  We consider the design of cascaded diffractive optical elements (DOEs) for
generating specified intensity distributions for several incident beams with
different wavelengths. For each incident beam with a given wavelength, the
cascaded DOE forms a different specified intensity distribution. The problem of
DOE design is formulated as the problem of minimizing a functional that depends
on the functions of diffractive microrelief height of the cascaded DOE and
represents the deviations of the intensity distributions generated at the
operating wavelengths from the specified ones. Explicit expressions are
obtained for the derivatives of the functional, and on this basis, a gradient
method for calculating a cascaded DOE is formulated. The proposed gradient
method is used for the calculation of cascaded DOEs focusing radiation of three
different wavelengths into different areas. In particular, the calculation of a
cascaded DOE generating a complex color image of parrots is considered. The
presented numerical simulation results demonstrate high performance of the
proposed method.
