Excitation of plasmons in two-dimensional electron gas with defects by   microwaves: Wake-field method
  We develop an analytical method to find plasmons generated by microwaves in a two-dimensional electron gas with defects. The excitations are expressed in terms of the wake field of a charged particle moving in plasma. The result explicitly addresses the efficiency of the photon-to-plasmon conversion and the type of excitation. While strong absorption of the radiation by the excitations is reached at larger plasmon wave numbers, intense persistent plasma waves are created at optimal ones. The latter wave numbers depend on the spectrum of plasmons and the distance that the waves are required to travel without being substantially attenuated. Their type, which can be traveling or standing, is governed by the geometry of the defects and the polarization of the radiation. We identify such types of traveling plasmons as circular plasmons, excited at dot defects, and traverse plasmons, excited at straight wire defects and traveling away from (toward) the wires if their group velocity is positive (negative). Nonlinear excitations are also accounted for. In particular, we analyze the zeroth harmonic, linear in the microwave intensity, which has the character of a frozen charge density wave. The interference of elementary wakes from defects arranged in truncated periodic sets can produce amplified plasmons, which are easily portrayed. 
Eduard Takhtamirov and Roderick V. N. Melnik
cond-mat.mes-hall physics.plasm-ph