  The laser interaction with an electron-positron-ion mixed plasma is studied,
from the perspective of the associated high-order harmonic generation. For an
idealized mixed plasma which is assumed with a sharp plasma-vacuum interface
and uniform density distribution, when it is irradiated by a weakly
relativistic laser pulse, well-defined signals at harmonics of the plasma
frequency in the harmonic spectrum are observed. These characteristic signals
are attributed to the inverse two-plasmon decay of the counterpropagating
monochromatic plasma waves which are excited by the energetic electrons and the
positron beam accelerated by the laser. Particle-in-cell simulations show the
signal at twice the plasma frequency can be observed for a pair density as low
as $\sim 10^{-5}$ of the plasma density. In the self-consistent scenario of
pair production by an ultraintense laser striking a solid target,
particle-in-cell simulations, which account for quantum electrodynamic effects
(photon emission and pair production), show that dense (greater than the
relativistically-corrected critical density) and hot pair plasmas can be
created. The harmonic spectrum shows weak low order harmonics, indicating a
high laser absorption due to quantum electrodynamic effects. The characteristic
signals at harmonics of the plasma frequency are absent, because broadband
plasma waves are excited due to the high plasma inhomogeneity introduced by the
interaction. However, the high frequency harmonics are enhanced due to the
high-frequency modulations from the direct laser coupling with created pair
plasmas.
