Finite size effects in surface emitting Terahertz quantum cascade lasers

We analyze surface-emitting distributed feedback resonators for Terahertz quantum cascade lasers fabricated from double-metal waveguides. We explain the influence on resonances and surface-emission properties of the finite length and width of the gratings in connection with absorbing boundary conditions, and show that, contrary to the infinite case, the modes on either side of the photonic band-gap have finite surface losses. The lateral design of the resonator is shown to be important to avoid transverse modes of higher order and anti-guiding effects. Experimental findings are indeed in excellent agreement with the simulations. Both modeling and fabrication can easily be applied to arbitrary gratings, of which we discuss here a first interesting example.