Abstract

The existence of localized or defect modes in a periodic array of symmetric and lossless micro-ring resonators is demonstrated for both finite and infinite structures using the transfer matrix method, for two types of array: one consisting of a cascade of coupled resonators coupled to an input and an output waveguide, and another consisting of uncoupled resonators periodically coupled between two bus waveguides. The defect can be introduced either by removing one ring, or by making one ring bigger or smaller. The 1-D periodic dielectric waveguide structures consisting of micro-ring resonators can exhibit photonic bandgaps, and when point defects are introduced defect states can form within the bandgaps, giving rise to donor and acceptor modes similar to other photonic crystals. The results based on the transfer matrix model agree with the finite-difference time-domain method, and are compared with those of a quarter-wave mirror stack.

© 2005 Optical Society of America

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IEEE J. Quantum Electron. (1)

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IEEE Photonics Technol. Lett. (2)

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

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[CrossRef]

IEEE Photonics. Technol. Lett. (4)

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

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[CrossRef]

B. E. Little, S. T. Chu, W. Pan, and Y. Kokubun, �??Microring resonator arrays for VLSI photonics,�?? IEEE Photonics. Technol. Lett. 12, 323-325 (2000).
[CrossRef]

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[CrossRef]

J. Lightwave Technol. (2)

R. Grover, V. Van, T.A. Ibrahim, P.P. Absil, L. C. Calhoun, F. G. Johnson, J. V. Hryniewicz, and P.-T. Ho, �??Parallel-cascaded semiconductor microring resonators for high-order and wide-FSR filters,�?? J. Lightwave Technol. 20, 900-905 (2002).
[CrossRef]

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[CrossRef]

J. Opt. Soc. Am. A. (1)

A. A. Tovar and L. W. Casperson, �??Generalized Sylvester theorems for periodic applications in matrix optics,�?? J. Opt. Soc. Am. A. 12, 578-590 (1995).

J. Opt. Soc. Am. B (3)

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. B (2)

K. Sakoda and H. Shiroma, �??Numerical method for localized defect modes in photonic lattices,�?? Phys. Rev. B 56, 4830 (1997).
[CrossRef]

G. Gutroff., M. Bayer., J. P. Reithmaier., A. Forchel., P. A. Knipp., T. L. Reinecke., �??Photonic Defect States in chains of coupled microresonators,�?? Phys. Rev. B 64, 155313 (2001).
[CrossRef]

Phys. Rev. Lett. (2)

E. Yablonovitch, �??Inhibited spontaneous emission in solid-state physics and electronics,�?? Phys. Rev. Lett. 58, 2059�??2062 (1987).
[CrossRef]

S. L. McCall, P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, �??Microwave propagation in twodimensional dielectric lattices,�?? Phys. Rev. Lett. 67, 2017 (1991).
[CrossRef]

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