Abstract
We demonstrate numerically that it is possible to trap light in the structure shown in Figure la using four-wave mixing. We define two resonant frequencies associated with the structure: ω{O,i}=c/(neffR{o,i}), where "i" and "o" refer to the inner resonators (not shaded) and the outer resonators (shaded) respectively, and R; and Ro are the radii of the inner and outer resonators. The quantity neff is a linear effective index of refraction, assumed to be common to all the resonators and the channel guides, furthermore the frequency dependence of neff is ignored; these assumptions simplify the presentation of the effect. The outer microresonators couple the channel waveguides, so that forward travelling light in the bottom (top) channel is coupled to backward travelling light in the top (bottom) channel1,2. If light has frequency at or near NωO, where N is an integer, then the coupling is resonant, and a stop gap opens in the transmission spectrum of the structure1,2. These gaps lead to the dips in the transmission spectrum of the structure shown by the solid line in Figure lb; the dotted lines in Figure lb show some resonances of the inner microresonators (which do not lead to gaps). Material parameters, used throughout this paper, are neff=3.0, 2πRi,=25μm, 27πRo=30μm and σ=0.98 for all resonators.
© 2002 Optical Society of America
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