Design of harmonic diffractive optical elements for generating prescribed intensity distributions

We propose a method for designing diffractive optical elements (DOEs) with a smooth phase function generalizing harmonic diffractive lenses and intended for generating a prescribed intensity distribution at several harmonic wavelengths. In this method, the phase function is represented as an expansion over a certain set of smooth and differentiable functions. The expansion coefficients are considered as optimization parameters and are calculated using a gradient method from the condition of minimizing an error function describing the deviation of the generated intensity distribution from the prescribed one. We present examples of calculating harmonic DOEs with phase functions modulo 2πM, M>1 represented as a sum of B-splines. We show that in order to obtain good performance of a harmonic DOE, the error function has to take into account not only the intensity distribution generated at the central wavelength but also the distributions formed at the other harmonic wavelengths of interest. The obtained theoretical results are confirmed by the results of an experimental investigation, including the fabrication of the designed harmonic DOE using the direct laser writing technique and measurement of the generated intensity distributions.