Numerical design of three-dimensional gradient refractive index structures for beam shaping

A numerical design method is demonstrated for gradient refractive index (GRIN) beam shapers embedded in a medium. The three-dimensional refractive index profile ∆n(x, y, z) gradually changes the spatial characteristics of a beam during propagation. Diffraction effects such as beam expansion are controlled and compensated by the refractive index profile, resulting in efficient field transformations with no coherent artifacts. The solution is found using phase retrieval and a paraxial scalar wave beam propagation model. An example design is shown in which small changes in refractive index (∆n < 10⁻³) are used to transform a beam over a device length of 10 mm.