  We calculate the absorption spectra of a conductive disk in the presence of a
metal gate. In our analysis, we use the conductivity described by the Drude
model. We examine the frequency and line width of the absorption resonances
associated with the excited plasma waves. They are estimated both numerically
and analytically for the fundamental and axisymmetric plasma modes. The line
width is determined by the collisional and radiative losses. In high mobility
samples, the latter may dominate even when the resonant frequencies can be
described by a standard quasistatic approximation, i.e., neglecting
electromagnetic retardation. Placing a metal near the disk drastically affects
the radiative broadening of the line width due to the interference of
electromagnetic fields created by the disk and the metal charges. Bringing the
disk in close proximity to the gate makes the total field almost vanish. In
that case, the line width is defined solely by the collisional broadening. As
the disk is moved away from the gate, the line width first shows a reduction
since the plasmon transforms into plasmon-polariton, which is dressed with
undamped electromagnetic field surrounding the disk. Then it increases and
exhibits decaying oscillations, reaching the asymptotic value of the ungated
disk.
