In this paper we present a detailed theoretical investigation of the electric field induced mixing effect, in which the up and down frequency-conversion processes are obtained by inducing an effective second order susceptibility via the periodic spatial distribution of reversed biased p-i-n junctions. The possibility of realizing a frequency generation process within an integrated microring resonator is demonstrated here, by simulations, in the silicon on insulator platform. Furthermore, general physical features have been investigated by means of a comparative analysis of the frequency generation performance as a function of the input pump power, the linear and nonlinear losses, and the coupling factors. A conversion efficiency of 627.5 %/W has been obtained for the second harmonic generation process. Therefore, an improvement of 4 to 50 times with respect to the straight waveguides is achieved, depending on the cavity ring radius. Finally, for the up/down conversion, from telecom idler to mid-IR and from Mid-IR to telecom signal, respectively, an efficiency of 85.9%/W and 454.4 %/W has been obtained in the silicon microring resonator, respectively.
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