Surface plasmon polariton（SPP）, a sub-wavelength surface wave promising for photonic integration, always suffers from the large metallic loss that seriously restricts its practical application. Here, we propose a compact SPP amplifier based on a nonlinear hybrid waveguide（a combination of silver, LiNbO3, and SiO2）, where a couple of Bragg gratings are introduced in the waveguide to construct a cavity. This special waveguide is demonstrated to support a highly localized SPP-like hybrid mode and a low loss waveguide-like hybrid mode. To provide a large nonlinear gain, a pumping wave input from the LiNbO3 waveguide is designed to resonate inside the cavity and satisfy the cavity phase matching to fulfill the optical parametric amplification（OPA） of the SPP signal. Proper periods of gratings and the cavity length are chosen to satisfy the impedance matching condition to ensure the high input efficiency of the pump wave from the outside into the cavity. In theoretical calculations, this device demonstrates a high performance in a very compact scheme（3.32 μm） and a much lower pumping power for OPA compared with single-pass pumping. To obtain a comprehensive insight into this cavity OPA, the influences of the pumping power, cavity length, and the initial phase are discussed in detail.
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