Polarization and coherence properties of the diffraction by a double retarder rectangular aperture

• We apply the recently proposed FTJ-BCP formalism that combines the Fourier transform Jones (FTJ) matrix and the beam-coherence polarization (BCP) matrix to analyze the polarization and spatial coherence properties of the diffracted field produced by a rectangular aperture with different retarders on each half. The different distributions obtained under illumination with fully polarized and fully unpolarized light are described. • When illuminating this double retarder aperture with unpolarized light, the theoretical analysis shows that although the light remains unpolarized right after the aperture, the diffracted field exhibits a polarization and spatial coherence structure. • Theoretical predictions are validated experimentally by using a liquid–crystal on silicon spatial light modulator (LCOS-SLM) to display the double retarder rectangular aperture and an unpolarized He-Ne laser as light source. We verify experimentally the expected polarization properties by capturing polarimetric images of the diffracted field and obtaining the Stokes-parameter maps. • A digital double-slit experiment is performed by adding a second LCOS-SLM that affects one selected linear polarization component, which enables to measure the scalar complex degree of coherence when the diffracted field is projected onto a polarizer. • Our findings reveal spatial coherence variations both as a function of the spatial-frequency coordinates in the diffraction pattern and as a function of the polarization configuration. • This work demonstrates the potential of vectorial diffractive optical elements as tools for engineering scalar coherence patterns. These coherence patterns maintain their spatial distribution on nanosecond timescales, limited only by the intrinsic polarization dynamics of the unpolarized laser source. In this work we analyze the diffraction properties of a rectangular aperture with different retarders on each half. Thus, under polarized illumination, the two halves yield distinct output polarization states, which in turn generate a structured polarization distribution in the diffracted field. Using the combined Fourier transform Jones (FTJ) matrix and beam-coherence-polarization (BCP) matrix formalism, we also show that even when the aperture is illuminated with unpolarized light, and the field therefore remains unpolarized right after the aperture, the diffracted field yet exhibits a polarization and spatial coherence structure. Experimental verification is conducted using a liquid–crystal spatial light modulator (LCOS-SLM) as a pixelated linear retarder to encode the double retarder aperture, and a polarimetric camera to analyze the polarization of the diffracted field. The experimental system is completed with a second LCOS-SLM to implement a digital double-slit experiment affecting one selected linear polarization component. This enables to measure the scalar complex degree of coherence and shows that the double-retarder aperture can generate spatially-structured scalar coherence patterns under unpolarized illumination.