  We analyse recently measured nonlinear photoemission spectra from Ag surfaces
that reveal resonances whose energies do not scale with the applied photon
energy but stay pinned to multiples of bulk plasmon energy $\hbar\omega_p$
above the Fermi level. To elucidate these unexpected and peculiar features we
investigate the spectra of plasmons generated in a solid by the optically
pumped electronic polarization and their effect on photoemission. By combining
quadratic response formalism for calculations of photoemission yield, a
nonperturbative approach to inelastic electron scattering, and first-principles
calculations for the electronic structure, we demonstrate the dependence of
probability amplitude for single- and multiplasmon excitations on the basic
parameters characterizing the photon pulse and the system. The resulting
multiexcitation spectrum evolves towards a truncated plasmonic coherent state.
Analogous concept is extrapolated to interpret plasmon generation by
multiphoton excited electronic polarization. Based on this we elaborate a
scenario that the thus created real plasmons act as supplementary
frequency-locked pump field for non-Einsteinian plasmonically assisted channels
of photoemission from metals. The established paradigm enables assignment and
assessment of the observed linear $\hbar\omega_p$- and nonlinear
$2\hbar\omega_p$-electron yields from Ag. Such effects may be exploited for
selective filtering of optical energy conversion in electronic systems.
