Fig. 1. Focused Gaussian beam with waist radius w0 is incident upon a graphene-coated polystyrene spherical particle with radius R.

Fig. 2. Vertical optical force Fz exerted on a graphene-coated polystyrene particle by a focused Gaussian beam as a function of wavelength with different (a) particle radius and (b) Fermi energy. (c) and (d) plot the resonant wavelength as a function of particle radius and Fermi energy, respectively.

Fig. 3. Optical forces as a function of the displacement of beam center along the x axis on a graphene-coated polystyrene particle with radius R=50  nm at resonant excitation wavelength λ=5151  nm: (a) horizontal direction Fx and (b) vertical direction Fz with different Fermi energy impactions. Inset: Optical force Fz with Fermi energy Ef=0.6  eV.

Fig. 4. Vertical forces Fz as a function of the displacement of beam center along the z axis with different Fermi energy of the graphene coating. λ=5151  nm, R=50  nm.

Fig. 5. Optical force as a function of the particle radius: (a) polystyrene particle; (b) graphene-coated polystyrene particle; (c) empty graphene particle.

Fig. 6. WGM of electric field patterns of: (a), (d) polystyrene particle, (b), (e) graphene-coated polystyrene particle, (c), (f) bare graphene shell, at resonance of (a)–(c) electric field multipoles a12 and (d)–(f) magnetic multipoles b12, respectively.