  In this paper, we quantitatively analyzed the trade-off between energy per
bit for switching and modulation bandwidth of classical electro-optic
modulators. A formally simple energy-bandwidth limit (Eq. 10) is derived for
electro-optic modulators based on intra-cavity index modulation. To overcome
this limit, we propose a dual cavity modulator device which uses a coupling
modulation scheme operating at high bandwidth (> 200 GHz) not limited by cavity
photon lifetime and simultaneously features an ultra-low switching energy of
0.26 aJ, representing over three orders of magnitude energy consumption
reduction compared to state-of-the-art electro-optic modulators.
