Abstract

We derive a coupled mode theory for the interaction of an optical cavity with a waveguide that includes waveguide dispersion. The theory can be applied to photonic crystal cavity waveguide structures. We derive an analytical solution to the add and drop spectra arising from such interactions in the limit of linear dispersion. In this limit, the spectra can accurately predict the cold cavity quality factor (Q) when the interaction is weak. We numerically solve the coupled mode equations for the case of a cavity interacting with the band edge of a periodic waveguide, where linear dispersion is no longer a good approximation. In this regime, the density of states can distort the add and drop spectra. This distortion can lead to more than an order of magnitude overestimation of the cavity Q.

© 2005 Optical Society of America

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App. Phy. Lett. (2)

M. Loncar et al. �??Low-threshold photonic crystal laser,�?? App. Phy. Lett. 81, 2680�??2682 (2002).

M.F. Yanik and S. Fan. �??High-contrast all-optical bistable switching in photonic crystal microcavities,�?? App. Phy. Lett. 83, 2739 (2003)

App. Phys. Lett. (3)

Y. Akahane et al. �??Design of a channel drop filter by using a donor-type cavity with high-quality factor in a two-dimensional photonic crystal slab�?? App. Phys. Lett. 82, 1341�??1343 (2003).
[CrossRef]

J. Vuckovic and Y. Yamamoto. �??Photonic crystal microcavities for cavity quantum electrodynamics with a single quantum dot,�?? App. Phys. Lett. 82, 2374�??2376 (2003).
[CrossRef]

T. Asano et al. �??Investigation of channel-add/drop-filtering device using acceptor-type point defects in a two-dimensional photonic-crystal slab,�?? App. Phys. Lett. 83, 407�??409 (2003)
[CrossRef]

IEEE J. Quantum Electron. (3)

C. Seassal et al. �??Optical coupling between a two-dimensional photonic crystal-based microcavity and single-line defect waveguide on inp membranes,�?? IEEE J. Quantum Electron. 38 811�??815 (2002)
[CrossRef]

C. Manolatou et al. �??Coupling of modes analysis of resonant channel add-drop filters,�?? IEEE J. Quantum Electron. 35, 1322 (1999)
[CrossRef]

S. Olivier et al. �??Cascaded photonic crystal guidesand cavities: spectral studies and their impact on intergrated optics design,�?? IEEE J. Quantum Electron. 38, 816�??824 (2002)
[CrossRef]

J. Lightwave Technol. (1)

Nature (1)

Y. Akahane et al. �??High-q photonic nanocavity in a two-dimensional photonic crystal,�?? Nature 425, 944�??947 (2003)
[CrossRef]

Opt. Commun. (1)

B.K. Min, J.E. Kim, and H.Y. Park. �??Channel drop filters using resonant tunneling processes in two-dimensional triangular lattice photonic crystal slabs,�?? Opt. Commun. 237 59�??63 (2004)
[CrossRef]

Opt. Express (2)

Phys. Rev. B (1)

M. Okano, S. Kako, and S. Noda. �??Coupling between a point-defect cavity and a line-defect waveguide in three-dimensional photonic crystal,�?? Phys. Rev. B 68, 235110 (2003)
[CrossRef]

Phys. Rev. E (1)

Y. Xu et al. �??Scattering-theory analysis of waveguide-resonator coupling,�?? Phys. Rev. E 62, 7389�??7404 (2000)
[CrossRef]

Other (1)

A. Yariv. Optical Electronics. Saunders College Publishing, Philadelphia, 1991.

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