It is proposed a novel approach to increase considerably the sensitivity and dynamic range of optical sensors by exploiting more beneficial than linear relation between the shifts of resonant frequency and the length of optical resonator (OR). This is achieved by means of inserting in OR a medium with transparent anomalous dispersion. When appropriately designed that medium eliminates conventional linear dependence between the shifts of OR length and its resonant frequency. Then resonant frequency becomes proportional to the square or cubic root upon the shift of OR length so is highly increased. Due to that the performance of such sensor improves considerably, enabling detection of extremely small displacements and rotation rates.