Numerical gradient-index design for coherent mode conversion

We present a numerical gradient-index (GRIN) design methodology for application in coherent mode conversion. Within the framework of geometric optics, a one-to-one correspondence between the field description and the ray description of the propagating beam is established using optical path lengths and the conservation of energy within a bundle of rays. A family of ray paths is chosen to transform the initial ray distribution into a target ray distribution. The specified ray paths are used to calculate the index profile of the GRIN structure required to effect the gradual transformation from the input beam to the desired output beam. We demonstrate our approach with a GRIN structure design that converts a Gaussian beam into a flat-top beam.