  We consider an arbitrary quantum mechanical system, initially in its
ground-state, exposed to a time-dependent electromagnetic pulse with a carrier
frequency $\omega_0$ and a slowly varying envelope of finite duration. By
working out a solution to the time-dependent Schr\"odinger equation in the
high-$\omega_0$ limit, we find that, to the leading order in $\omega_0^{-1}$, a
perfect self-cancellation of the system's linear response occurs as the pulse
switches off. Surprisingly, the system's observables are, nonetheless,
describable in terms of a combination of its linear density response function
and nonlinear functions of the electric field. An analysis of jellium slab and
jellium sphere models reveals a very high surface sensitivity of the considered
setup, producing a richer excitation spectrum than accessible within the
conventional linear response regime. On this basis, we propose a new
spectroscopic technique, which we provisionally name the Nonlinear
High-Frequency Pulsed Spectroscopy (NLHFPS). Combining the advantages of the
extraordinary surface sensitivity, the absence of constraints by the
traditional dipole selection rules, and the clarity of theoretical
interpretation utilizing the linear response time-dependent density functional
theory, NLHFPS has a potential to evolve into a powerful characterization
method for nanoscience and nanotechnology.
