  Effective control of terahertz radiation requires the development of
efficient and fast modulators with a large modulation depth. This challenge is
often tackled by using metamaterials, artificial sub-wavelength optical
structures engineered to resonate at the desired terahertz frequency.
Metamaterial-based devices exploiting graphene as the active tuneable element
have been proven to be a highly effective solution for THz modulation. However,
whilst the graphene conductivity can be tuned over a wide range, it cannot be
reduced to zero due to the gapless nature of graphene, which directly limits
the maximum achievable modulation depth for single-layer metamaterial
modulators. Here, we demonstrate two novel solutions to circumvent this
restriction: Firstly, we excite the modulator from the back of the substrate,
and secondly, we incorporate air gaps into the graphene patches. This results
in a ground-breaking graphene-metal metamaterial terahertz modulator, operating
at 2.0-2.5 THz, which demonstrates a 99.01 % amplitude and a 99.99 % intensity
modulation depth at 2.15 THz, with a reconfiguration speed in excess of 3 MHz.
Our results open up new frontiers in the area of terahertz technology.
