The refractor problem in reshaping light beams (Q834764)

This paper is concerned with the study of some refraction phenomena in connection with the synthesis of refracting surfaces capable of reshaping the intensity of a light beam. Using energy conservation arguments, the authors formulate the concept of a weak solution to the refractor problem. Then it is established the existence and uniqueness of solutions, converting the problem into an optimal mass transfer problem with a suitable cost function. Most of the arguments are variational and the authors study the refractor problem both in the case \(\kappa<1\) and if \(\kappa>1\).