Iterative calculation of diffractive optical elements focusing into a three-dimensional domain and onto the surface of the body of rotation

The present paper deals with algorithms for calculating phase diffractive elements aimed at focusing the laser light into three-dimensional domains or onto the surface of the body of rotation. The algorithms are based on the expansion of the desired transmission function of the optical element in terms of a suitable orthogonal basis. The moduli of the expansion coefficients are assumed to be pre-given, whereas the arguments are free parameters of the task. Calculational results of focusing onto the surface of a diverging and a converging cone and onto the surface of a circular cylinder are presented.