High-Speed Efficient On-Chip Electro-Optic Modulator Based on Midinfrared Hyperbolic Metamaterials

Integrated modulators are key components for on-chip optical communication and information processing, which have become leading technologies in the current information-growth era. Hence, high-speed, efficient, and compact integrated modulators are in high demand. However, the current integrated midinfrared modulators meet these requirements with difficulty. Here, we present a high-speed and efficient on-chip electro-optic modulator based on midinfrared hyperbolic metamaterials using stacking of graphene and hexagonal boron nitride. The length of the modulation region is only 60 nm, which is integrated on a plasmonic waveguide composed of hyperbolic metamaterials. The maximum modulation depth is up to 30 dB, and the 3-dB modulation speed can reach up to 50 GHz, which is supported by a detailed study of a small-signal frequency-response model. Our work provides an alternative scheme for the design of modulators with the requirements of sub-100-nm integration and 50-GHz modulation speed or even beyond, which can be directly implemented into a two-dimensional-materials-based photonic integrated circuits platform.

Figure 1

Schematic depiction of the proposed integrated planar waveguide modulator on quartz substrate. It is composed of five segments, namely signal propagation region, modulation region, buffer region, modulation region, and signal propagation region in turn. W and H are the width and thickness of HMM2Ds, respectively. $W_g$ is the width of the air gap. The chemical potential of the graphene layer in modulation regions can be tuned by applied voltage supported by graphene nanoribbons. In order to obtain different voltages for different graphene layers, L-type graphene is stacked alternately (see Sec. S1 of the Supplemental Material for details [26]). Note that the graphene layers between each region are separated for electrical insulation. Here, only the top two layers of graphene in modulation regions are depicted as the latticelike atomic-structure diagram, while the rest are represented by slabs. The total number of pairs for HMM2Ds depends on the thickness H, and only a few pairs are presented here as representative.

Figure 2

The effective permittivity and isofrequency dispersion contours. The real and imaginary parts of effective permittivity tensors varying with chemical potential at (a) 3 µm and (c) 5 µm. ${ϵ}_{\mathrm{\perp }}$ and ${ϵ}_{\parallel }$ denote the out-of-plane and in-plane components of effective permittivity tensors, respectively. The inset in (a) shows a schematic of HMM2Ds. D, dielectric; I, type I; II, type II. Isofrequency dispersion contours for different chemical potentials at fixed wavelengths of (b) 3 µm and (d) 5 µm. The blue line represents type I and the red line type II. Note that due to the influence of loss, the dispersion of the type-I isofrequency dispersion contour varies more slowly at 5 µm compared with that at 3 µm.

Figure 3

The geometrical size optimization of HMM2Ds with air gap W_g = 200 nm at an operation wavelength of 5 µm. (a) The relationship between propagation loss and thickness of HMM2Ds when W = 600 nm. (b) The relationship between propagation loss and width of HMM2Ds when H = 150 nm. (c)–(e) The electric field strength distribution of different components for the resonant lossy mode with H = 147 and W = 600 nm, which is not preferred for the design of a low-loss modulator due to the very limited allowed propagation distance. (f)–(h) The electric field strength distribution of different components for the long-propagation mode with H = 200 and W = 600 nm. Here, the chemical potential of graphene is doped at 400 meV.

Figure 4

Modulation depth and speed analysis based on the small-signal frequency-response model. (a) Modulation depth as a function of the applied voltage $V_a$. The modulation depth is defined as the energy ratio $10\mathrm{LO}{\mathrm{g}}_{10}(\mathrm{on}/\mathrm{off})$, where “on” means on state with maximum transmittance while “off” represents the opposite case. The inset shows one example of off-state modulation. (b) Normalized modulation voltage as a function of small-signal frequency. The inset shows the corresponding equivalent small-signal high-frequency circuit model of the proposed device. $V_S$ represents the small-signal square wave voltage from the function generator. $R_0$ is the resistance of the function generator, which is typically 50 Ω. $R_G$ is the total resistance per graphene layer, including the internal resistance of graphene $R_g$ with a sheet resistance of 40 Ω/sq [40] and contact resistance of graphene-graphene nanoribbons $R_{gg}$ (1000 Ω) [27]. $C_m$ is the capacitance of the mth graphene capacitor with value $C_G$ and $2m$ is the number of doped graphene layers. (c) Modulation depth as a function of the small-signal frequency. (d)–(g) The energy flow distributions in yz and xy planes when the modulator is on and off, respectively. Note that the yz plane is cut in the center of the air gap while the xy plane is in the middle of the HMM waveguide.