Iterative optimization approach for the design of diffractive phase elements simultaneously implementing several optical functions

A new iterative optimization method based on the Yang–Gu (Y-G) algorithm for the design of diffractive phase elements (DPE’s) that incorporate several optical functions is presented. The Y-G algorithm has been previously used to deal with various amplitude-phase retrieval problems in linear optical transform systems involving a monochromatic wave. We extend the general theory to the case of linear imaging systems with the illumination consisting of a number of components at different wavelengths. Based on a rigorous mathematical derivation, an iterative algorithm is developed to integrate several functions into one DPE. In the first set of examples numerical simulations are carried out in the design of several one-dimensional DPE’s capable of both demultiplexing different wavelength components and focusing each component wave. The second example illustrates the design of a two-dimensional DPE that performs as a demultiplexer in one direction and an array generator in the other direction.