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.
W. Minster Kunkel and James R. Leger, "Numerical design of gradient-index beam shapers," Proc. SPIE 10090, Laser Resonators, Microresonators, and Beam Control XIX, 100900Y (Presented at SPIE LASE: January 31, 2017; Published: 20 February 2017); https://doi.org/10.1117/12.2253122.
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