Mechanical actuation of graphene sheets via optically induced forces

In this paper, we theoretically demonstrate the strong mechanical response of graphene sheets actuated by near-field optical forces. We study single-layer graphene and a two-layer graphene stack with large separation and show that tunable attractive and repulsive forces can be generated. A large nonlinear mechanical response can be obtained by driving the sheets through external radiation and guided modes. We report formation of graphene bubbles of several nanometers in height. Our study points towards new routes for mechanical actuation of graphene, providing new platforms for straintronics and flexible optoelectronics.

Figure 1

(a) Schematic representation of stacked layers of graphene sheets separated by dielectric layers. (b) The integration path chosen to calculate force per unit area on a graphene sheet using Maxwell stress tensor method.

Figure 2

(a, b) Reflection of graphene and gold as a function of the transverse component of wave vector $k_{\rho }$. The insets show sketches of a graphene sheet and gold thin film excited by a TM evanescent light. (c, d) Optical pressure on the graphene sheet and the gold thin film versus $k_{\rho }$ at different wavelengths.

Figure 3

(a, b) Pressure distribution and deflection of a graphene sheet resulting from excitation by a vertically oriented dipole source of $\lambda =8\mu \mathrm{m}$ with a radiated power of $1.5\mathrm{mW}$ placed 50 nm above the sheet. The SPP wavelength is ${\lambda }_{\mathrm{SPP}}=238.2\mathrm{nm}$. The inset shows a schematic of a circular graphene sheet with a radius of $1\mu \mathrm{m}$ excited by scattering from an atomic force microscope (AFM) tip modeled with a vertical dipole depicted as the red arrow. (c, d) Results at lower wavelength of $\lambda =5\mu \mathrm{m}$, which leads to repulsion phenomena. The SPP wavelength is ${\lambda }_{\mathrm{SPP}}=93.1\mathrm{nm}$. (e) Comparison of the deflection predicted by the axisymmetric, quasicontinuum, and approximate solutions for the nonlinear von Kármán plate theory.

Figure 4

(a) Reflection versus $k_{\rho }$ from a two-layer graphene stack with a separation distance $d=100\mathrm{nm}$ for $\lambda =10\mu \mathrm{m}$. The field profiles of the transverse electric field are plotted in the inset. (b) Optical pressure on the top graphene sheet. (c) Pressure versus $k_{\rho }$ and normalized separation distance for $\lambda =10\mathrm{m}$. (d) Pressure versus $k_x$ and incident wavelength for $d=\lambda /100$. (e, f) Pressure distribution and deformation of the graphene sheets for $d=10\mathrm{nm}$ excited by a vertical dipole source with radiated power of $1.5\mathrm{mW}$ at $\lambda =5\mu \mathrm{m}$. (g, h) Same as above for a separation distance of $d=40\mathrm{nm}$.

Figure 5

(a, b) Dependence of the magnitude of the attractive and repulsive pressures between the sheets on the separation distance and incident wavelength, respectively. (c, d) Deformation of the sheets for the attractive and repulsive modes for a separation distance of 100 nm for $\lambda =10\mu \mathrm{m}$. The deflection profiles across the top sheets are shown in the inset to clarify the asymmetry. The inset in (c) depicts a schematic of two graphene sheets excited by a guided mode injected from the side.