Plasmonic ship-wake on graphene

Kelvin predicted that the semi-angle of the V-shaped wedge behind a ship moving in deep water region is 19.5°, independent of the ship´s velocity. The predication has been challenged recently that the semi-angle would transit from the Kelvin angle to the Mach angle as the ship´s velocity increases. In this paper, we show the graphene plasmons excited by a swift charged particle would have the similar phenomenon. When the velocity of the charged particle is relatively slow, the graphene plasmons excited would accumulate along the caustic boundary of the graphene plasmons pattern, forming the plasmonic Kelvin angle. At large velocity, however, no graphene plasmons would accumulate along any boundary, thereby the caustics disappear and the effective semi-angle of the graphene plasmons approaches the Mach angle.