Design of GRIN laser beam shaping system

Geometrical optics is used for design of gradient-index (GRIN) laser beam shapers with the conditions of con- servation of energy and constant optical path length for all rays passing through the system. The exact ray intercepts for a Gaussian to top-hat beam transform at the output plane are the ray trace target values used during the optimization process. After constructing a beam shaping merit function, the commercial software ZEMAX has been used to minimize the merit function for a well known two-element plano-aspheric beam shaper to establish the effectiveness of this new beam shaping merit function. Then, this method is used to design of several GRIN laser beam shapers while using ZEMAX's catalog GRADIUM elements from LightPath glass types. The optical component shape and spacing parameters are also used for optimization variables. Both spherical surfaces and conic surfaces of the different elements of the GRIN laser beam shaper are studied. The ZEMAX software was used for performance analysis of the GRIN beam shapers and is discussed. In this paper, we present a new way to incorporate the conditions of conservation of energy and constant optical path length in the definition of a beam shaping merit function that has been used with ZEMAX22 optimization methods for design of GRIN beam shapers. In Sect. 2, we derive an expression for the output ray coordinate as a function of the input ray coordinate for a plane wave Gaussian beam transformed into a plane wave top-hat output beam. Then, we define a beam shaping merit function and give a brief describation on the ZEMAX optimization methods that will be used to design laser beam shapers by minimization of the merit function. In Sect. 3, results of using this method to design laser beam shapers are presented and discussed. The ZEMAX software has been applied to analyze the designed systems. Conclusions are given in Sect. 4.