Source code and simulation results for the computation of eigenfrequency sensitivities using Riesz projections for efficient optimization of nanophotonic resonators (Q728): Difference between revisions

Summary Data and source code relate to the article Computation of eigenfrequency sensitivities using Riesz projections for efficient optimization of nanophotonic resonators [1]. It combines direct differentiation of scattering problems with a contour integral method [2]to compute eigenfrequency sensitivities. An optimization is used to demonstrate the relevance of the method. Structure The most important elements of this publication are the MATLAB scripts sensitivities.m and optimization.m, which can be used to reproduce the most important results of the paper. The directoriescode,scatteringandresultscontain the software RPExpand[3], input files for JCMsuite [4] and results produced with the scripts, respectively. Furthermore, the latter contains the subfoldertabulated,which contains text filestabulatingdata presentedin Figures 2 and 4 of the paper. Eventually, the function code/observation.m evaluates the target for the optimization. Additional Information The applicaton is based on an example from the literature [5]. Using apriori knowledge about the eigenmode of interest, we chose the scalar observable, as defined in Section B of the paper, to bethe component of the electric field normal to the plane defining the solidof revolution. The convergence studies are based on the discrete, circular contour\(\tilde{C} = \big\{ c_n~|~ c_n=r_0 e^{2\pi i n/8}, n \in \{0,1,...,7\}\big\}\)with center \(\omega_0 = 2 \pi c/(1600~\mathrm{nm})\)and radius \(r_0 = \omega_0\times10^{-2}\). For finite element degrees \(d\) higher than 5, the error saturates. For this reason, the differences between results for \(d=5\) and \(d = 6\) may depend on the hardware architecture. A larger radius\(r = 4\times10^{13}\) has been chosen for the optimization to include information from poles located further away from the frequency of interest. The target function \(t(p_1,\dots,p_5) = -q_n \left(1 - \frac{(\omega_n-\omega_0)^2}{r^2} \right)\)is minimized. The first factor is the negative Q-Factor and the second factor ensures that the target is zero at the boundary. If no eigenfrequency\(\omega_n\)is located inside the contour, the target is set to zero. For the purpose of this data publication some numerical parameters have been improved. This resulted in a faster convergence of the optimization. Requirements JCMsuite (version 5.2.0 or newer) MATLAB (tested with version R2019b) In order to run the scripts you must replace the corresponding place holders in the files bya path to your installation of JCMsuite. Free trial licenses are available, please refer to the homepage ofJCMwave. References [1] Felix Binkowski, Fridtjof Betz, Martin Hammerschmidt, Philipp-Immanuel Schneider, Lin Zschiedrich, Sven Burger,Computation of eigenfrequency sensitivities using Riesz projections for efficient optimization of nanophotonic resonators, Communications Physics5, 202(2022),https://doi.org/10.1038/s42005-022-00977-1 [2] Felix Binkowski, Lin Zschiedrich,Sven Burger,A Riesz-projection-based method for nonlinear eigenvalue problems,Journal of Computational Physics419, 109678 (2020),https://doi.org/10.1016/j.jcp.2020.109678 [3]Fridtjof Betz, Felix Binkowski, Sven Burger, RPExpand: Software for Riesz projection expansion of resonance phenomena, SoftwareX 15,100763 (2021), https://doi.org/10.1016/j.softx.2021.100763 [4] Jan Pomplun, Sven Burger, Lin Zschiedrich, Frank Schmidt,Adaptive finite element method for simulation of optical nano structures, Physica Status Solidi B244, 3419 (2007),http://dx.doi.org/10.1002/pssb.200743192 [5]Kirill Koshelev, Sergey Kruk, Elizaveta Melik-Gaykazyan, Jae-Hyuck Choi, Andrey Bogdanov, Hong-Gyu Park, Yuri Kivshar,Subwavelength dielectric resonators for nonlinear nanophotonics, Science367, 288 (2020), http://dx.doi.org/%2010.1126/science.aaz3985