All-optical circuits for signal processing could be a promising solution to overcome the speed bottleneck of electronics. For the photonics industry, silicon becomes a competitive material of choice in the field of integrated optics for designing and implementing high-speed and compact photonic devices. To further increase the integration density, it is a critical challenge to manipulate light on scales much smaller than the wavelength for the dielectric waveguides due to the diffraction limitation. Surface plasmon-polaritons (SPPs), which break the diffraction limitation, are receiving increasing attentions in recent years. This paper compares the advantages and disadvantages between electronic devices and optical devices taking differentiator as an example, and proposes an optical parametric amplifier (OPA) using silicon-based hybrid plasmonic waveguide.