Continuous-relief fan-out elements with optimized fabrication tolerances

The design of kinoform fan-out elements with high efficiency and reduced sensitivity to vertical profile scaling errors is presented. We start from a high-efficiency continuous-phase fan-out solution and optimize the position of the 0-2π transitions in the phase function, in order to achieve a high fabrication-error tolerance. The sensitivity of Fourier-transform and focusing fan-out elements to vertical etch-depth errors is analyzed. The limitations for the fabrication of such structures by laser-beam writing are discussed. In particular, the influence of the finite writing-spot diameter on the fan-out performance is investigated. Design rules for fan-out elements, which consider fabrication constraints, are derived. Experimental results are presented for cylindrical focusing fan-out elements with small uniformity error (2) and weak profile scaling dependence.