Reconstruction of photonic crystal geometries using a reduced basis method for nonlinear outputs

Abstract

Moreover, I would like to thank Dr. Phillip Manley for proofreading parts of the manuscript pertaining ix to the English language. I acknowledge funding provided by the German Federal Ministry of Education and Research within the program NanoMatFutur (No. 03X5520) the Einstein Foundation Berlin through ECMath within subproject OT9. Parts of the results have been obtained in the scope of the Berlin Joint Lab for Optical Simulations for Energy Research (BerOSE) of HZB, ZIB and Freie Universität Berlin. I would like to thank the developers of the Scikit-learn Python library for providing a state-of-the-art, open-source and solid implementation of machine learning algorithms, without which the clustering results of this work would not have been obtained. The same holds for the active users and developers at news.povray.org, who guided me on the way to achieve a high quality animation of excitation enhancement using actual physical data. Finally, I would like to thank the members of my family who supported me all these years, no matter which path I walked. Specifically, I cannot express the gratitude I feel for the support, love and patience that Yvonne found for me-but I think you know. We went through a wonderful, but hard time. Thank you Levy for making me laugh, and cry; for letting me finish this project although you deserve all of my attention;-and for being the first miracle I have ever laid eyes on. x 7 Classification of Field Distributions Using Machine Learning 7.1 Justification of mode clustering .

Increased fluorescence of PbS quantum dots in photonic crystals by excitation enhancement

“…2. A comparison with the measured reflectance maps allowed us to reconstruct the exact geometrical parameters of the produced sample using the reduced basis method 28 . While a first guess from experimental scanning electron microscopic images yielded a silicon thickness of ∼ 130 nm and a hole diameter of ∼ 360 nm, the numerical reconstruction generated more exact values with a silicon thickness of 116 nm, a hole diameter of 367 nm and a lattice pitch of 600 nm.…”

Computing parametrized solutions for plasmonic nanogap structures

“…Recently, RB methods have been used for the time-harmonic Maxwell's equations in combination with DG [10,13,28,44] and integral [16,25] methods to successfully generate fast responses for complex electromagnetic devices, where the frequency and material properties are treated as parameters. Furthermore, there has been considerable work to incorporate geometry as a parameter for electromagnetic applications, using either affine geometry transformations [9,18,23,57] or parametrized meshes [22].…”

Machine learning classification for field distributions of photonic modes

“…More sophisticated techniques such as the reduced basis method 19 for finite element method (FEM) simulations have successfully been applied to speed-up this optimization process for large parameter spaces. Inverse design tasks introduce a high-dimensional input parameter space, typically by allowing for arbitrary changes in the permittivity distribution (r) of the nanostructure.…”

“…We directly apply the technique to a specific dataset of our previous publication on fluorescence enhancement of lead sulfide (PbS) quantum dots (QDs) on a silicon PhC slab surface 52 , however, without loss of generality. A similar setup was used in previous studies 19,53,54 .…”