Fig. 1. Configuration of the model. The objective lens with an NA of 0.75 is used.

Fig. 2. (a) Extinction spectrum of the spherical gold nanoparticles with a radius of 30 nm. (b) The optical intensity of the focused field is plotted as a function of the average power P_ave, increasing from 0 to 0.5 W. (c) The real and imaginary parts of the nonlinear polarizability change with the increasing average power P_ave.

Fig. 3. Distribution of the focused electric field intensity in the focal plane and the corresponding polarizability of the dipolar sphere. (a)–(c) The peak value of the individual field components |E_x|², |E_y|², and |E_z|², respectively. (d)–(f) Real parts of three components of the polarizability Re{α_x}, Re{α_y}, and Re{α_z}.

Fig. 4. Nonlinear gradient forces in the focal plane. (a)–(c) The plot of x-component of gradient forces derived from Re{α_x}, Re{α_y}, and Re{α_z}, respectively. Red indicates that the direction of the gradients is along the x-axis, and the force value is positive. Blue denotes the negative force is in the opposite direction of the x-axis. (d)–(f) The plot of y-component of the gradient forces calculated with the vector method. The positive value means the direction of the force is pointing to the y-axis and vice versa for the negative force.

Fig. 5. Total gradient forces obtained by the scalar and vectorial methods. (a) The total gradient forces calculated with the scalar method. (b) The total gradient forces calculated with polarizability vector. (c) Plots of gradient forces along the x-axis for the comparison of two methods. The green line means the gradient force is calculated by the scalar method and the black line for the calculation results based on the vectorial method. (d) The y-component of the gradient forces calculated with scalar polarizability.

Fig. 6. Nonlinear optical potential well on the focal plane. (a) The nonlinear optical potential well on the focal plane with the vectorial method. (b) The parallel projection of the potential well to the direction of the y-axis. (c) The parallel projection of the potential well to the direction of the x-axis. (d) The potential well with the scalar method. (e) and (f) Parallel projections to the y-axis and x-axis, respectively.