Tunable supermode converters based on Jx graphene waveguide arrays with transversely linear modulation

Conventional mode converters are usually based on wave-number matching in the propagation direction. This often requires applying the periodic modulation in the longitudinal orientation. Here, we propose to construct an efficient supermode converter with only transverse modulation. By linearly changing the surface conductivity of ${J}_{x}$ graphene waveguide arrays, we build a synthetic ${J}_{x}$ lattice with linearly varying on-site potential in the modal dimension. It turns out that each supermode can fully transfer to its corresponding symmetric partner. The conversion distance of supermodes is inversely proportional to the ramp of linear modulation. In this way, tunable supermode converters can be readily implemented by modulating the surface conductivity of graphene sheets. This study may find promising applications in developing mode converters and mode-division multiplexers utilizing plasmonic waveguide arrays.