Abstract
Resonant optical phenomena related to Fano resonances have elegantly applied to highly sensitive sensor. Here, we explore the photonic Fano formula based on the model of two directly coupled loss-loss and gain-loss optical microcavities using the temporal coupled-mode theory. The dependence of the Fano formula (the asymmetric parameter and the reduced frequency) and excitation criterion on the property parameters of the optical waveguide based microresonators is studied. In the meanwhile, the excitation criterion of Fano resonance is systematically analyzed. We found that the sensitivity of refractive index of the Fano-like resonator can be magnified by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7.27 \times 10^{6}$ </tex-math></inline-formula> compared with the loss-loss cavity by adjusting the device parameters.
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