Gradient method for designing cascaded DOEs focusing radiation of different wavelengths

The design of cascaded diffractive optical elements (DOEs) generating several specified intensity distributions for several incident beams with different wavelengths is considered. The problem of designing a cascaded DOE is formulated as that of minimizing a functional that depends on the height functions of the diffractive microrelief of the cascaded DOEs and represents the error in the generation of specified intensity distributions at the operating wavelengths. Explicit expressions are obtained for the derivatives of the functional, and on this basis, a gradient method for designing cascaded DOEs is formulated. Using the gradient method, cascaded DOEs are calculated, which focus optical radiation of three different wavelengths into three different regions. The presented numerical simulation results demonstrate good performance of the proposed method.