Gain-loss inhomogeneity sensing by dielectric metasurfaces operated on the trapped mode

Dielectric metasurfaces are a promising platform for implementing lasers and sensors. This paper proposes a metasurface operated on a trapped mode that strongly responds to gain-loss perturbations. The metasurface under study is made of dielectric disk-shaped resonators regularly arranged on a thick substrate and covered by a superstrate. The perturbations are caused by the inhomogeneity of the doping of the superstrate or semiconductor disks. The randomized Weierstrass function describes the dielectric properties of an inhomogeneous substance. The presence of inhomogeneity in the constitutive material leads to the appearance of radiative losses, which in turn results in the trapped mode excitation in the metasurface. Thus, the resonance quality factor can be considered as a measure of the inhomogeneity in the doped material.