Theoretical modeling of photo-induced lens formation in a polymerizable matrix containing quantum dots

Abstract

We present a theoretical model describing the dynamic modulation of the refractive index of quantum dots (QDs) containing a photopolymerizable mixture under spatially non-uniform illumination. The case of a laser beam with Gaussian spatial intensity distribution is used to model the process of non-uniform polymerization, followed by the processes of diffusion of monomers, polymers, and QDs. This results in the creation of a lens-like refractive index transversal distribution. The contribution of QDs is taken into account by using the conservation of the sum of volume fractions of polymers, monomers, and QDs. Dynamic variations of different parameters influencing the lens formation and the focal length of the lens are obtained. In particular, it is shown how the change of time of irradiation varies the profile of the refractive index and, hence, controls the focal length of the lens.