Fig. 2. Exceptional points in optical binding.

a Schematic of a pair of counter-propagating plane waves that are applied to confine particles on the xy plane. Despite the incident light intensity is uniform over the xy plane, the scattering of light among the spheres modifies the spatial light distribution, as shown in b–e, which induces binding forces. The colored contour plots in b–e represent the normalized total field intensity for the spheres with b $r_{\mathrm{S}}=0.31\lambda$ and $n_{\mathrm{r}}=1.2$, c $r_{\mathrm{S}}=0.31\lambda$ and $n_{\mathrm{r}}=1.2$, d $r_{\mathrm{S}}=0.41\lambda$ and $n_{\mathrm{r}}=1.2$, and e $r_{\mathrm{S}}=0.27\lambda$ and $n_{\mathrm{r}}=1.51$. All figures are drawn to scale. Red (yellow) circles denote positive (negative) momentum vorticity C (see main text) near each sphere. f–g plot the real (f) and imaginary (g) components of the eigenvalues for the force matrix of e against the particle radius. The exceptional point is marked by purple crosses.