Nanophotonic waveguides can be engineered in order to exhibit slow mode propagation thereby enhancing the nonlinear responses. In such waveguides, loss and nonlinear coefficients are strongly wavelength dependent, a property that must be considered when the signal to pump detuning is large. Exact formulas for the parametric gain and conversion efficiency, accounting for the dispersion of losses and nonlinearity, are derived here. They can be applied to any waveguide presenting such features; in particular they have been calculated for a III–V semiconductor photonic crystal waveguide, where narrow- and broad-band amplification are predicted. The asymmetry of losses causes major asymmetries in the gain and conversion efficiency, which are no longer simply related as in the case of waveguides in which loss do not depend on the wavelength.
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