Research Article

Fast simulation of the influence of a refractive free-form microstructure on a wave field based on scalar diffraction theory

¹ BIAS-Bremer Institut für angewandte Strahltechnik, Klagenfurter Str. 5, 28359 Bremen, Germany
² University of Bremen, Faculty of Physics and Electrical Engineering, Otto-Hahn-Allee 1, 28359 Bremen, Germany
³ National Institute of Laser Enhanced Sciences (NILES), Cairo University, 12613 Giza, Egypt
⁴ Centre for Photonics and Smart Materials, Zewail City of Science, Technology and Innovation, October Gardens, 6th of October City, 12578 Giza, Egypt
⁵ Center for Nanotechnology, Zewail City of Science, Technology and Innovation, October Gardens, 6th of October City, 12578 Giza, Egypt
⁶ Mathematics and Engineering Physics Department, Faculty of Engineering, University of Mansoura, 35516 Mansoura, Egypt
⁷ Faculty of Science, Department of Physics, Aswan University, 81528 Aswan, Egypt
⁸ Electronics and Communications Engineering Department, Faculty of Engineering, University of Mansoura, 35516 Mansoura, Egypt
⁹ University of Bremen, MAPEX Center for Materials and Processes and Faculty of Physics and Electrical Engineering, Otto-Hahn-Allee 1, 28359 Bremen, Germany

^* Corresponding author: thiemicke@bias.de

Received: 7 November 2024
Accepted: 16 December 2024

Abstract

We present a novel fast simulation approach to simulate the influence of refractive freeform microstructures on a wave field. The FRISP (Finite Refractive Index Selective Propagation) method combines the Rayleigh-Sommerfeld diffraction integral with a thin element approximation and provides a comprehensive framework for understanding the optical properties of these microstructures. The main advantage of this method is its reduced complexity, which leads to a remarkable reduction in computation time by more than two orders of magnitude compared to finite-difference time-domain (FDTD) methods. This efficiency facilitates the iterative optimization of refractive microstructures and thus represents a practical tool to improve this type of microstructures. The verification of the FRISP method is realized by comparing the focal position and spot size of refractive microstructures. For this purpose, we compare FDTD, Mie theory and experimental data on microspheres with the predictions of FRISP. This comparison demonstrates the robustness and reliability of the approach, emphasizes its validity and demonstrates it as a valuable tool for the design and analysis of microstructures.