Phase-locked beam splitting with continuously tunable intensity ratio using stochastic phase masks

We introduce a common-path beam splitter based on a randomly partitioned phase mask displayed on a spatial light modulator (SLM). The SLM aperture is divided into square patches, each randomly assigned to one of three phase ramps that steer light to three independent foci: two phase-locked beams and a dump that takes up the surplus power. We observe the beams in the focal plane of a lens. The fractions of patches assigned to each ramp set the focal intensities, with the focus positions controlled by the ramp slopes.We first demonstrate experimentally that the intensity ratio between the two foci can be tuned from 0 to 1 without distorting either of the spatial modes, and with their relative phase constant to within a few tens of mrad. We then derive a closed-form expression for the ensemble-averaged focal intensity, which decomposes into coherent foci of the desired pattern and a speckle background whose shape and amplitude are set by the patch size. The model is validated against experiment and against numerical Fraunhofer propagation, with quantitative agreement over about three orders of magnitude in intensity. We also identify the patch size as the central design parameter and characterize its experimental bounds.