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# General Solution of Two-Dimensional Beam-Shaping with Two Surfaces

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## Abstract

Beam shaping is a technique, by which a known input irradiance is transformed into a desired output irradiance by changing the local propagation vector of the wave front. Unlike one-dimensional beam-shaping, which leads to a simple differential equation which can be integrated in a straight forward manner, the two-dimensional beam shaping problem leads to a Monge–Ampere type equation, which is difficult to solve. In this paper, we generalize the problem to refractive and reflective systems and use the shifted-base-function approach to obtain a general solution.

## Keywords

Order Partial Derivative Beam Shaping Exit Plane Surface Gradient Entrance Plane
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