  Optical frequency combs (FCs), that establish a rigid phase-coherent link
between the microwave and optical domains of the electromagnetic spectrum, are
emerging as a key high-precision tools for the development of quantum
technology platforms. These include potential applications for communication,
computation, information, sensing and metrology, and can extend from the
near-infrared with micro-resonator combs, up to the technologically attractive
terahertz (THz) frequency range, with powerful and miniaturized quantum cascade
laser (QCL) FCs. The recently discovered ability of the QCLs to produce a
harmonic frequency comb (HFC), a FC with large intermodal spacings, has
attracted new interest in these devices for both applications and fundamental
physics, particularly for the generation of THz tones of high spectral purity
for high data rate wireless communication networks, for radiofrequency
arbitrary waveform synthesis, and for the development of quantum key
distributions. The controlled generation of harmonic states of a specific order
remains, however, elusive in THz QCLs. Here we devise a strategy to obtain
broadband HFC emission of a pre-defined order in QCL, by design. By patterning
n regularly spaced defects on the top-surface of a double-metal Fabry-Perot
QCL, we demonstrate harmonic comb emission with modes spaced by (n+1) free
spectral range and with a record optical power/mode of ~270 $\mu W$.
