A theoretical investigation of radiation field produced by a charge moving through the dielectric concentrator for Cherenkov radiation is performed for the general case where a charge trajectory is shifted with respect to the target axis. The idea of dielectric target with specific profile of the outer surface was presented and investigated in our previous papers for the symmetric case. Here we show how nonsymmetric field components generated in the bulk of the target affect field distribution near the focus where strong concentration of the energy occurs. Possible applications of this target are discussed.