We discuss the existence of nonlinear modes sustained by graphene layers in dielectric waveguides. Taking advantage of the almost two dimensional nature of graphene, we introduce the nonlinear effect as a parameter in the continuity equations. We then apply our modeling to a simple slab waveguide to enlighten how graphene can be used to induce huge nonlinear phase shifts at easily accessible power levels.

We investigate the tuning of the coupling of surface plasmon polaritons between two spatially separated graphene layers. We demonstrate that by slightly changing the chemical potential, a graphene coupler can switch from the bar to the cross state; as a consequence, the coupling coefficient in such structures can be easily controlled by means of an applied electrical signal.

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We obtain dark and antidark soliton solutions in binary waveguide arrays with focusing and/or defocusing Kerr nonlinearity and with alternating positive and negative linear couplings between adjacent waveguides. For both stationary and moving solitons, we analyze the properties of these solutions in the presence of uniform and nonuniform nonlinearity along the array