A source of intense coherent high-frequency electromagnetic radiation such as soft x-rays. A circularly polarized incident beam of coherent radiation is directed at a frequency multiplication medium that includes constituents of approximate C.sub.n symmetry, oriented so that the symmetry axes of the constituents are parallel to the incident beam. The interaction of the incident beam and the constituents of the medium produces higher harmonics of the incident frequency, up into the x-ray band. If the C.sub.n symmetry of the medium constituents is exact then the harmonic frequencies are multiples ln.+-.l of the frequency of the incident beam, where l is an integer. If the C.sub.n symmetry is only approximate, then the harmonics are centered around these multiples. Suitable medium constituents include dipolar molecules of C.sub.5v symmetry and circular rings of nanoparticles.