensors. 1, 569–572, Oct. 2003.
  6. A. Yariv, Y. Xu, R. K. Lee, A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
    [CrossRef]
  7. J. E. Heebner, V. Wong, S. Schweinsberg, R. W. Boyd, D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40, 726–730 (2004).
    [CrossRef]
  8. G. Griffel, “Synthesis of optical filters using ring resonator arrays,” IEEE Photon. Technol. Lett. 12, 810–812 (2000).
    [CrossRef]
  9. J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90–103 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-90.
    [CrossRef] [PubMed]
  10. John E. Heebner, P. Chak, S. Pereira, J. E. Sipe, R. W. Boyd, “Distributed and localized feedback in microresonator sequences for linear and nonlinear optics”, J. Opt. Soc. Am. B 21, 1818–1832 (2004).
    [CrossRef]
  11. Y. M Landobasa, S. Darmawan, M. K. Chin, “Matrix analysis of 2-D micro-resonator lattice optical filters,” submitted to IEEE J. Quantum Electron.
  12. George T. Paloczi, Yanyi Huang, A. Yariv,“Polymeric Mach-Zehnder interferometer using serially coupled microring resonators,” Opt. Express. 11, 2666–2671 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-21-2666.
    [CrossRef] [PubMed]
  13. G. Lenz, B.J. Eggleton, C. R. Giles, C. K. Madsen, R.E. Slusher, “Dispersive properties of optical filters for WDM systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
    [CrossRef]
  14. 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).
    [CrossRef]

2005

L. Liao, D. Samara-Rubio, M. Morse, Ansheng Liu, D. Hodge, D. Rubin, U. D. Keil, T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express. 13, 3130–3135 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3129.
[CrossRef]

2004

J. E. Heebner, V. Wong, S. Schweinsberg, R. W. Boyd, D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40, 726–730 (2004).
[CrossRef]

Li Chun-Fei, Bananej Alireza, “Finesse-enhanced ring resonator coupled Mach-Zehnder Interferometer all-optical switches,” Chin. Phys. Lett. 21, 90–93 (2004).
[CrossRef]

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90–103 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-90.
[CrossRef] [PubMed]

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).
[CrossRef]

John E. Heebner, P. Chak, S. Pereira, J. E. Sipe, R. W. Boyd, “Distributed and localized feedback in microresonator sequences for linear and nonlinear optics”, J. Opt. Soc. Am. B 21, 1818–1832 (2004).
[CrossRef]

2003

C.-Y. Chao, L. J. Guo,“A new interferometric sensor with ring-feedback MZI”, in Proceedings of IEEE on Sensors. 1, 569–572, Oct. 2003.

George T. Paloczi, Yanyi Huang, A. Yariv,“Polymeric Mach-Zehnder interferometer using serially coupled microring resonators,” Opt. Express. 11, 2666–2671 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-21-2666.
[CrossRef] [PubMed]

2001

2000

G. Griffel, “Synthesis of optical filters using ring resonator arrays,” IEEE Photon. Technol. Lett. 12, 810–812 (2000).
[CrossRef]

1999

John E. Heebner, Robert W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt Lett. 24, 847–849, June 1999.
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[CrossRef]

1998

G. Lenz, B.J. Eggleton, C. R. Giles, C. K. Madsen, R.E. Slusher, “Dispersive properties of optical filters for WDM systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
[CrossRef]

Absil, P. P.

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).
[CrossRef]

Alireza, Bananej

Li Chun-Fei, Bananej Alireza, “Finesse-enhanced ring resonator coupled Mach-Zehnder Interferometer all-optical switches,” Chin. Phys. Lett. 21, 90–93 (2004).
[CrossRef]

Boyd, R. W.

Boyd, Robert W.

John E. Heebner, Robert W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt Lett. 24, 847–849, June 1999.
[CrossRef]

Chak, P.

Chao, C.-Y.

C.-Y. Chao, L. J. Guo,“A new interferometric sensor with ring-feedback MZI”, in Proceedings of IEEE on Sensors. 1, 569–572, Oct. 2003.

Chin, M. K.

Y. M Landobasa, S. Darmawan, M. K. Chin, “Matrix analysis of 2-D micro-resonator lattice optical filters,” submitted to IEEE J. Quantum Electron.

Chu, S. T.

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).
[CrossRef]

Chun-Fei, Li

Li Chun-Fei, Bananej Alireza, “Finesse-enhanced ring resonator coupled Mach-Zehnder Interferometer all-optical switches,” Chin. Phys. Lett. 21, 90–93 (2004).
[CrossRef]

Darmawan, S.

Y. M Landobasa, S. Darmawan, M. K. Chin, “Matrix analysis of 2-D micro-resonator lattice optical filters,” submitted to IEEE J. Quantum Electron.

Eggleton, B.J.

G. Lenz, B.J. Eggleton, C. R. Giles, C. K. Madsen, R.E. Slusher, “Dispersive properties of optical filters for WDM systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
[CrossRef]

Franck, T.

L. Liao, D. Samara-Rubio, M. Morse, Ansheng Liu, D. Hodge, D. Rubin, U. D. Keil, T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express. 13, 3130–3135 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3129.
[CrossRef]

Giles, C. R.

G. Lenz, B.J. Eggleton, C. R. Giles, C. K. Madsen, R.E. Slusher, “Dispersive properties of optical filters for WDM systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
[CrossRef]

Gill, D.

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).
[CrossRef]

Griffel, G.

G. Griffel, “Synthesis of optical filters using ring resonator arrays,” IEEE Photon. Technol. Lett. 12, 810–812 (2000).
[CrossRef]

Guo, L. J.

C.-Y. Chao, L. J. Guo,“A new interferometric sensor with ring-feedback MZI”, in Proceedings of IEEE on Sensors. 1, 569–572, Oct. 2003.

Heebner, J. E.

J. E. Heebner, V. Wong, S. Schweinsberg, R. W. Boyd, D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40, 726–730 (2004).
[CrossRef]

R. W. Boyd, J. E. Heebner, “Sensitive disk resonator photonic biosensor,” Appl. Opt. 40, 5742–5747 (2001).
[CrossRef]

Heebner, John E.

John E. Heebner, P. Chak, S. Pereira, J. E. Sipe, R. W. Boyd, “Distributed and localized feedback in microresonator sequences for linear and nonlinear optics”, J. Opt. Soc. Am. B 21, 1818–1832 (2004).
[CrossRef]

John E. Heebner, Robert W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt Lett. 24, 847–849, June 1999.
[CrossRef]

Hodge, D.

L. Liao, D. Samara-Rubio, M. Morse, Ansheng Liu, D. Hodge, D. Rubin, U. D. Keil, T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express. 13, 3130–3135 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3129.
[CrossRef]

Hryniewicz, J. V.

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).
[CrossRef]

Huang, Y.

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90–103 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-90.
[CrossRef] [PubMed]

Huang, Yanyi

George T. Paloczi, Yanyi Huang, A. Yariv,“Polymeric Mach-Zehnder interferometer using serially coupled microring resonators,” Opt. Express. 11, 2666–2671 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-21-2666.
[CrossRef] [PubMed]

Jackson, D. J.

J. E. Heebner, V. Wong, S. Schweinsberg, R. W. Boyd, D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40, 726–730 (2004).
[CrossRef]

Johnson, F. G.

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).
[CrossRef]

Keil, U. D.

L. Liao, D. Samara-Rubio, M. Morse, Ansheng Liu, D. Hodge, D. Rubin, U. D. Keil, T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express. 13, 3130–3135 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3129.
[CrossRef]

King, O.

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).
[CrossRef]

Landobasa, Y. M

Y. M Landobasa, S. Darmawan, M. K. Chin, “Matrix analysis of 2-D micro-resonator lattice optical filters,” submitted to IEEE J. Quantum Electron.

Lee, R. K.

Lenz, G.

G. Lenz, B.J. Eggleton, C. R. Giles, C. K. Madsen, R.E. Slusher, “Dispersive properties of optical filters for WDM systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
[CrossRef]

Liao, L.

L. Liao, D. Samara-Rubio, M. Morse, Ansheng Liu, D. Hodge, D. Rubin, U. D. Keil, T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express. 13, 3130–3135 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3129.
[CrossRef]

Little, B.E.

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).
[CrossRef]

Liu, Ansheng

L. Liao, D. Samara-Rubio, M. Morse, Ansheng Liu, D. Hodge, D. Rubin, U. D. Keil, T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express. 13, 3130–3135 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3129.
[CrossRef]

Madsen, C. K.

G. Lenz, B.J. Eggleton, C. R. Giles, C. K. Madsen, R.E. Slusher, “Dispersive properties of optical filters for WDM systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
[CrossRef]

Mookherjea, S.

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90–103 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-90.
[CrossRef] [PubMed]

Morse, M.

L. Liao, D. Samara-Rubio, M. Morse, Ansheng Liu, D. Hodge, D. Rubin, U. D. Keil, T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express. 13, 3130–3135 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3129.
[CrossRef]

Paloczi, G. T.

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90–103 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-90.
[CrossRef] [PubMed]

Paloczi, George T.

George T. Paloczi, Yanyi Huang, A. Yariv,“Polymeric Mach-Zehnder interferometer using serially coupled microring resonators,” Opt. Express. 11, 2666–2671 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-21-2666.
[CrossRef] [PubMed]

Pereira, S.

Poon, J. K. S.

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90–103 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-90.
[CrossRef] [PubMed]

Rubin, D.

L. Liao, D. Samara-Rubio, M. Morse, Ansheng Liu, D. Hodge, D. Rubin, U. D. Keil, T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express. 13, 3130–3135 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3129.
[CrossRef]

Samara-Rubio, D.

L. Liao, D. Samara-Rubio, M. Morse, Ansheng Liu, D. Hodge, D. Rubin, U. D. Keil, T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express. 13, 3130–3135 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3129.
[CrossRef]

Scherer, A.

Scheuer, J.

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90–103 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-90.
[CrossRef] [PubMed]

Schweinsberg, S.

J. E. Heebner, V. Wong, S. Schweinsberg, R. W. Boyd, D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40, 726–730 (2004).
[CrossRef]

Seiferth, F.

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).
[CrossRef]

Sipe, J. E.

Slusher, R.E.

G. Lenz, B.J. Eggleton, C. R. Giles, C. K. Madsen, R.E. Slusher, “Dispersive properties of optical filters for WDM systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
[CrossRef]

Trakalo, M.

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).
[CrossRef]

Van, V.

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).
[CrossRef]

Wong, V.

J. E. Heebner, V. Wong, S. Schweinsberg, R. W. Boyd, D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40, 726–730 (2004).
[CrossRef]

Xu, Y.

Yariv, A.

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90–103 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-90.
[CrossRef] [PubMed]

George T. Paloczi, Yanyi Huang, A. Yariv,“Polymeric Mach-Zehnder interferometer using serially coupled microring resonators,” Opt. Express. 11, 2666–2671 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-21-2666.
[CrossRef] [PubMed]

A. Yariv, Y. Xu, R. K. Lee, A. Scherer, “Coupled-resonator optical waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713 (1999).
[CrossRef]

Appl. Opt.

Chin. Phys. Lett.

Li Chun-Fei, Bananej Alireza, “Finesse-enhanced ring resonator coupled Mach-Zehnder Interferometer all-optical switches,” Chin. Phys. Lett. 21, 90–93 (2004).
[CrossRef]

IEEE J. Quantum Electron.

J. E. Heebner, V. Wong, S. Schweinsberg, R. W. Boyd, D. J. Jackson, “Optical transmission characteristics of fiber ring resonators,” IEEE J. Quantum Electron. 40, 726–730 (2004).
[CrossRef]

G. Lenz, B.J. Eggleton, C. R. Giles, C. K. Madsen, R.E. Slusher, “Dispersive properties of optical filters for WDM systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
[CrossRef]

IEEE Photon. Technol. Lett.

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).
[CrossRef]

G. Griffel, “Synthesis of optical filters using ring resonator arrays,” IEEE Photon. Technol. Lett. 12, 810–812 (2000).
[CrossRef]

in Proceedings of IEEE on Sensors.

C.-Y. Chao, L. J. Guo,“A new interferometric sensor with ring-feedback MZI”, in Proceedings of IEEE on Sensors. 1, 569–572, Oct. 2003.

J. Opt. Soc. Am. B

Opt Lett.

John E. Heebner, Robert W. Boyd, “Enhanced all-optical switching by use of a nonlinear fiber ring resonator,” Opt Lett. 24, 847–849, June 1999.
[CrossRef]

Opt. Express.

George T. Paloczi, Yanyi Huang, A. Yariv,“Polymeric Mach-Zehnder interferometer using serially coupled microring resonators,” Opt. Express. 11, 2666–2671 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-21-2666.
[CrossRef] [PubMed]

L. Liao, D. Samara-Rubio, M. Morse, Ansheng Liu, D. Hodge, D. Rubin, U. D. Keil, T. Franck, “High speed silicon Mach-Zehnder modulator,” Opt. Express. 13, 3130–3135 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-8-3129.
[CrossRef]

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, A. Yariv, “Matrix analysis of microring coupled-resonator optical waveguides,” Opt. Express. 12, 90–103 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-1-90.
[CrossRef] [PubMed]

Opt. Lett.

Other

Y. M Landobasa, S. Darmawan, M. K. Chin, “Matrix analysis of 2-D micro-resonator lattice optical filters,” submitted to IEEE J. Quantum Electron.

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Figures (7)

Fig. 1.
Fig. 1.

The effective transmission phase shift versus the ring single-pass phase shift for a single ring coupled to one waveguide (red), and to two waveguides (blue).

Fig. 2.
Fig. 2.

Side Coupled REMZI (inter-resonator coupling occurs within the columns, but not between the columns).

Fig. 3.
Fig. 3.

SC-REMZI: Ring effective phase (upper curve) and the bar output transmission (lower curve) as a function of the ring round trip phase δ for (a) a single column of M (=1,2,3) resonators; (b) a single row of N (=1,2,3) resonators, and (c) N×M 2D arrays (lossless case a=1 ; r=0.8). The insets show the ring and REMZI configurations. Since T=1 throughout, the amplitude responses are not shown.

Fig. 4.
Fig. 4.

Coupled REMZI (inter-resonator coupling occurs within the columns, but not between the columns).

Fig. 5.
Fig. 5.

C-REMZI: Transmission amplitude T (top curve), effective phase e Δφeff (middle) and the bar output transmission (bottom), in the absence of loss (a=1), as a function of the ring round trip phase δ, for (a) a single column of M (=1,3,5) resonators; (b) a single row of N (=1,3,5) resonators; (c) N×M 2D arrays (r=0.8). The insets show the ring and the REMZI configurations.

Fig. 6.
Fig. 6.

The effect of coupling coefficient, or reflectivity (r), on the ring phase and the MZI bar output for the two ring array configurations. (a) r=0, (b) r=0.8.

Fig. 7.
Fig. 7.

The effect of ring loss on the 3×2 Array (a) SC-REMZI and (b) C-REMZI configurations.

Equations (3)

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

[ E bar E cross ] = [ r i κ i κ r ] [ T exp ( i Δ φ eff ) 0 0 exp ( i Δ φ b ) ] [ r i κ i κ r ] [ E in 0 ]
P b = E bar 2 = ( 1 + T 2 2 T cos Δ φ eff ) 4
P c = E cross 2 = ( 1 + T 2 + 2 T cos Δ φ eff ) 4

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