Beam shaping algorithm with optimization parameters

In this article, we present a general mode-conversion algorithm allowing to build an optical system composed of an alternation of phase masks and free propagations. The originality of our approach lies in the introduction of free parameters that can be used to perform an optimization regarding some properties of interest. Here, we apply this algorithm to overlap balancing, for the conversion of an important number of modes with limited phase resources. Moreover, we discuss about the convergence and the limitations of such an algorithm, notably concerning the loss of unitarity that tends to occur in a practical implementation.