  We study the dynamical dielectric function of a two-dimensional hole gas,
exemplified on [001]-GaAs and InAs quantum wells, within the Luttinger model
extended to the two lowest subbands including bulk and structure inversion
asymmetric terms. The plasmon dispersion shows a pronounced anisotropy for
GaAs- and InAs-based systems. In GaAs this leads to a suppression of plasmons
due to Landau damping in some orientations. Due to the large Rashba
contribution in InAs, the lifetime of plasmons can be controlled by changing
the electric field. This effect is potentially useful in plasmon field effect
transistors as previously proposed for electron gases.
