Phase-matched relativistic second harmonic generation in clusters with density ripple

An intense short-pulse laser obliquely incident on a clustered gas quickly converts the atomic clusters into hot plasma balls. The laser beam produces a second harmonic due to nonlinear response of cluster and plasma electrons. For enhancement of efficiency of second harmonic generation, there should be appropriate phase-matching between the incident laser beam and the generated harmonic. To achieve the required phase-matching, the ripple in cluster density and plasma electron density outside the cluster is introduced. The efficiency of second harmonic generation is sensitive to the angle between ripple wave vector k→o and the direction of the incident laser beam.