We present a theoretical study on the possibilities to achieve nonlinear frequency conversion in plasmonic slot waveguides having a nonlinear medium as its core. Second-harmonic generation is used as a referential process to discuss the possibilities in achieving strong nonlinear interactions. We show that geometrical dispersion allows for the possibility of modal phase matching without resorting to other mechanisms like birefringence phase matching or periodic poling of the nonlinear medium. We disclose that in strongly dissipative systems two effects, the damping of individual modes and the phase-matching condition, have to be carefully balanced to assure an efficient energy conversion. Besides second-harmonic generation, emphasis is put on exploring the application of potentially more importance: the parametric amplification in the waveguide with the purpose to enhance its propagation length.
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