We propose a highly efficient graphene-on-gap modulator (GOGM) by employing the hybrid plasmonic effect, whose modulation efficiency (up to 1.23 dB/μm after optimization) is ∼12-fold larger than that of the present graphene-on-silicon modulator (∼0.1  dB/μm). The proposed modulator has the advantage of a short modulation length of ∼3.6  μm, a relatively low insertion loss of ∼0.32  dB, and a larger modulation bandwidth of ∼0.48  THz. The physical insight is investigated, showing that both the slow light effect and the overlap between graphene and the mode field contribute. Moreover, an efficient taper coupler has been designed to convert the quasi-transverse electric mode of conventional silicon waveguide to the hybrid plasmonic mode of GOGM, with a high coupling efficiency of 91%. This Letter may promote the design of high-performance on-chip electro-optical modulators.

We have systematically investigated the wideband slow light in two-dimensional material graphene, revealing that graphene exhibits much larger slow light capability than other materials. The slow light performances including material dispersion, bandwidth, dynamic control ability, delay-bandwidth product, propagation loss, and group-velocity dispersion are studied, proving graphene exhibits significant advantages in these performances. A large delay-bandwidth product has been obtained in a simple yet functional grating waveguide with slow down factor c/vg at 163 and slow light bandwidth Δω at 94.4 nm centered at 10.38 μm, which is several orders of magnitude larger than previous results. Physical explanation of the enhanced slow light in graphene is given. Our results indicate graphene is an excellent platform for slow light applications, promoting various future slow light devices based on graphene.

Enlarged group index has been reported previously when surface plasmons propagate through the graphene sheet, yet a clear slow wave performance in graphene has not been explored. We proposed and numerically analyzed here for the first time to the best of our knowledge an extremely wideband slow surface wave in a graphene-based grating waveguide. The strongly delayed wave (120Δf>0.7 THz) can be dynamically controlled via the gate-voltage dependent optical properties of graphene. Our results suggest that graphene may be a very promising slow light medium, promoting future slow light devices based on graphene.

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