Distributed feedback terahertz frequency quantum cascade lasers with   dual periodicity gratings
  We have developed terahertz frequency quantum cascade lasers that exploit a double-periodicity distributed feedback grating to control the emission frequency and the output beam direction independently. The spatial refractive index modulation of the gratings necessary to provide optical feedback at a fixed frequency and, simultaneously, a far-field emission pattern centered at controlled angles, was designed through use of an appropriate wavevector scattering model. Single mode THz emission at angles tuned by design between 0{\deg} and 50{\deg} was realized, leading to an original phase-matching approach, lithographically independent, for highly collimated THz QCLs. 
F. Castellano, S. Zanotto, L. H. Li, A. Pitanti, A. Tredicucci, E. H.   Linfield, A. G. Davies, and M. S. Vitiello
physics.optics