  We suggest a novel approach for generating second-harmonic radiation in
subwavelength graphene waveguides. We demonstrate that quadratic phase matching
between the plasmonic guided modes of different symmetries can be achieved in a
planar double-layer geometry when conductivity of one of the layers becomes
spatially modulated. We predict theoretically that, owing to graphene nonlocal
conductivity, the second-order nonlinear processes can be actualized for
interacting plasmonic modes with an effective grating coupler to allow external
pumping of the structure and output of the radiation at the double frequency.
