Wavelength conversion in modulated coupled-resonator systems and their design via an equivalent linear filter representation.

We propose wavelength converters based on modulated coupled resonators that achieve conversion by matching the modulation frequency to the frequency splitting of the supermodes of the unmodulated system. Using temporal coupled-mode theory, we show that these time-variant systems have an equivalent linear, time-invariant filter representation that simplifies the optimal engineering of design parameters for realistic systems. Applying our model to carrier plasma-dispersion modulators as an example implementation, we calculate conversion efficiencies between -5.4 and -1.7  dB for intrinsic quality factors of 10(4)-10(6). We show that the ratio of the resonance shift to the total linewidth is the most important parameter when determining conversion efficiency. Finally, we discuss how this model can be used to design devices such as frequency shifters, widely tunable radio frequency oscillators, and frequency combs.