We present theoretical modeling of a novel configuration for quasi-phase-matched parametric amplification in which the pump and the signal fields form guided waves of a planar waveguide while the idler is radiated into the substrate. We follow a coupled-mode approach to study the parametric amplification in periodically domain-reversed proton-exchanged LiNbO3 waveguides upon a Z-cut substrate and present numerical results relevant to the amplification process. In particular, for given pump and signal wavelengths we have studied the dependence of the gain coefficient on the periodicity of a grating formed by domain inversion. This configuration, which is referred to as the Čerenkov-idler configuration, is shown to provide a large signal gain bandwidth and is more tolerant to variations in pump frequency.
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