  We consider a quantum-mechanical system, finite or extended, initially in its
ground-state, exposed to a time-dependent potential pulse, with a slowly
varying envelope and a carrier frequency $\omega_0$. By working out a rigorous
solution of the time-dependent Schr\"odinger equation in the high-$\omega_0$
limit, we show that the linear response is completely suppressed after the
switch-off of the pulse. We show, at the same time, that to the lowest order in
$\omega_0^{-1}$, observables are given in terms of the linear density response
function $\chi(\rv,\rv',\omega)$, despite the problem's nonlinearity. We
propose a new spectroscopic technique based on these findings, which we name
the Nonlinear High-Frequency Pulsed Spectroscopy (NLHFPS). An analysis of the
jellium slab and sphere models reveals very high surface sensitivity of NLHFPS,
which produces a richer excitation spectrum than accessible within the
linear-response regime. Combining the advantages of the extraordinary surface
sensitivity, the absence of constraints by the conventional dipole selection
rules, and the ease of theoretical interpretation by means of the linear
response time-dependent density functional theory, NLHFPS has the potential to
evolve into a powerful characterization method in nanoscience and
nanotechnology.
