Design methods are illustrated to produce beam shaping elements in which the refractive index is a continuous function of position. An index profile yielding a desired gradual transformation of the field can be computed in two ways. A ray theory approach yields a solution consistent with the eikonal equation, while diffraction effects can be incorporated into the index profile by using a split step representation of the medium and performing a series of phase retrieval calculations. The methods are demonstrated in an example of mode conversion and coherent laser beam combining, where a near-unity conversion efficiency can theoretically be achieved.
The refractive index profile of one-dimensional gradient-index (GRIN) samples can be measured using the incident and exit beam angles of multiple beams passing through the sample at different positions along the index gradient. Beginning from a region of known refractive index, the collective angular deflection measurement of multiple beams is bootstrapped to compute the index profile of the entire sample. An alternative method using an approximate beam displacement model and a corrective algorithm is also presented. The two techniques are used to measure the index profile of a thick GRIN sample, and experimental results show good agreement with a maximum discrepancy of 1.5×10 −3 in the calculated index. An index accuracy of 5×10 −4 is predicted for the bootstrap method employing typical micron-level spatial measurements.