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

• Published in: Optics and lasers in engineering 2012-12, Vol.50 (12), p.1706-1715
• Main Authors: Gómez-Varela, A.I., Flores-Arias, M.T., Bao-Varela, C., Gómez-Reino, C.
• Format: Article
• Language: English
• Subjects: Active material; Beam shaping; Beam transformation; Beams (radiation); Collimation; Focusing; Gain; Gaussian beams (optics); GRIN optics; Lenses; Matlab; Selfoc rod lens; Simulation
• ISSN: 0143-8166; 1873-0302
• DOI: 10.1016/j.optlaseng.2012.07.011

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 1mm and length 8. 252mm 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 4.936mm. Besides, an input Gaussian beam is focused by an active GRIN lens of semiaperture 1mm at a propagation length of 9.99mm, for both on-axis gain and loss material, being turned into a uniform collimated beam when the propagation length is 19.99mm. ► We propose active GRIN rods as extra-cavity compact laser beam shaping elements. ► Active GRIN materials work like quadratic phase transformers with a Gaussian mask. ► General conditions to obtain optical functions by active GRIN rods are determined. ► We evaluate irradiance and beam parameters evolution in active GRIN rod lenses. ► Simulation of uniform beams by active GRIN rod lenses is presented.