We present an analytic theory of the transmission of electromagnetic waves through a structure “two-dimensional electron system with a flowing current – grating coupler.” The transmission coefficientT(&ohgr;,vdr)is calculated as a function of frequency, drift velocityvdr,and other physical and geometrical parameters of the structure. Threshold conditions for amplification[T(&ohgr;,vdr)>1] are analyzed. A number of ideas for a reduction of the threshold velocity and an enhancement of the amplification are proposed. Our results can be used for designing tunable solid-state terahertz wave amplifiers (generators), based on the grating coupled low-dimensional electron systems. ©1997 American Institute of Physics.