ar X iv : p hy si cs / 0 50 40 77 v 1 1 1 A pr 2 00 5 Coupled mode theory for photonic crystal cavity - waveguide interaction

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 OCIS codes: 03.67.Dd,42.50Dv References and links 1. M. Loncar et al. Low-threshold photonic crystal laser. App. Phy. Lett., 81(15):2680–2682, 2002. 2. 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(9):1341–1343, 2003. 3. J. Vuckovic and Y. Yamamoto. Photonic crystal microcavities for cavity quantum electrodynamics with a single quantum dot. App. Phys. Lett., 82(15):2374–2376, 2003. 4. C. Manolatou et al. Coupling of modes analysis of resonant channel add-drop filters. IEEE J. Quant. Electron., 35(9):1322, September 1999. 5. Y. Akahane et al. High-q photonic nanocavity in a two-dimensional photonic crystal. Nature, 425(6961):944– 947, 2003. 6. A. Yariv. Optical Electronics. Saunders College Publishing, Philadelphia, 1991.