  Existing methods for the localization of light at the nanoscale use either a
structure with negative permittivity, by exploiting subwavelength plasmonic
resonances, or a dielectric structure with a high refractive index, which
reduces the wavelength. In this paper, we provide an alternative to these two
methods based on a modification of the modes of dielectric resonators by means
of an active medium. We show that an active medium can promote subwavelength
light localization in the dielectric structure. We consider a dielectric layer
of size substantially smaller than a half-wavelength of light in the dielectric
medium, and demonstrate that at a certain value of gain in the active medium,
the phase change on reflection at the layer boundaries compensates for the
change in phase due to propagation over the layer. At this value of the gain,
the gain-assisted mode forms, in which the phase shift during a round trip of
the electromagnetic wave is zero. This gain-assisted mode exists only at a
positive gain in the dielectric medium, and can be used to create dielectric
lasers and sensors of subwavelength size.
