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Speckle patterns are inherent features of coherent light propagation throughcomplex media. As a result of interference, they are sensitive to multipleexperimental parameters such as the configuration of disorder or thepropagating wavelength. Recently, developments in wavefront shaping haveenabled to control speckle pattern statistics and correlations, for exampleusing the concept of the transmission matrix. In this article, we address theproblem of correlating scattered fields across multiple degrees of freedom. Wehighlight the common points between the specific techniques alreadydemonstrated and propose a general framework based on the singular valuedecomposition of a linear combination of multiple transmission matrices.Following analytical predictions, we experimentally illustrate the technique onspectral and temporal correlations and show that both the amplitude and thephase of the field correlations can be tuned. Our works open new perspectivesin speckle correlation manipulation, with potential applications in coherentcontrol and proposing a generalization of the concept speckle memory effect.

Correlating light fields through disordered media across multiple degrees of freedom