  We investigate a plasmonic electro-optic modulator with an extinction ratio
exceeding 1 dB/um by engineering the optical mode to be in-plane with the
graphene layer, and show how lowering the operating temperature enables steeper
switching. We show how cooling Graphene enables steeping thus improving dynamic
energy consumption. Further, we show that multi-layer Graphene integrated with
a plasmonic slot waveguide allows for in-plane electric field components, and
3-dB device lengths as short as several hundred nanometers only. Compact
modulators approaching electronic length-scales pave a way for ultra-dense
photonic integrated circuits with smallest footprints
