Fig. 1. (a) Schematic illustration of SHG from a tiny nonlinear particle. (b) The SHG is quenched when a linear ENZ particle is placed very close to the tiny nonlinear particle.

Fig. 2. (a) Schematic layout of the configuration for exploring the SHG quenching effect. It is composed of a linear ENZ spherical particle accompanied with a tiny nonlinear spherical particle in the deep-subwavelength scale. The green curve denotes the trajectory of the nonlinear particle moving around the ENZ particle. Positions 1 and 4 are close to the poles, positions 2 and 3 are on the equatorial plane, and position 5 is far from the ENZ particle. The two particles are illuminated by a plane wave propagating along the z direction with the electric field polarized in the x direction. (b) The blue solid line denotes the normalized scattering cross section of SHG SCS2ω as a function of the position of the nonlinear particle along the trajectory in (a). The red dots show the SCS2ω from the nonlinear particle alone, which is normalized to 1.

Fig. 3. (a) Distribution of normalized fundamental electric-field amplitude on the ENZ particle’s surface on the air side in the absence of the nonlinear particle. The numbers 1–5 denote five different positions of the nonlinear particle in Fig. 2. (b) Normalized fundamental electric-field amplitude |Eiω|/E0ω at position i (i=1,2,3,4,5) as a function of the εe. (c) The ratio |E2ω|/|E1ω| with respect to the ratio re/d. Here re is kept unchanged at λ0/100. The red dashed line shows the ideal value of εe−1. The inset illustrates the configuration. (d) The ratio |SCS22ω|/|SCS12ω| with respect to the ratio rn/d. Here d is kept unchanged at λ0/2000. The SCS12ω (or SCS22ω) denotes the SHG scattering cross section when the nonlinear particle is placed at position 1 (or 2), as illustrated by the inset.

Fig. 4. (a) and (c) Distribution of normalized fundamental electric-field amplitude on the surface of an (a) isotropic, (c) anisotropic ENZ film on the air side in the absence of the nonlinear particle. The incident light is polarized in the z direction and propagates along the x direction. (b) and (d) Normalized SCS2ω from a nonlinear particle alone (red) and the nonlinear particle placed above the (b) isotropic ENZ film with different εe, (d) anisotropic ENZ film with different εe,z at an edge-to-edge distance of λ0/2000 (blue). The nonlinear particle is the same as that in Fig. 2. The insets illustrate the configurations.

Fig. 5. (a) and (b) Schematic graphs of an optical metasurface which can be dynamically switched to exhibit (a) high, (b) low SHG conversion efficiency through controlling the phase states of its constituent GeTe. The metasurface is composed of a square array of meta-atoms on a SiO2 substrate. Each meta-atom consists of a central CdO–GeTe multilayered structure and two small graphene-covered SiO2 cuboids, as illustrated by the insets. The length unit is nanometer. (c) The real part of εy,eff, i.e., Re(εy,eff), of the central CdO–GeTe multilayer with GeTe in the crystalline (blue) or amorphous (red) phase as a function of wavelength. The inset shows the imaginary part of εy,eff, i.e., Im(εy,eff). (d) The SHG energy from the metasurface with its constituent GeTe in the crystalline (green) or amorphous (yellow) phase. The SHG energy in the amorphous phase is enlarged by 10 times for better visualization. In each phase, the left and right bars correspond to the case with the central CdO–GeTe multilayer considered as an effective medium and the case with the original multilayer structure, respectively. The incident light is polarized in the y direction and propagates along the z direction. The operating wavelength is 6.93 μm.

Fig. 6. (a) Schematic layout of the configuration, which is the same as that in Fig. 2 in the main text. Here, the tiny nonlinear particle is placed at position 1 where the SHG quenching effect is expected. (b)–(d) Normalized SHG scattering cross section SCS2ω with respect to the (b) re/λ0 in the case of rn/λ0=0.001 and d/λ0=0.0005, (c) rn/λ0 in the case of re/λ0=0.01 and d/λ0=0.0005, and (d) d/λ0 in the case of re/λ0=0.01 and rn/λ0=0.001. In (b)–(d), the SCS2ω is normalized to the SCS2ω in Fig. 2, in which case the geometrical parameters are set as re/λ0=0.01, rn/λ0=0.001, and d/λ0=0.0005 (marked by the vertical dashed lines).

Fig. 7. (a) Normalized scattering cross section of SHG SCS2ω from the tiny nonlinear particle when it is successively moved from position 1 to position 5 along the trajectory 1→2→3→4→5. The configuration is the same as that in Fig. 2. (b)–(d) Simulated fundamental electric-field amplitude on the ENZ sphere’s surface on the air side for the cases with material losses.

Fig. 8. Distributions of normalized fundamental electric-field amplitude in one unit cell of the optical metasurface on the plane that contains the graphene. The metasurface is the same as that in Fig. 5. (a) Effective-medium model in the crystalline phase; (b) effective-medium model in the amorphous phase; (c) multilayer-structure model in the crystalline phase; and (d) multilayer-structure model in the amorphous phase.