Abstract

We present a pole–zero analysis, based on the transfer matrix method, for ring resonator (RR)-based filters of Type I and Type II, consisting of mutually coupled and side-coupled RRs. The pole–zero plot determines the filter spectral characteristics and is determined primarily by the coupling coefficient between the resonators. The pole–zero dynamics (or root locus) shows how the poles and zeros move in the complex frequency plane as we vary the coupling coefficient. We show that the pole–zero dynamics for the two types of filter are complementary and, furthermore, that the pole–zero plots are related to the conditions of critical coupling and oscillation in the presence of loss or gain. We also show a pole–zero analysis for the apodization of these filters based on an actively tunable Mach–Zehnder-type coupler, where it is shown that apodization corresponds to designing pole–zero pairs with wide separations, whereas the required bandwidth determines the specific values of the coupling coefficient.

© 2007 IEEE

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  24. 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).
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  26. 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).

2007 (1)

2006 (2)

S. Darmawan, M.-K. Chin, "Critical coupling, oscillation, reflection and transmission in optical waveguide-ring resonator systems," J. Opt. Soc. Amer. B, Opt. Phys. 23, 834-841 (2006).

D. A. May-Arrioja, N. Bickel, P. Likamwa, "Robust 2 × 2 multimode interference optical switch ," Opt. Quantum Electron. 38, 557-566 (2006).

2005 (3)

2004 (5)

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

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. 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. Amer. B, Opt. Phys. 21, 1818-1832 (2004).

Y. Chen, S. Blair, "Nonlinearity enhancement in finite coupled-resonator slow-light waveguides," Opt. Express 12, 3353-3366 (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).

2003 (1)

H. Ma, X. J. Yi, S. H. Chen, "1.55 μm AlGaInAs/InP polarization insensitive optical amplifier with tensile strained wells grown by MOCVD," Opt. Quantum Electron. 35, 1107-1112 (2003).

2002 (2)

D. G. Rabus, M. Hamacher, U. Troppenz, H. Heidrich, "Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GaInAsP–InP," IEEE J. Sel. Topics Quantum Electron. 8, 1405-1411 (2002).

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

2001 (2)

2000 (5)

B. E. Little, S. T. Chu, W. Pan, Y. Kokubun, "Microring resonator arrays for VLSI photonics," IEEE Photon. Technol. Lett. 12, 323-325 (2000).

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

G. Griffel, "Synthesis of optical filters using ring resonator arrays," IEEE Photon. Technol. Lett. 12, 810-812 (2000).

A. Yariv, "Universal relations for coupling of optical power between microresonators and dielectric waveguides," Electron. Lett. 36, 321-322 (2000).

M. A. Dupertuis, J. L. Pleumeekers, T. P. Hessler, P. E. Selbmann, B. Deveaud, B. Dagens, J. Y. Emery, "Extremely fast high-gain and low-current SOA by optical speed-up at transparency," IEEE Photon. Technol. Lett. 12, 1453-1455 (2000).

1997 (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).

1995 (2)

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).

A. A. Tovar, L. W. Casperson, "Generalized Sylvester theorems for periodic applications in matrix optics," J. Opt. Soc. Amer. A, Opt. Image Sci. 12, 578-590 (1995).

Electron. Lett. (1)

A. Yariv, "Universal relations for coupling of optical power between microresonators and dielectric waveguides," Electron. Lett. 36, 321-322 (2000).

IEEE J. Quantum Electron. (1)

Y. M. Landobasa, S. Darmawan, M.-K. Chin, "Matrix analysis of 2-D micro-resonator lattice optical filters," IEEE J. Quantum Electron. 41, 1410-1418 (2005).

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

D. G. Rabus, M. Hamacher, U. Troppenz, H. Heidrich, "Optical filters based on ring resonators with integrated semiconductor optical amplifiers in GaInAsP–InP," IEEE J. Sel. Topics Quantum Electron. 8, 1405-1411 (2002).

IEEE Photon. Technol. Lett. (5)

M. A. Dupertuis, J. L. Pleumeekers, T. P. Hessler, P. E. Selbmann, B. Deveaud, B. Dagens, J. Y. Emery, "Extremely fast high-gain and low-current SOA by optical speed-up at transparency," IEEE Photon. Technol. Lett. 12, 1453-1455 (2000).

B. E. Little, S. T. Chu, W. Pan, Y. Kokubun, "Microring resonator arrays for VLSI photonics," IEEE Photon. Technol. Lett. 12, 323-325 (2000).

G. Griffel, "Synthesis of optical filters using ring resonator arrays," IEEE Photon. Technol. Lett. 12, 810-812 (2000).

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).

J. Lightw. Technol. (3)

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

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).

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. Opt. Soc. Amer. A, Opt. Image Sci. (1)

A. A. Tovar, L. W. Casperson, "Generalized Sylvester theorems for periodic applications in matrix optics," J. Opt. Soc. Amer. A, Opt. Image Sci. 12, 578-590 (1995).

J. Opt. Soc. Amer. B, Opt. Phys. (2)

J. 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. Amer. B, Opt. Phys. 21, 1818-1832 (2004).

S. Darmawan, M.-K. Chin, "Critical coupling, oscillation, reflection and transmission in optical waveguide-ring resonator systems," J. Opt. Soc. Amer. B, Opt. Phys. 23, 834-841 (2006).

Opt. Express (5)

Opt. Lett. (3)

Opt. Quantum Electron. (2)

H. Ma, X. J. Yi, S. H. Chen, "1.55 μm AlGaInAs/InP polarization insensitive optical amplifier with tensile strained wells grown by MOCVD," Opt. Quantum Electron. 35, 1107-1112 (2003).

D. A. May-Arrioja, N. Bickel, P. Likamwa, "Robust 2 × 2 multimode interference optical switch ," Opt. Quantum Electron. 38, 557-566 (2006).

Other (2)

M. Hamacher, U. Troppenz, H. Heidrich, "Optically amplifying microring resonator components based on GaInaAsP/InP: Challenges and perspectives," Proc. IEEE Semicond. Conf.—CAS (2004) pp. 179-187.

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

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