Exploiting the Time-Reversal Operator for Adaptive Optics, Selective Focusing, and Scattering Pattern Analysis

We report on the experimental measurement of the backscattering matrix of a weakly scattering medium in optics, composed of a few dispersed gold nanobeads. The decomposition of the time-reversal operator is applied to this matrix and we demonstrate selective and efficient focusing on individual scatterers, even through an aberrating layer. Moreover, we show that this approach provides the decomposition of the scattering pattern of a single nanoparticle. These results open important perspectives for optical imaging, characterization, and selective excitation of nanoparticles.

Figure 1

Schematic of the apparatus. The 532 nm laser is expanded and reflected off a Holoeye LC-R 2500 liquid crystal SLM. Polarization optics (polarizer $P_1$ and analyzer $P_2$) allow phase modulation. The modulated beam is focused on the plane containing the gold particles by a $20\times$ objective ($\mathrm{NA}=0.5$) and the backscattered intensity is imaged by a first CCD camera (CCD1). The second CCD camera (CCD2) images the same plane in transmission with a $60\times$ oil immersion objective ($\mathrm{NA}=1.4$). Analyzers $P_2$ and $P_3$ are oriented in a cross-polarized configuration. In order to maximize the interference signal onto CCD1, a half-wave plate ($\lambda /2$) is set in the reference arm such that the linear polarization of the reference beam matches the orientation of $P_3$. $L$, lens. BS, beam splitter.

Figure 2

Experimental results for selective focusing on nanobeads through an aberrating layer using the DORT method. (a) Aberrated image of the object plane on CCD1 in reflection for a plane wave illumination. (b) Singular value distribution of the measured BM. (c)–(f) [(g)–(j)] Images in reflection by camera CCD1 [in transmission by the control camera CCD2], when sending the four first singular vectors. All images from CCD1 (CCD2) share the same intensity scale. All images correspond to the same area of the sample.

Figure 3

Phase of the first input singular vector ${\mathbf{V}}_{\mathbf{1}}$ (b),(c) and the corresponding focal spots recorded by CCD1 (a),(d) in free space and in the presence of an aberrating layer, respectively.

Figure 4

Singular value decomposition of the experimental and theoretical BM with a single scatterer. (a),(b) Emission and recording geometry of the experiment. (c),(d) Singular value distributions of the measured and the calculated BM: The three first output singular vectors are shown in the insets.