Micron-scale semiconductor, crystalline and polymer lasers exploit emission of light from the cavities made of active dielectric materials, which are able to display inversed population under pumping and thus provide optical gain [1–9]. They are intensively studied both experimentally and theoretically, as coherent sources of the visible, infrared and terahertz waves. Here, well developed etching and epitaxial technologies enable fabrication of thin planar cavities with controlled contour shape. Thus, the laser resonators either stand on small pedestals in free space or lay on a substrate, with in-plane dimensions comparable to and thickness much smaller than the optical wavelength.