Focusing of light within and beyond a strong scattering disordered medium via wavefront shaping (WFS) using a spatial light modulator (SLM) has been demonstrated for speckle-sized target regions over a decade ago, and has since been explored extensively with potential applications for imaging, phototherapy, communications and cryptography. The intensity enhancement scales linearly with the number, M1, of SLM pixels and is unaffected by any correlations in the speckle field of transmitted or reflected light. However, a fundamental question of great importance for applications is the possibility of focusing to regions much larger than a single speckle, where neglect of correlations would predict a decrease in the enhancement as 1/M2, where M2 is the number of speckles in the target region.
It has been known for many years that speckle patterns from highly scattering media have long-range field correlations. We have developed a quantitative theory of the effect of these correlations on large scale focusing and demonstrated excellent agreement between the theory and experiments on the transmission of light through ZnO nanoparticles. The correlations between speckles allows much greater control via WFS of focusing to larger target regions than the simple prediction above. Specifically, for a given sample, each set of experimental illumination conditions defines a measurable dimensionless number, g, which controls focusing efficiency. When the dimensionless size of the target region, M2 > g, significantly enhanced focusing through WFS is possible due to correlations, with the maximal enhancement increasing by M2/g compared to the result in the absence of correlations.
A. Douglas Stone, Chiawei Hsu, Seng-Fatt Liew, Arthur Goetschy, and Hui Cao, "Correlation-enhanced control of wave focusing in disordered media (Conference Presentation)," Proc. SPIE 10502, Adaptive Optics and Wavefront Control for Biological Systems IV, 105020T (Presented at SPIE BiOS: January 28, 2018; Published: 15 March 2018); https://doi.org/10.1117/12.2293693.5752139969001.
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