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The extreme nonlinear optical process of high-harmonic generation (HHG) makesit possible to map the properties of a laser beam onto a radiating electronwavefunction, and in turn, onto the emitted x-ray light. Bright HHG beamstypically emerge from a longitudinal phased distribution of atomic-scalequantum antennae. Here, we form a transverse necklace-shaped phased array ofHHG emitters, where orbital angular momentum conservation allows us to tune theline spacing and divergence properties of extreme-ultraviolet and soft X-rayhigh harmonic combs. The on-axis HHG emission has extremely low divergence,well below that obtained when using Gaussian driving beams, which furtherdecreases with harmonic order. This work provides a new degree of freedom forthe design of harmonic combs, particularly in the soft X-ray regime, where verylimited options are available. Such harmonic beams can enable more sensitiveprobes of the fastest correlated charge and spin dynamics in molecules,nanoparticles and materials.

Necklace-structured high harmonic generation for low-divergence, soft X-ray harmonic combs with tunable line spacing