  In addition to charge plasmons, a 2D electron system with Rashba-type
spin-orbit coupling (SOC) also supports three collective modes in the spin
sector: the chiral-spin modes. We study the dispersions of the charge and spin
modes and their coupling to each other within a generalized Random Phase
Approximation for arbitrarily strong SOC, and both in 2D and 3D systems. In
both 2D and 3D, we find that the charge plasmons are coupled to only one of the
three chiral-spin modes. This coupling is shown to affect the dispersions of
the modes at finite but not at zero wavenumbers. In 3D, the chiral-spin modes
are strongly damped by particle-hole excitations and disappear for weak
electron-electron interaction. Landau damping of the chiral-spin modes in 3D is
directly related to the fact that, in contrast to 2D, there is no gap for
particle-hole excitations between spin-split subbands. The gapless continuum is
also responsible for Landau damping of the charge plasmon in 3D - a
qualitatively new feature of the SOC system. We also discuss the optical
conductivity of clean 2D and 3D systems and show that SOC introduces spectral
weight at finite frequency in a such way that the sum rule is satisfied. The
in-plane tranverse chiral-spin mode shows up as dispersing peak in the optical
conductivity at finite number which can can be measured in the presence of
diffraction grating. We also discuss possible experimental manifestations of
chiral-spin modes in semiconductor quantum wells such InGaAs/AlGaAs and 3D
giant Rashba materials of the BiTeI family.
