Influence of the Local Scattering Environment on the Localization Precision of Single Particles

We study the fundamental limit on the localization precision for a subwavelength scatterer embedded in a strongly scattering environment, using the external degrees of freedom provided by wavefront shaping. For a weakly scattering target, the localization precision improves with the value of the local density of states at the target position. For a strongly scattering target, the localization precision depends on the dressed polarizability that includes the backaction of the environment. This numerical study provides new insights for the control of the information content of scattered light by wavefront shaping, with potential applications in sensing, imaging, and nanoscale engineering.

Figure 1

Representation of a slab composed of several dipole scatterers and illuminated by a SLM. In all simulations, the thickness of the system is set to $L_z=10\lambda$, and the transverse dimension is set to $L_x=50\lambda$.

Figure 2

CRLB as a function of the normalized scattering mean free path $k\ell$ for plane-wave illumination. Dotted lines correspond to $\ell =L_z$ (defining the transition to the multiple-scattering regime) and dashed lines correspond to $\zeta =L_z$ (defining the onset of Anderson localization). Each point represents the geometric mean over 1000 configurations of the disordered medium, and error bars represent 1-sigma intervals. The inset shows the same data on a smaller scale.

Figure 3

Intensity $I/I_0$ around the target for a scattering medium illuminated by a wavefront optimized for (a) the transverse coordinate $x_0$, (b) the longitudinal coordinate $z_0$, and (c) both coordinates simultaneously. An area of $2\lambda \times 2\lambda$ is displayed on each map. (d) Histogram of the intensity ratio $I/I_{\max }$ at the target position when optimizing for $x_0$, $z_0$ and both coordinates simultaneously.

Figure 4

Left: ${\mathcal{C}}_{xz}$ for a weakly scattering target as a function of the normalized LDOS. The black line is a fit to the optimized data by a power law with an exponent of $-1/2$ (a linear regression gives an exponent of $-0.46$). Right: Observed distribution of the CRLB. Log-normal distributions (solid lines) are fitted to numerical observations (data points).

Figure 5

Left: ${\mathcal{C}}_{xz}$ for a strongly scattering target as a function of the normalized effective scattering strength $|\tilde{\alpha }/{\alpha }_0{|}^2$. The black line is a fit to the optimized data by a power law with an exponent of $-1/2$ (a linear regression gives an exponent of $-0.36$). Right: Observed distribution of the CRLB. Log-normal distributions (solid lines) are fitted to numerical observations (data points).