Focusing, collimation and beam shaping by active GRIN rod lenses: Theory and simulation

This work presents a theoretical analysis as well as the simulation of different optical functions that can be obtained from Gaussian beam transformations by active GRIN (GRadient-INdex) rod lenses having quadratic gain or loss. Profiles of the real and imaginary parts of the complex refractive index have been studied in order to show guidance behaviour and gain or loss effects of active rod lenses on the Gaussian beam propagation. General conditions for obtaining focusing, collimation and beam shaping by active rod lenses as circle diagrams plotted in the complex plane of the real and imaginary parts of the input complex curvature are discussed. MATLAB simulations of on-axis gain and loss selfoc GRIN rod lenses, acting as uniform beam shapers, focusers and collimators are presented. In particular, it is shown that an on-axis gain GRIN lens of semiaperture 1 mm and length 8.252 mm transforms an input Gaussian beam into a uniform beam. On the other hand, an on-axis loss GRIN lens with the same semiaperture can carry out the same transformation for a propagation length of 4.936 mm. Besides, an input Gaussian beam is focused by an active GRIN lens of semiaperture 1 mm at a propagation length of 9.99 mm, for both on-axis gain and loss material, being turned into a uniform collimated beam when the propagation length is 19.99 mm. (C) 2012 Elsevier Ltd. All rights reserved.