Custom-tailored spatial mode sorting by controlled random scattering

The need to increase data transfer rates constitutes a key challenge in modern information-driven societies. Taking advantage of the transverse spatial modes of light to encode more information is a promising avenue for both classical and quantum photonics. However, to ease access to the encoded information, it is essential to be able to sort spatial modes into different output channels. Here, we introduce a way to customize the sorting of arbitrary spatial light modes. Our method relies on the high degree of control over random scattering processes by preshaping of the phase structure of the incident light. We demonstrate experimentally that various sets of modes, irrespective of their specific modal structure, can be transformed to a broad range of output channel arrangements. Thus, our method enables full access to all of the information encoded in the transverse structure of the field; for example, azimuthal and radial modes. We also demonstrate that coherence is retained in this complex mode transformation, which opens up applications in quantum and classical information science.

Figure 1

Sketch of the experimental setup for custom-tailored spatial mode sorting. Spatial light modes are generated by modulating the transverse spatial structure of a laser beam by means of a SLM. The laser light is then redirected onto a control-SLM and focused into a strongly scattering medium (${\mathrm{TiO}}_2$ powder). The appropriate phase modulation structure of the control-SLM (inset left side, gray value stands for phase modulation depth up to $2\pi$) is found by use of a genetic algorithm and the feedback signal from a CMOS camera. For more details see main text.

Figure 2

Sorting of spatial modes carrying $\pm 1$ unit of OAM. (a) Upper part: Either of two OAM modes is sent into the sorter. The color depicts their phase structure while the brightness shows the intensity distribution. Lower part: Experimentally recorded intensities after transmission of either mode through the setup. We find OAM modes with $+1$ and $-1$ quanta of OAM to be sent to the two predefined output channels A and B, respectively (false color recording). Inset: Cross-talk matrix of the sorter from which a sorting ability of $97.7\pm 0.6$% can be deduced. (b) Coherence test of the mode-sorting process. If equally weighted superpositions are sent through the sorter, both output channels A and B show equal intensities for different phases $\phi$. After propagation to the far field, an interference pattern ($\sim 88$% visibility) is found, which shifts laterally depending on the input phases of the OAM superpositions.

Figure 3

Sorting of up to seven OAM modes carrying up to $\pm 3$ quanta of OAM and its stability. (a) The sorter can be programed to sort three, five, and seven neighboring and four randomly chosen OAM modes. All measurements demonstrate very good sorting abilities of $94\pm 1\%, 85\pm 3\%, 72\pm 4\%$, and $90\pm 3\%$, respectively, which is nicely visualized by the high probabilities along the diagonal axis of the cross-talk matrices. (b) Stability measurement of the sorting of the five modes described in (a) over the course of 24 h. Only a slight decrease was found, which demonstrates the long-term stability of the sorting scheme.

Figure 4

Demonstration of sorting to different output-channel arrangements. (a) The distance between the two output locations A and B can be adjusted from 88 $\mu \mathrm{m}$ to 2.8 mm without a detectable reduction of sorting ability (97%–98%). Note that the four results were recorded in separate runs but are embedded in one image here to illustrate the distances graphically. (b) The arrangement of the output channels can be arbitrarily chosen with similar sorting abilities of approximately 93%. Examples of vertical, triangular, and corner-shape sorting of three modes are shown. (c) Different input modes can be sorted to the same output position, e.g., $-2$ and 0 to A, $-1$ and $+1$ to B, with no reduction on the sorting ability (see cross-talk matrix). Color coding of modes as in Fig. 2.

Figure 5

Sorting of different types of light modes. (a) Radial modes that differ only by their radial structure are sorted to different spatial locations and high sorting ability of $92\pm 2\%$. (b) The four lowest-order Hermite-Gauss (HG) modes are sorted with a sorting ability of $85\pm 3\%$. Color coding for all modes as in Fig. 2.