Graphene-Coated Two-Layer Dielectric Loaded Surface Plasmon Polariton Rib Waveguide With Ultra-Long Propagation Length and Ultra-High Electro-Optic Wavelength Tuning

A graphene-coated two-layer dielectric loaded surface plasmon polariton (GTDLSPP) rib waveguide is designed. The mode characteristics and electro-optic (EO) modulation performances of the four hybrid plasmonic modes (HPMs) in the designed waveguide are simulated by using the finite element method. The simulation results show that a 10
³
mm-scale propagation length and an effective mode field area of
$\sim \lambda ^{2}$
/1333 are obtained by adjusting the bias voltage. The EO wavelength tunings are −68.6, −42.0, −49.7, and −11.1 nm/V for the HPM 1, HPM 2, HPM 3, and the peak 2 of HPM 4, which are two orders of magnitude larger than those of other EO modulation structures. For the peak 1 of the HPM 4, the EO wavelength tuning is the piecewise linear. For a 150-
$\mu \text{m}$
long waveguide, the modulation depths of ~98.7, ~87.9, and 99.5%, and FWHMs of ~450, ~100, and ~42 nm can be achieved for the HPM 1, HPM 2, and HPM 3. For the HPM 4, there are two peaks in the transmission spectrum. The modulation depths are ~97.3 and 75.2%, and FWHMs are ~92 and ~34 nm for the peaks 1 and 2. There is a tradeoff between the modulation depth and FWHM for different waveguide lengths. The GTDLSPP rib waveguide designed has small size, high modulation depth, broad bandwidth, and compatibility with the CMOS technology, so it has potential applications in the EO tunable devices, optical interconnects, and optical switches.