J. Eur. Opt. Society-Rapid Publ. 2025, 21, 4 Ó The Author( s), published by EDP Sciences, 2025 https:// doi. org / 10.1051 / jeos / 2024049 Available online at: https:// jeos. edpsciences. org
Journal of the European Optical Society-Rapid Publications
RESEARCH ARTICLE
Fast simulation of the influence of a refractive free-form microstructure on a wave field based on scalar diffraction theory
Fabian Thiemicke 1, 2,*
, Ramy El-Bashar 3, 4, Mohamed F. M. Hameed 5, 6, Mostafa Agour 1, 7, Salah S. A. Obayya 4, 8, Ralf B. Bergmann 1, 9, and Claas Falldorf 1
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
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.
Keywords: Refractive micro structure, Scalar diffraction, Nanojet, Wave field propagation.
1 Introduction
In the field of nanophotonics, the precise control and manipulation of light is of key relevance. Here, photonic nanojets represent a well described and demonstrated method of diffracting light below the classical diffraction limit [ 1 – 3 ]. For the generation of photonic nanojets, typically dielectric microspheres or other nanostructures are used. In order to understand and realize photonic nanojets’ potential, sophisticated and time-efficient simulation techniques play a crucial role. The simulation of photonic nanojets is typically based on a numerical solution of Maxwell’ s equations. In the case of spherical elements, Mie theory [ 4 ] offers a suitable and efficient basis for understanding the interaction of light with circular symmetric
* Corresponding author: thiemicke @ bias. de dielectric structures and the formation of photonic nanojets [ 5, 6 ]. Microstructures which are not spherical require more involved methods such as Finite-Difference Time-Domain( FDTD) simulation [ 1, 7, 8 ]. The shape of microstructures is a significant parameter for the properties of photonic nanojets, especially in terms of the size and position of the focus spot of the nanojet [ 6, 8 – 10 ]. For the purpose of shape optimization it would be very important to simulate a large number of different geometries in a short time and optimize the shape of the micro structures to achieve the expected properties. As explained above, Mie theory is limited to circular symmetric structures [ 5 ]. In the case of more complex structures or cylinders, usually FDTD methods are used to solve Maxwell’ s equations. A disadvantage of these methods is the high computational effort and the resulting computation times of several hours for each structure [ 11 ]. The approach is thus not practical for numerical
This is an Open Access article distributed under the terms of the Creative Commons Attribution License( https:// creativecommons. org / licenses / by / 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.