  We present an analytic and numerical study of the creation of an
uni-directional spin-wave emission in ultra-thin ferromagnetic films sandwiched
in an asymmetric layer stack. For this we extend the analytical description of
spin waves in spin-wave waveguides by the incorporation of the influence of the
interfacial Dzyaloshinskii-Moriya interaction on the spin-wave propagation. By
exploring the model system Ni$_{81}$Fe$_{19}$/Pt we show that it is possible to
achieve an uni-directional spin-wave emission by combining wave-vector
selective excitation sources with the frequency splitting which arises from
interfacial Dzyaloshinskii-Moriya interaction. Hereby we focus on device
feature sizes and spin-wave wavelengths compatible with state-of-the art
excitation and detection schemes. We demonstrate that the optimum operation
conditions for the non-reciprocal emission can be predicted using the presented
analytical formalism
