We show that a moving Josephson vortex in spatially modulated layered superconductors generates out-of-plane THz radiation. Remarkably, the magnetic and in-plane electric fields radiated are of the same order, which is very unusual for any good-conducting medium. Therefore, the out-of-plane radiation can be emitted to the vacuum without the standard impedance mismatch problem. Thus, the proposed design can be more efficient for tunable THz emitters than previous proposals, for radiation only propagating along the ab-plane. ; Comment: 7 pages, 1 figure. Phys. Rev. B (2005), in press