[I.M Vellekoop and A.P. Mosk, Opt. Lett., 15, 2309, 2007]
In 2007 I.M. Vellekoop and A.P. Mosk published their work on the first demonstration of focusing light through a highly scattering medium. Most techniques to image or focus through scattering media relied on selecting only the part of the light that has not been scattered - the ballistic light. The ballistic signals decay exponentially with the thickness of the medium, limiting drastically the depth at which light can be focused. The idea developed by the authors is to use the scattered waves, that are randomly mixed, to focus light through the medium. A scattering sample illuminated by a coherent wave gives rise to a so-called speckle pattern, that results from the interference of the scattered waves. Using a spatial light modulator (SLM), the authors are able to control independently the phase of the different parts of the incident beam. Each segment gives an output seemingly random complex field. By testing different values of the phase for each segment, they are able to put in phase all the contributions, giving rise to a very bright focus spot.
figure 1. (a) A plane wave is focused on a disordered medium, and a speckle pattern is transmitted. (b) The wavefront of the incident light is shaped so that scattering makes the light focus at a predeﬁned target. (image from I.V. Vellekoop et al, Opt. Lett., 15, 2007)
figure 2. (a) Transmission micrograph with an unshaped incident beam. (b) Transmission after optimization for focusing on a single target. (image from I.V. Vellekoop et al, Opt. Lett., 15, 2007)
At the target spot, the complex field is the algebraic sum of the contributions of each input segment. Before optimization, the phases of these contributions are random. The total amplitude can be seen as the result of a random walk in the complex plane and is proportional to the square root of the number of segments N. During the optimization, the contributions are aligned one by one to increase the amplitude of the sum. At the end of the process, the amplitude is proportional to the number of segments N.
figure 3. Representation in the complex plane of the amplitude at the target during the optimization process.