Silicon waveguides with graphene: coupling of waveguide mode to surface plasmons

Abstract

Silicon waveguides with graphene layers have been recently intensively studied for their potential as fast and low-power electro-optic modulators with small footprints. In this paper we show that in the optical wavelength range of 1.55 μm, surface plasmons supported by the graphene layer with the chemical potential exceeding ∼0.5 eV can couple with the guided mode of the silicon waveguide and affect its propagation. On the other hand, this effect might be possibly utilized in technical applications like a very low-power amplitude modulation, temperature sensing, etc.

Coupling of waveguide mode and graphene plasmons

“…The dispersion equation for such modes can be written in the form of the transverse resonance condition (in the x direction in Fig. 2) [8]. Then, reflection of a surface plasmon from the edge of a graphene stripe is assumed to be total, and is modelled with a perfectly magnetic wall.…”

“…Here, we applied the principles of the complex CMT [15,16] and used it for determination of modes of the composed structure. Our implementation [8] is based on several simplifications; namely, we ignore mutual coupling among various graphene modes and assume symmetrical matrix of coupling coefficients. Such procedure helps significantly simplify the calculation while keeping all aspects important for our analysis.…”

“…In principle, a graphene layer can thus be utilized for both amplitude and phase electro-optic modulation [1][2][3][4][5][6][7]. Interestingly, the phase modulation can be accompanied with coupling of the waveguide mode with surface plasmon modes supported by the graphene stripe ("graphene modes"), even at the telecommunication optical wavelength band around 1550 nm [8]. In this paper, we consider a simplified example of a graphene-on-silicon modulator (see Fig.…”

“…We approximately describe the plasmon modes as the superposition two graphene plasmons reflected at the edges of the graphene stripe. Based on our recent comparison of various approaches to numerical modelling of light propagation in a silicon waveguide with graphene overlay [9], we employ a simplified coupled mode theory (CMT) [8] and calculate the complex propagation constant of the quasi-TE mode propagating in the waveguide modulator. We compare the result with a full-wave numerical simulation using the commercial software packet COMSOL Multiphysics.…”

Symmetric Graphene Dielectric Nanowaveguides as Ultra-Compact Photonic Structures

“…More importantly, the combination of graphene and silicon-on-insulator (SOI) waveguides make it possible to design graphene-based photonic integration devices [ 32 ], such as waveguides [ 33 , 34 , 35 , 36 , 37 , 38 , 39 ], sensors [ 40 , 41 ], filters [ 42 ], modulators [ 43 , 44 ], etc. Recently, graphene–SiO 2 –Si coaxial-like waveguides [ 45 ], graphene layer–SiO 2 –Si planar structures [ 46 , 47 , 48 , 49 , 50 ], and graphene-coated nanowires integrated with SiO 2 or Si substrates [ 51 , 52 , 53 , 54 , 55 , 56 ] were presented to demonstrate ultra-compact photonic integrated circuits in the mid- and far-infrared bands.…”