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A general electrodynamic theory of a grating coupled two dimensional electronsystem (2DES) is developed. The 2DES is treated quantum mechanically, thegrating is considered as a periodic system of thin metal strips or as an arrayof quantum wires, and the interaction of collective (plasma) excitations in thesystem with electromagnetic field is treated within the classicalelectrodynamics. It is assumed that a dc current flows in the 2DES. We considera propagation of an electromagnetic wave through the structure, and obtainanalytic dependencies of the transmission, reflection, absorption and emissioncoefficients on the frequency of light, drift velocity of 2D electrons, andother physical and geometrical parameters of the system. If the drift velocityof 2D electrons exceeds a threshold value, a current-driven plasma instabilityis developed in the system, and an incident far infrared radiation isamplified. We show that in the structure with a quantum wire grating thethreshold velocity of the amplification can be essentially reduced, as comparedto the commonly employed metal grating, down to experimentally achievablevalues. Physically this is due to a considerable enhancement of the gratingcoupler efficiency because of the resonant interaction of plasma modes in the2DES and in the grating. We show that tunable far infrared emitters, amplifiersand generators can thus be created at realistic parameters of modernsemiconductor heterostructures.Comment: 28 pages, 15 figures, submitted to Phys. Rev.

Plasma instability and amplification of electromagnetic waves in low-dimensional electron systems