We demonstrate, to our knowledge, the first bright circularly polarized high-harmonic beams in the soft X-ray region of the electromagnetic spectrum, and use them to implement X-ray magnetic circular dichroism measurements in a tabletop-scale setup. Using counterrotating circularly polarized laser fields at 1.3 and 0.79 μm, we generate circularly polarized harmonics with photon energies exceeding 160 eV. The harmonic spectra emerge as a sequence of closely spaced pairs of left and right circularly polarized peaks, with energies determined by conservation of energy and spin angular momentum. We explain the single-atom and macroscopic physics by identifying the dominant electron quantum trajectories and optimal phasematching conditions. The first advanced phase-matched propagation simulations for circularly polarized harmonics reveal the influence of the finite phase-matching temporal window on the spectrum, as well as the unique polarization-shaped attosecond pulse train. Finally, we use, to our knowledge, the first tabletop X-ray magnetic circular dichroism measurements at the N 4,5 absorption edges of Gd to validate the high degree of circularity, brightness, and stability of this light source. These results demonstrate the feasibility of manipulating the polarization, spectrum, and temporal shape of high harmonics in the soft X-ray region by manipulating the driving laser waveform.X-rays | high harmonics generation | magnetic material | ultrafast light science | phase matching H igh-harmonic generation (HHG) results from an extreme nonlinear quantum response of atoms to intense laser fields. When implemented in a phase-matched geometry, bright, coherent HHG beams can extend to photon energies beyond 1.6 keV (1, 2). For many years, however, bright HHG was limited to linear polarization, precluding many applications in probing and characterizing magnetic materials and nanostructures, as well as chiral phenomena in general. Although X-ray optics can in principle be used to convert extreme UV (EUV) and X-ray light from linear to circular polarization, in practice such optics are challenging to fabricate and have poor throughput and limited bandwidth (3). A more appealing option is the direct generation of elliptically polarized (4-6) and circularly polarized (7-9) high harmonics. In recent work we showed that by using a combination of 0.8 and 0.4 μm counterrotating driving fields, bright (i.e., phase-matched) EUV HHG with circular polarization can be generated at wavelengths λ > 18 nm and used for EUV magnetic dichroism measurements (10-13).Here we make, to our knowledge, the first experimental demonstration of circularly polarized harmonics in the soft X-ray region to wavelengths λ < 8 nm, and use them to implement soft X-ray magnetic circular dichroism (XMCD) measurements using a tabletop-scale setup. By using counterrotating driving lasers at 0.79 μm (1.57 eV) and 1.3 μm (0.95 eV), we generate bright circularly polarized soft X-ray HHG beams with photon energies greater than 160 eV (14) and with flux comparable...
