Two optical elements fully characterized by their transmission matrix, which relates the incident wave front to the transmitted one. In the case of a thin lens, the transformation of the wave front is described by a 2×2 matrix operating on a vector describing the wave front curvature. For more complex elements such as a sugar cube the transmission matrix operates in a basis of transversal modes, which is very large. Full knowledge of the transmission matrix enables disordered materials to focus light as lenses.
If you know enough about the way light is scattered through materials then you can see through opaque substances, such as a sugar cube. Information characterizing an opaque material can allow the opaque material to be put to put to work as a high quality optical component, comparable to the glass lens.
The transmission of light through a disordered medium is described in microscopic detail by a high-dimensional matrix. Researchers have now measured this transmission matrix directly, providing a new approach to control light propagation
The approach of Popoff and colleagues marks the beginning of a highly exciting road towards a deeper understanding of light transport. Technological progress will enable the measurement of larger and larger matrices that contain all available information about the samples. Ongoing developments in random matrix analysis will allow one to make sense of these enormous quantities of information. When the information in the transmission matrix is fully known, any disordered system becomes a high-quality optical element. From a technological point of view this has great promise: quite possibly disordered scattering materials will soon become the nano-optical elements of choice.
Physical Review Letters – Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media
We introduce a method to experimentally measure the monochromatic transmission matrix of a complex medium in optics. This method is based on a spatial phase modulator together with a full-field interferometric measurement on a camera. We determine the transmission matrix of a thick random scattering sample. We show that this matrix exhibits statistical properties in good agreement with random matrix theory and allows light focusing and imaging through the random medium. This method might give important insight into the mesoscopic properties of a complex medium.