Low-Divergence, Soft X-Ray Harmonic Combs with Tunable Line Spacing from Necklace-Structured Driving Lasers

High-harmonic generation (HHG) is among the most extreme nonlinear optical processes to date. In HHG, some of the driving laser beam properties are imprinted on the dynamics of the radiating electron, and, in turn, on the emitted extreme-ultraviolet/soft X-ray light. As a consequence, it is now possible to coherently manipulate the HHG pulse duration (attosecond waveforms), the photon energy (UV to soft X-rays [1] ), polarization and orbital angular momentum (OAM) [2] , [3] , among others. However, precise coherent control over the frequency content—a key property to perform high-harmonic spectroscopy—has not been achieved yet. Also, equally important to the frequency content is the transverse confinement of the HHG radiation [4] , [5] is a key aspect for applications in imaging and scatterometry.