Overcoming the Diffraction Limit on the Size of Dielectric Resonators Using an Amplifying Medium

Existing methods for the creation of subwavelength resonators use either structures with negative permittivity, by exploiting subwavelength plasmonic resonances, or dielectric structures with a high refractive index, which reduce the wavelength. Here, we provide an alternative to these two methods based on a modification of the modes of dielectric resonators by means of an active medium. On the example of the dielectric active layer of size substantially smaller than a half-wavelength of light, we demonstrate that there is a gain at exceeding of which the change in phase due to the reflection at the layer boundaries compensates the change in phase due to propagation over the layer. Above this value of the gain, an unconventional mode forms, in which the phase shift after a round-trip of the light is zero. We show that this mode can be exploited to create a laser, the size of which is much smaller than the wavelength of the generated light and scales inversely with the square of absolute value of the refractive index in the active medium. Our results pave the way to creation of dielectric lasers of subwavelength size.