Statistical Optical Replication and Mixing of Spatial Information across Wavelengths

Abstract

Accessing and combining the spatial information carried by light at different wavelengths is important for linking structured-light encoding with spectrally distinct detection channels. Here, we introduce a correlation-enabled linear-optical framework for cross-wavelength imaging, bidirectional replication, and spatial information mixing. Shared random holographic modulation establishes correlations between nondegenerate optical fields, allowing spatial information to be retrieved from joint intensity fluctuations. In the demonstrated replicator, a spatial pattern encoded at one wavelength is read out in the detection coordinates of another through intensity correlations. Selecting diffraction-order pairs produces correlation kernels containing either the product or the conjugate product of two input field envelopes. These operations reproduce the spatial algebra underlying sum- and difference-frequency generation, while the optical fields retain their original carrier frequencies. The theory accounts for wavelength-dependent propagation and coordinate scaling, linking the input structures to observable correlation patterns. Together, these results establish a common framework for cross-wavelength spatial information processing through engineered optical correlations and joint detection.