Light Induced Inverse-Square Law Interactions between Nanoparticles: “Mock Gravity” at the Nanoscale

The interaction forces between identical resonant molecules or nanoparticles, optically induced by a quasimonochromatic isotropic random light field, are theoretically analyzed. In general, the interaction force exhibits a far-field oscillatory behavior at separation distances larger than the light wavelength. However, we show that the oscillations disappear when the frequency of the random field is tuned to an absorption Fröhlich resonance, at which the real part of the particle’s electric polarizability is zero. At the resonant condition, the interaction forces follow a long-range gravitylike inverse square distance law which holds for both near- and far-field separation distances.

Figure 1

Forces between nonabsorbing particles. Log-log plot of the absolute value of the interaction force between nonabsorbing particles with $\alpha$ given by Eq. (3), with ${\omega }_0=0.1{\omega }_F$, ${\mathrm{\Gamma }}_0=0$, and $a={\lambda }_F/100$ for (a) the resonant frequency $\omega ={\omega }_F$ and (b) strongly off resonance $\omega =0.1{\omega }_F$. Red shadowed regions indicate repulsive interaction force.

Figure 2

Forces between absorbing particles. Log-log plot of the absolute value of the interaction force between absorbing particles with $\alpha$ given by Eq. (3), with ${\omega }_0=0.1{\omega }_F$, $\omega ={\omega }_F$, and $a={\lambda }_F/100$ for different damping coefficients (shown in each plot). Red shadowed regions indicate repulsive interaction force.

Figure 3

Forces between silver nanoparticles. (top) Real (black line) and imaginary part (red line) of the polarizability versus wavelength in vacuum for a silver nanoparticle with $a=5\mathrm{nm}$. Log-log plots of the force between two silver nanoparticles calculated for a power density of $10\mathrm{W}/\mu {\mathrm{m}}^2$ at different wavelengths (vertical dashed lines): (a) $\lambda =317\mathrm{nm}$, (b) $\lambda =337\mathrm{nm}$, (c) $\lambda =352\mathrm{nm}$, and (d) $\lambda =47\mathrm{nm}$. Red shadowed regions indicate repulsive forces.