Fig. 1. Multilayer core-shell structure model for studying spontaneous radiation

Fig. 2. Real part (a) and Imaginary part (b) of dielectric function of graphene

Fig. 3. When the radius of the core-shell structure of Au@SiO₂@Graphene is {$r$₁,$r$₂,$r$₃} = {30,40,50} nm: the normalized radiative and non-radiative decay rate versus $r$_d when $\lambda$ = 600 nm (a); the normalized radiative and nonradiative decay rate versus $\lambda$ when $r$_d = 70 nm (b)

Fig. 4. Normalized radiative and non-radiative decay rate versus $r$_d for Au@SiO₂@Graphene models with different radius. (a) {$r$₁,$r$₂,$r$₃} = {10,40,50} nm; (b) {$r$₁,$r$₂,$r$₃} = {20,40,50} nm; (c) {$r$₁,$r$₂,$r$₃} = {30,40,50} nm; (d) Purcell factor comparison of the structure with {$r$₁,$r$₂,$r$₃} = {10,40,50} nm and {$r$₁,$r$₂,$r$₃} = {20,50,60} nm

Fig. 5. (a) Normalized radiation and non-radiation decay rate versus wavelength for Au@SiO₂@Graphene model with {$r$₁,$r$₂,$r$₃} = {10,40,50} nm when $r$_d=60 nm; (b) Normalized radiation and non-radiation decay rate versus $r$_d for Au@SiO₂@Graphene model with {$r$₁,$r$₂,$r$₃} = {10,40,50} nm when wavelength is 633 nm

Fig. 6. Normalized radiative and non-radiative decay rate versus wavelength_{for Au@SiO2@Graphene models with different radium. (a) {$r$1,$r$2,$r$3} = {20,40,50} nm; (b) {$r$1,$r$2,$r$3} = {30,40,50} nm}

Fig. 7. Electric field distribution map of Au@SiO₂@Graphene model at wavelength of 633 nm. (a) {$r$₁,$r$₂,$r$₃} = {10,40,50} nm;(b) {$r$₁,$r$₂,$r$₃} = {20,40,50} nm; (c) {$r$₁,$r$₂,$r$₃} = {30,40,50} nm; (d) {$r$₁,$r$₂,$r$₃} = {20,50,60} nm

Fig. 8. Real ${ϵ}_{\mathrm{r}}$ and imaginary ${ϵ}_{\mathrm{i}}$ part of dielectric function of GO

Fig. 9. Normalized radiation and non-radiation decay rate versus $r$_d at wavelength of 633 nm for Au@SiO₂@GO model with {$r$₁,$r$₂,$r$₃} = {10,40,50} nm

Fig. 10. Scattering pattern of two models with {$r$₁,$r$₂,$r$₃} = {10,40,50} nm at wavelength of 633 nm.(a) Au@SiO₂@Graphene; (b) Au@SiO₂@GO