A linear variational route is explored for computing the first non-linear polarizability (beta) of single carrier quantum dots with anharmonicity in the confinement potential. Variations in beta with variations in the strength of the confining potential (omega(0)), the perpendicular magnetic field strength (omega(c)) and the strength of a specific form of anharmonic coupling (lambda) are analyzed. A 2 x 2 model is used to predict analytically the nature of lambda, omega(c) and omega(0) dependence of P and compare with what is obtained from a more detailed calculation. (C) 2004 Elsevier B.V. All rights reserved.