Theory of second harmonic generation in plasma crystals

Second harmonic generation in plasma crystals is studied. Starting from a linear chain model, a set of coupled nonlinear differential equations for second harmonic generation is derived. It is shown that with some modifications these equations are also applicable to a two-dimensional (2D) lattice. The solutions show that the amplitude of the harmonic attains a maximum away from the excitation region. An efficiency factor, which is the ratio of the energy in the pump wave to the maximum energy in the harmonic is defined and estimated using Lindemann's criterion for melting and phase matching conditions. The efficiency is limited by the damping due to the background gas. Relevance of these results to recent experiments on harmonic generation in 2D plasma crystals is discussed. (C) 2004 American Institute of Physics.