High-numerical-aperture extreme ultraviolet flat optics via a cascaded momentum relay

High-numerical-aperture extreme-ultraviolet flat optics are constrained by undersampling of steep edge phase gradients, which reduces phase fidelity and high-angle diffraction efficiency. Here, we introduce a momentum-relay architecture that partitions large wavevector deflections across two cascaded elements. A 4:1 demagnification platform operating at 532 nm synthesizes an effective numerical aperture of 0.80, producing a measured first-dark-ring radius of 413.2 nm and resolving ~555 nm image-plane features across a 100 μm-diameter field of view. We further translate the concept to 13.24 nm using a compact xenon laser-produced-plasma source. Two Fresnel zone plates, each with a numerical aperture of approximately 0.33, cooperatively synthesize an effective numerical aperture of approximately 0.53. Here, we show that cascaded momentum relay provides a compact route to high-numerical-aperture extreme-ultraviolet projection while relaxing the feature-size and spatial-sampling requirements imposed on each element.