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J. Eur. Opt. Society-Rapid Publ. 21, 4( 2025)
Figure 1. Schematic representation of the calculation of the wavefront for a dielectric microsphere. a) Slicing the simulation volume with a micro sphere with refractive index n 1 in an environment with n 0 into M separate layers with a thickness Dz. Scheme of the calculation of the wave front U m for a layer with 2 different refractive indices( n 0 and n 1). In( i) the regions with different refractive indices n i are identified. The wavefront U m �1 serves in( ii) as input wavefront and will be propagated over the distance Dz. The propagation is determined separately for each refractive index( n 0 and n 1) resulting in the wavefronts U m, n 0 and U m, n 1. Finally, these wavefronts will be combined in( iii) to U m.
Figure 2. Flowchart of the simulation of a 3D microstructure with N different refractive indices n i and M layers with a layer thickness Dz. During the calculation of the 3D wave front stack, there are 2 loops. The outer loop( bold lines) represents the propagation of the M layers( see Fig. 1a)). The inner loop is used to calculate the wavefront U m with several refractive indices n i( see Fig. 1b)).
indices to calculate the wavefront behind the actual layer at the distance Dz. The individual refractive indices can also be complex and contain an individually defined absorption for each refractive index. An individual absorption was, however, not taken into account for the validation described in the following sections. The 2-dimensional( 2D) wavefront is subsequently stored in a stack to generate the 3D wavefront information. This procedure is then repeated for all M layers. In each case, the wavefront of the previous layer is used as the input wavefront for the currently calculated layer.
Figure 2 shows a flow chart of the simulation of the entire structure and their influence on the wavefront. The calculation of the influence of the refractive index distribution on the wavefront is performed in two loops.
An outer loop calculates the influence of a complete layer on the wavefront at a distance Dz while the inner loop calculates the influence of the different refractive indices inside the layer.
3 Simulation results and experimental verification
3.1 Intensity calculation and validation
To validate the introduced FRISP method for the computation of focusing properties of optical micro structures with a size in the single- to double-digit micrometer range by methods of coherent optics, a comparison of different simu-