  We report a critical narrowing of resonances of a driven potential well, when
their eigenfrequencies approach the edge of the continuum. The resonances also
obtain unusual sharp-peak shapes at the continuum boundary. The situation can
be realized for the electromagnetic wave propagating across the dielectric thin
films with a periodically modulated interface(s). We show the general
phenomenon semi-analytically on a simplified model of a driven quantum
potential well, also by rigorous numerical analysis of Maxwell equations for
the wave propagation across the thin film with a modulated interface(s). We
justify the phenomenon experimentally, by the measurements of light reflection
from the dielectric thin film deposited on a periodically modulated surface.
The narrow and sharp-peak resonances can be used for an efficient narrow-band
frequency- and spatial filtering of light.
