Separating partially coherent light

Most light we see is partially coherent, but our ability to analyze and manipulate such light has been limited. In particular, though any such light can always be expressed as a sum of mutually incoherent and orthogonal modes – sometimes known as the “natural modes” or the Karhunen-Loève decomposition – we have never been able to separate partially coherent light this way, and fully measuring multimode partially coherent fields has been challenging. Now we propose a method that physically performs this separation and fully measures the partially coherent field – technically, measuring the coherency matrix.

The concept uses successive layers of Mach-Zehnder interferometers. These layers are structured in a so-called “self-configuring layer” architecture; a simple example is a “diagonal line” of such interferometers. Each such layer is configured by adjusting the phase shifters in the interferometers to maximize the power at the “top” output, starting with the first such layer, and proceeding successively through the others. Then the settings of the interferometers allow us to deduce the form of the corresponding “natural” mode, which constitute the eigenvectors of the coherency matrix, and the output powers give us the corresponding eigenvalues. With these eigenvectors and eigenvalues established, the coherency matrix is fully measured.

Note, too, that we have now physically separated the partially coherent field into these modes, which has apparently not been possible before. Interestingly, the different outputs should all be completely mutually incoherent – there should be no resulting interference when mixing these outputs.

This opens many new possibilities in working with the partially coherent light.

C. Roques-Carmes, S. Fan, and D. A. B. Miller, “Measuring, processing, and generating partially coherent light with self-configuring optics,” Light Sci Appl 13, 260 (2024). https://doi.org/10.1038/s41377-024-01622-y Supplementary material