This article has been reviewed according to Science X's editorial process and policies. Editors have highlighted the following attributes while ensuring the content's credibility: When light travels through a strongly scattering material, such as biological tissue or other disordered opaque media, it follows many different paths and produces a seemingly random speckle pattern. Wavefront shaping makes it possible to control this complex interference and focus light through such materials.
The success of this focusing process is commonly characterized by the enhancement factor—a measure of how much brighter the optimized focus becomes compared with the diffuse background. While reproducible enhancement is essential for applications, much less attention has been paid to how the enhancement factor fluctuates from one realization or target position to another. In a study published in Nature Communications, research led by Hasan Yilmaz, Ph.D., an assistant professor in the Department of Electrical and Computer Engineering at Saint Louis University's School of Science and Engineering (SSE), in collaboration with professor Grégory Schehr of the French National Center for Scientific Research (CNRS) and Sorbonne Université in France, reveals that these fluctuations contain information about the scattering medium itself.
By combining optical experiments, numerical simulations and random-matrix theory, the researchers uncover giant fluctuations in the enhancement factor produced by long-range mesoscopic correlations. The findings establish the enhancement factor not only as a measure of focusing performance but also as a physical and statistical observable whose fluctuations provide a simple and experimentally accessible probe of the underlying correlations in complex scattering media. "You can think of a complex scattering material as a maze for light," said Yilmaz.
"In our experiment, that maze is created by a layer of zinc oxide nanoparticles, similar to the particles that make paint appear white. "The stronger the scattering or the thicker the material, the more light wanders through this maze before it escapes. These giant fluctuations carry a fingerprint of that journey, allowing us to learn about the material itself from the way the focused light fluctuates." The collaboration brings together Yilmaz's expertise in wavefront shaping and complex photonics with Schehr's expertise in extreme-value statistics, statistical mechanics and disordered systems.
The researchers used finite-size Laguerre–Wishart random-matrix statistics to establish a parameter-free statistical reference for the enhancement factor. This framework accurately predicts both the average enhancement and its fluctuations when long-range mesoscopic correlations are negligible. Experiments and numerical simulations of strongly scattering media, however, revealed a striking contrast.
While the average enhancement remains essentially unchanged, its fluctuations can become several times larger than the correlation-free prediction. Simulations further show that these giant enhancement fluctuations become increasingly pronounced as the scattering medium becomes thicker. "What surprised us is that the average enhancement can agree remarkably well with theory while its fluctuations become giant," said Yilmaz.
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