We explore the profiles of off-diagonal components of frequency-dependent linear, first, and second nonlinear polarizabilities of impurity doped quantum dot. The dopant propagates in an environment that damps the motion. Simultaneous presence of noise inherent to the system has also been considered. The dopant has a Gaussian potential and noise considered is a Gaussian white noise. Noise-damping coupling strength appears to be the key parameter that designs the profiles of polarizability components. The frequency of external field also affects the profiles of Polarizability components. The present investigation highlights some interesting features in the optical properties of doped quantum dots. (C) 2014 Elsevier B.V. All rights reserved.