TY - JOUR A1 - Gutsche, Philipp A1 - Schneider, Philipp-Immanuel A1 - Burger, Sven A1 - Nieto-Vesperinas, Manuel T1 - Chiral scatterers designed by Bayesian optimization JF - J. Phys.: Conf. Ser. Y1 - 2018 U6 - https://doi.org/10.1088/1742-6596/963/1/012004 VL - 963 SP - 012004 ER - TY - JOUR A1 - Gutsche, Philipp A1 - Santiago, Xavier Garcia A1 - Schneider, Philipp-Immanuel A1 - McPeak, Kevin A1 - Nieto-Vesperinas, Manuel A1 - Burger, Sven T1 - Role of Geometric Shape in Chiral Optics JF - Symmetry Y1 - 2020 U6 - https://doi.org/10.3390/sym12010158 VL - 12 SP - 158 ER - TY - CHAP A1 - Schneider, Philipp-Immanuel A1 - Santiago, Xavier Garcia A1 - Binkowski, Felix A1 - Gutsche, Philipp A1 - Höhne, Theresa A1 - Hammerschmidt, Martin A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - Light Management for Engineering Luminescence in Nanoscale Environments By Numerical Optimization T2 - The Electrochemical Society, Meeting Abstracts Y1 - 2018 U6 - https://doi.org/10.1149/MA2018-01/16/1164 SN - 2151-2043 VL - 16 SP - 1164 ER - TY - CHAP A1 - Gregersen, Niels A1 - de Lasson, Jakob Rosenkrantz A1 - Frandsen, Lars Hagedorn A1 - Kim, Oleksiy S. A1 - Breinbjerg, Olav A1 - Wang, Fengwen A1 - Sigmund, Ole A1 - Ivinskaya, Aliaksandra A1 - Lavrinenko, Andrei A1 - Gutsche, Philipp A1 - Burger, Sven A1 - Häyrynen, Teppo A1 - Merk, Jesper T1 - Comparison of five numerical methods for computing quality factors and resonance wavelengths in photonic crystal membrane cavities T2 - CLEO/Europe-EQEC Y1 - 2017 U6 - https://doi.org/10.1109/CLEOE-EQEC.2017.8087750 ER - TY - CHAP A1 - Gregersen, Niels A1 - Rosenkrantz de Lasson, Jakob A1 - Hagedorn Frandsen, Lars A1 - Häyrynen, Teppo A1 - Lavrinenko, Andrei A1 - Moerk, Jesper A1 - Wang, Fengwen A1 - Sigmund, Ole A1 - Kim, Oleksiy S. A1 - Breinbjerg, Olav A1 - Ivinskaya, Aliaksandra A1 - Gutsche, Philipp A1 - Burger, Sven T1 - Benchmarking five computational methods for analyzing large photonic crystal membrane cavities T2 - Numerical Simulation of Optoelectronic Devices (NUSOD) Y1 - 2017 U6 - https://doi.org/10.1109/NUSOD.2017.8010005 SP - 89 ER - TY - JOUR A1 - de Lasson, Jakob Rosenkrantz A1 - Frandsen, Lars Hagedorn A1 - Gutsche, Philipp A1 - Burger, Sven A1 - Kim, Oleksiy S. A1 - Breinbjerg, Olav A1 - Ivanskaya, Aliaksandra A1 - Wang, Fengwen A1 - Sigmund, Ole A1 - Häyrynen, Teppo A1 - Lavrinenko, Andrei A1 - Mork, Jesper A1 - Gregersen, Niels T1 - Benchmarking five numerical simulation techniques for computing resonance wavelengths and quality factors in photonic crystal membrane line defect cavities JF - Opt. Express Y1 - 2018 U6 - https://doi.org/10.1364/OE.26.011366 VL - 26 SP - 11366 ER - TY - GEN A1 - Gutsche, Philipp A1 - Nieto-Vesperinas, Manuel A1 - Mäusle, Raquel A1 - Burger, Sven T1 - Chiral Nanophotonics: Theory and Simulation T2 - Doctoral Summer School on Nanophotonics and Metamaterials, ITMO University N2 - The interaction of light and chiral matter is subject of recent research both in fundamental science and applications. Among these are the helicity of electromagnetic fields described with the optical chirality density and emitters sensitive to circular polarization employed in quantum communications. In the weak coupling regime of chiral emitters, we analyze the conversion of chirality which can be regarded as an analogue to absorption of energy describing the change of circular polarization of the incident field. This enables the tailoring of chiral near-fields close to metamaterials, e.g. composed of gold helices, and gives insights into extinction measurements such as circular dichroism. We show relation of the weak and strong coupling regime. The latter can be modelled with cross electric-magnetic polarizabilities or with effective chiral materials, i.e. bi-anisotropic media. Accordingly, we motivate the necessity for rigorous numerical simulations to accurately describe chiral light-matter interaction. Y1 - 2017 ER - TY - GEN A1 - Gutsche, Philipp A1 - Burger, Sven A1 - Nieto-Vesperinas, Manuel T1 - Fundamentals and Applications of an Optical Theorem for Chiral Optical Fields T2 - 4th International Conference on Optical Angular Momentum N2 - The helicity of light is of great interest in both fundamental research and in applications such as dichroism spectroscopy. Its time-harmonic formulation is directly proportional to the density of optical chirality. Recently, both an helicity optical theorem (HOT) and a chirality conservation law (CCL) have been formulated for arbitrary scatterers taking into account an underlying continuity equation of this quantity. We summarize these two equivalent fundamental laws and analyze their potential applications. Y1 - 2017 ER - TY - CHAP A1 - Novitsky, Andrey A1 - Rosenkrantz de Lasson, Jakob A1 - Hagedorn Frandsen, Lars A1 - Gutsche, Philipp A1 - Burger, Sven A1 - Kim, Oleksiy S. A1 - Breinbjerg, Olav A1 - Ivinskaya, Aliaksandra A1 - Wang, Fengwen A1 - Sigmund, Ole A1 - Häyrynen, Teppo A1 - Lavrinenko, Andrei A1 - Mørk, Jesper A1 - Gregersen, Niels T1 - Comparison of five computational methods for computing Q factors in photonic crystal membrane cavities T2 - 19th International Conference on Transparent Optical Networks (ICTON) Y1 - 2017 U6 - https://doi.org/10.1109/ICTON.2017.8024813 ER - TY - JOUR A1 - Poulikakos, Lisa A1 - Gutsche, Philipp A1 - McPeak, Kevin A1 - Burger, Sven A1 - Niegemann, Jens A1 - Hafner, Christian A1 - Norris, David T1 - The Optical Chirality Flux as a Useful Far-Field Probe of Chiral Near Fields JF - ACS Photonics Y1 - 2016 U6 - https://doi.org/10.1021/acsphotonics.6b00201 VL - 3 SP - 1619 ER - TY - JOUR A1 - Gutsche, Philipp A1 - Poulikakos, Lisa A1 - Hammerschmidt, Martin A1 - Burger, Sven A1 - Schmidt, Frank T1 - Time-harmonic optical chirality in inhomogeneous space JF - Proc. SPIE Y1 - 2016 U6 - https://doi.org/10.1117/12.2209551 VL - 9756 SP - 97560X ER - TY - GEN A1 - Gutsche, Philipp A1 - Poulikakos, Lisa A1 - Burger, Sven A1 - Hammerschmidt, Martin A1 - Schmidt, Frank T1 - Optical chirality: conservation law in arbitrary space T2 - 606. WE-Heraeus-Seminar on Nanophotonics and Complex Spatial Modes of Light N2 - The introduction of the near-field quantity of optical chirality has emerged in various numerical and few experimental studies of local chirality enhancement due to its relation to the excitation rate of chiral molecules. This time-even pseudoscalar has been dismissed as being a higher-order version of helicity. Nevertheless, we revisit the derivation of the underlying conservation law and define optical chirality in media similar to. We identify the mechanism of chirality conversion by either inhomogeneous or anisotropic space to complement the conservation of optical chirality. The conservation law of optical chirality in arbitrary space enables the extension of the concept of polarization to the near-field where no distiniguished propagation direction of light is present. We show that the connection of electromagnetic energy and optical chirality provide the ability to define a circular polarization basis in time-harmonic near-field analysis. In order to illustrate our theory, we present electromagnetic field simulations of simple as well as more complex nanostructures. Results using the well-known far-field polarization concept are readily reproduced and extended from the point of view of chirality conversion. Y1 - 2016 ER - TY - GEN A1 - Gutsche, Philipp A1 - Läuter, Matthias A1 - Schmidt, Frank T1 - Parameter-dependent Parallel Block Sparse Arnoldi and Döhler Algorithms on Distributed Systems N2 - We summarize the basics and first results of the analyses within our ZIB Bridge Project and give an outlook on further studies broadening the usage of hardware acceleration within the Finite Element Method (FEM) based solution of Maxwell’s equations. T3 - ZIB-Report - 16-15 KW - Generalized Eigenvalue Problem KW - Many Integrated Core Coprocessor (MIC) KW - Finite Element Method Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-58202 SN - 1438-0064 ER - TY - JOUR A1 - Pomplun, Jan A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Gutsche, Philipp A1 - Schmidt, Frank T1 - Method for fast computation of angular light scattering spectra from 2D periodic arrays JF - Proc. SPIE Y1 - 2016 U6 - https://doi.org/10.1117/12.2219666 VL - 9778 SP - 977839 ER - TY - CHAP A1 - Gutsche, Philipp A1 - Mäusle, Raquel A1 - Burger, Sven T1 - Tailoring local optical chirality in helical metamaterials T2 - 2016 10th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics Y1 - 2016 U6 - https://doi.org/10.1109/MetaMaterials.2016.7746440 SP - 73 EP - 75 ER - TY - GEN A1 - Wilson, Jon A1 - Herrmann, Sven A1 - Gutsche, Philipp A1 - Burger, Sven A1 - McPeak, Kevin T1 - The Chiral Coefficient: Rapid Optimization of Broadband Plasmonic Chirality T2 - 2016 MRS Fall Meeting & Exhibit Y1 - 2016 ER - TY - JOUR A1 - Abass, Aimi A1 - Gutsche, Philipp A1 - Maes, Bjorn A1 - Rockstuhl, Carsten A1 - Martins, Emiliano R T1 - Insights into directional scattering: from coupled dipoles to asymmetric dimer nanoantennas JF - Opt. Express N2 - Strong and directionally specific forward scattering from optical nanoantennas is of utmost importance for various applications in the broader context of photovoltaics and integrated light sources. Here, we outline a simple yet powerful design principle to perceive a nanoantenna that provides directional scattering into a higher index substrate based on the interference of multiple electric dipoles. A structural implementation of the electric dipole distribution is possible using plasmonic nanoparticles with a fairly simple geometry, i.e. two coupled rectangular nanoparticles, forming a dimer, on top of a substrate. The key to achieve directionality is to choose a sufficiently large size for the nanoparticles. This promotes the excitation of vertical electric dipole moments due to the bi-anisotropy of the nanoantenna. In turn, asymmetric scattering is obtained by ensuring the appropriate phase relation between the vertical electric dipole moments. The scattering strength and angular spread for an optimized nanoantenna can be shown to be broadband and robust against changes in the incidence angle. The scattering directionality is maintained even for an array configuration of the dimer. It only requires the preferred scattering direction of the isolated nanoantenna not to be prohibited by interference. Y1 - 2016 U6 - https://doi.org/10.1364/OE.24.019638 VL - 24 IS - 17 SP - 19638 EP - 19650 ER - TY - GEN A1 - de Lasson, Jakob Rosenkrantz A1 - Frandsen, Lars Hagedorn A1 - Burger, Sven A1 - Gutsche, Philipp A1 - Kim, Oleksiy S. A1 - Breinbjerg, Olav A1 - Sigmund, Ole A1 - Mork, Jesper A1 - Gregersen, Niels T1 - Comparison of four computational methods for computing Q factors and resonance wavelengths in photonic crystal membrane cavities T2 - Proceedings of the 7th International Conference on Metamaterials, Photonic Crystals and Plasmonics Y1 - 2016 UR - http://jakobrdl.dk/presentationfiles/2016/META16Poster_Niels_July2016.pdf ER - TY - JOUR A1 - Gutsche, Philipp A1 - Mäusle, Raquel A1 - Burger, Sven T1 - Locally Enhanced and Tunable Optical Chirality in Helical Metamaterials JF - Photonics Y1 - 2016 U6 - https://doi.org/10.3390/photonics3040060 VL - 3 SP - 60 ER - TY - CHAP A1 - Gutsche, Philipp A1 - Mäusle, Raquel A1 - Burger, Sven T1 - Circular polarization phenomena in chiral nano-optical devices T2 - Light, Energy and the Environment 2016 Y1 - 2016 U6 - https://doi.org/10.1364/FTS.2016.JW4A.4 SP - JW4A.4 ER - TY - JOUR A1 - Gutsche, Philipp A1 - Nieto-Vesperinas, Manuel T1 - Optical Chirality of Time-Harmonic Wavefields for Classification of Scatterers JF - Sci. Rep. Y1 - 2018 U6 - https://doi.org/10.1038/s41598-018-27496-w VL - 8 SP - 9416 ER - TY - GEN A1 - Gutsche, Philipp A1 - Judd, Thomas A1 - Schmidt, Frank T1 - A convergence study of different Rigorous Coupled Wave Analysis (RCWA) approaches to time-harmonic electromagnetic scattering problems with applications to nanooptical structures T2 - Verhandlungen der Deutschen Physikalischen Gesellschaft (DPG-Frühjahrstagung Berlin 2014) N2 - Reliable numerical simulations of nano-optical structures are the key for design and pre-fabrication processes in diverse disciplines such as lithography in semiconductor industries, spectroscopy of biological molecules, optimization of quantum dot cavities for single-photon sources, and computation of atomic forces like the Casimir Effect. For these purposes a variety of different methods, e.g. FDTD, FEM and RCWA, are in use. On the one hand, FDTD and FEM are investigated intensively - both in mathematics and numerical experiments - and their approximations and convergence properties are well known. On the other hand, there is a lack of these insights in RCWA. In spite of this, RCWA is commonly used to simulate a wide range of systems. We review historical and modern contributions to convergence improvements with respect to RCWA from the early sugesstions to modern developments. We study the convergence rates of the open-source software S4 and analyze the algorithmic properties in detail. Furthermore, we compare RCWA and FEM simulations for different classes of problems including 1D-binary gratings and 2D-periodic photonic crystals. Y1 - 2014 ER - TY - GEN A1 - Gutsche, Philipp A1 - Wolff, Christian A1 - Mirnaziry, Sayyed R. A1 - Poulton, Christopher G. T1 - Coupled-Mode Equations for Stimulated Brillouin Scattering T2 - CUDOS 14th Annual Workshop 2015 Handbook N2 - Stimulated Brillouin Scattering (SBS) is a third-order nonlinear optical effect which originates from the interplay of acoustics and optics. Recently, SBS has been harnessed in nano-photonic waveguides for applications such as narrow-linewidth lasers and Brillouin dynamic gratings [1]. Since the timescales of both phenomena differ significantly, coupled-mode equations derived from a slowly varying envelope approximation are well suited for numerical investigations of SBS [2]. We use the Relaxation Method (RM) [3] to study the optical power transfer and spatially resolved power distributions in long waveguides in the steady state limit. Y1 - 2015 ER - TY - CHAP A1 - Poulikakos, Lisa A1 - Gutsche, Philipp A1 - McPeak, Kevin A1 - Burger, Sven A1 - Niegemann, Jens A1 - Hafner, Christian A1 - Norris, David T1 - A Far-Field Interpretation of Optical Chirality in Analogy to Poynting’s Theorem T2 - META '15 Proceedings N2 - The optical chirality density is a valuable tool in locally characterizing chiral electromagnetic near-fields. However, how this quantity could translate into the far-field is not well understood. Here, we formulate a far-field interpretation of optical chirality by investigating its conservation law in isotropic media in analogy to Poynting’s Theorem. We define the global chirality and find that lossy materials, in particular plasmonic nanostructures, can act as chirality generators. This can enable chiral sensing applications at the single molecule level. Y1 - 2015 SP - 1215 EP - 1216 ER - TY - GEN A1 - Poulikakos, Lisa A1 - Gutsche, Philipp A1 - McPeak, Kevin A1 - Burger, Sven A1 - Niegemann, Jens A1 - Hafner, Christian A1 - Norris, David T1 - A Far-Field Interpretation of the Optical Chirality T2 - Frontiers in Nanophotonics (Congressi Stefano Franscini) N2 - A chiral structure is not super-imposable with its mirror image. Most commonly found in organic molecules, chirality can also occur in other systems, such as electromagnetic fields, where circularly polarized light is the most widespread example. Chiral electromagnetic fields can be a useful tool for biosensing applications. In particular, it has been shown that chiral plasmonic nanostructures have the ability to produce strongly enhanced chiral near-fields. Recently, our group has developed chiral plasmonic nanopyramids, which have the ability to focus chiral near-fields at their tip. This could enable chiral sensing at the single-molecule level. Chiral near-fields can be characterized in terms of the “optical chirality density”. This time-even and parity-odd pseudoscalar was first derived by Lipkin and was found to follow a conservation law analogous to the energy conservation of electromagnetic fields. More recently, Tang and Cohen identified the physical meaning of the “optical chirality density” as the degree of asymmetry in the excitation rate of a chiral molecule. However, how this near-field interpretation of the optical chirality could translate into the far-field is not well understood. Here, we formulate a far-field interpretation by investigating the conservation law for optical chirality in matter, and performing time-averaging in analogy to Poynting’s Theorem. In parallel to extinction energy, we define the “global chirality” as the sum of chirality dissipation within a material and the chirality flux leaving the system. With finite-element simulations, we place a dipole source at locations of enhanced local chirality and investigate the global chirality and ellipticity of emitted light in the far-field. Interestingly, we find that lossy materials with a complex dielectric function have the ability to generate global chirality when excited by achiral light. In particular, chiral plasmonic nanostructures are found to act as effective global chirality generators. The global interpretation of optical chirality provides a useful tool for biosensing applications with chiral plasmonic nanostructures, where the detection is routinely performed in the far-field. Y1 - 2015 ER - TY - CHAP A1 - Burger, Sven A1 - Gutsche, Philipp A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Pomplun, Jan A1 - Schmidt, Frank A1 - Wohlfeil, Benjamin A1 - Zschiedrich, Lin T1 - Hp-finite-elements for simulating electromagnetic fields in optical devices with rough textures T2 - Proc. SPIE Y1 - 2015 U6 - https://doi.org/10.1117/12.2190119 VL - 9630 SP - 96300S ER - TY - JOUR A1 - Wolff, Christian A1 - Gutsche, Philipp A1 - Steel, Michael J. A1 - Eggleton, Benjamin J. A1 - Poulton, Christopher G. T1 - Power limits and a figure of merit for stimulated Brillouin scattering in the presence of third and fifth order loss JF - Opt. Express N2 - We derive a set of design guidelines and a figure of merit to aid the engineering process of on-chip waveguides for strong Stimulated Brillouin Scattering (SBS). To this end, we examine the impact of several types of loss on the total amplification of the Stokes wave that can be achieved via SBS. We account for linear loss and nonlinear loss of third order (two-photon absorption, 2PA) and fifth order, most notably 2PA-induced free carrier absorption (FCA). From this, we derive an upper bound for the output power of continuous-wave Brillouin-lasers and show that the optimal operating conditions and maximal realisable Stokes amplification of any given waveguide structure are determined by a dimensionless parameter ℱ involving the SBS-gain and all loss parameters. We provide simple expressions for optimal pump power, waveguide length and realisable amplification and demonstrate their utility in two example systems. Notably, we find that 2PA-induced FCA is a serious limitation to SBS in silicon and germanium for wavelengths shorter than 2200nm and 3600nm, respectively. In contrast, three-photon absorption is of no practical significance. Y1 - 2015 U6 - https://doi.org/10.1364/OE.23.026628 VL - 23 IS - 20 SP - 26628 EP - 26638 ER - TY - JOUR A1 - Wolff, Christian A1 - Gutsche, Philipp A1 - Steel, Michael J. A1 - Eggleton, Benjamin J. A1 - Poulton, Christopher G. T1 - Impact of nonlinear loss on stimulated Brillouin scattering JF - J. Opt. Soc. Am. B N2 - We study the impact of two-photon absorption (2PA) and fifth-order nonlinear loss such as 2PA-induced free-carrier absorption in semiconductors on the performance of stimulated Brillouin scattering devices. We formulate the equations of motion including effective loss coefficients, whose explicit expressions are provided for numerical evaluation in any waveguide geometry. We find that 2PA results in a monotonic, algebraic relationship between amplification, waveguide length, and pump power, whereas fifth-order losses lead to a nonmonotonic relationship. We define a figure of merit for materials and waveguide designs in the presence of fifth-order losses. From this, we determine the optimal waveguide length for the case of 2PA alone and upper bounds for the total Stokes amplification for the case of 2PA as well as fifth-order losses. The analysis is performed analytically using a small-signal approximation and is compared to numerical solutions of the full nonlinear modal equations. Y1 - 2015 U6 - https://doi.org/10.1364/JOSAB.32.001968 VL - 32 IS - 9 SP - 1968 EP - 1978 ER - TY - JOUR A1 - Mrowinski, Paweł A1 - Schnauber, Peter A1 - Gutsche, Philipp A1 - Kaganskiy, Arsenty A1 - Schall, Johannes A1 - Burger, Sven A1 - Rodt, Sven A1 - Reitzenstein, Stephan T1 - Directional emission of a deterministically fabricated quantum dot – Bragg reflection multi-mode waveguide system JF - ACS Photonics Y1 - 2019 U6 - https://doi.org/10.1021/acsphotonics.9b00369 VL - 6 SP - 2231 ER - TY - JOUR A1 - Wilson, Jon A1 - Gutsche, Philipp A1 - Herrmann, Sven A1 - Burger, Sven A1 - McPeak, Kevin T1 - Correlation of circular differential optical absorption with geometric chirality in plasmonic meta-atoms JF - Opt. Express Y1 - 2019 U6 - https://doi.org/10.1364/OE.27.005097 VL - 27 SP - 5097 ER - TY - CHAP A1 - Malureanu, Radu A1 - de Lasson, Jakob Rosenkrantz A1 - Frandsen, Lars Hagedorn A1 - Gutsche, Philipp A1 - Burger, Sven A1 - Kim, Oleksiy S. A1 - Breinbjerg, Olav A1 - Ivinskaya, Aliaksandra A1 - Wang, Fengwen A1 - Sigmund, Ole A1 - Häyrynen, Teppo A1 - Lavrinenko, Andrei A1 - Mørk, Jesper A1 - Gregersen, Niels T1 - Which Computational Methods Are Good for Analyzing Large Photonic Crystal Membrane Cavities? T2 - 20th International Conference on Transparent Optical Networks (ICTON) Y1 - 2018 U6 - https://doi.org/10.1109/ICTON.2018.8473951 ER - TY - JOUR A1 - Gregersen, Niels A1 - de Lasson, Jakob Rosenkrantz A1 - Frandsen, Lars Hagedorn A1 - Gutsche, Philipp A1 - Burger, Sven A1 - Kim, Oleksiy S. A1 - Breinbjerg, Olav A1 - Ivinskaya, Aliaksandra A1 - Wang, Fengwen A1 - Sigmund, Ole A1 - Häyrynen, Teppo A1 - Lavrinenko, Andrei T1 - Benchmarking state-of-the-art numerical simulation techniques for analyzing large photonic crystal membrane line defect cavities JF - Proc. SPIE Y1 - 2018 U6 - https://doi.org/10.1117/12.2304338 VL - 10672 SP - 106721C ER - TY - CHAP A1 - Gregersen, Niels A1 - de Lasson, Jakob Rosenkrantz A1 - Frandsen, Lars Hagedorn A1 - Kim, Oleksiy S. A1 - Breinbjerg, Olav A1 - Wang, Fengwen A1 - Sigmund, Ole A1 - Ivinskaya, Aliaksandra A1 - Lavrinenko, Andrei A1 - Gutsche, Philipp A1 - Burger, Sven A1 - Häyrynen, Teppo A1 - Mørk, Jesper T1 - Benchmarking state-of-the-art optical simulation methods for analyzing large nanophotonic structures T2 - XXVI International Workshop on Optical Wave & Waveguide Theory and Numerical Modelling, Proceedings Y1 - 2018 SN - 978-3-921823-98-9 SP - 9 ER - TY - THES A1 - Gutsche, Philipp T1 - Convergence Study of the Fourier Modal Method for Nano-optical Scattering Problems in Comparison with the Finite Element Method N2 - Nano-optical scattering problems play an important role in our modern, technologically driven society. Computers, smartphones and all kinds of electronic devices are manufactured by the semiconductor industry which relies on production using photomasks as well as optical process control. The digital world, e.g. the world wide web, is based on optical interconnects and so-called quantum computers based on optics are supposed to be next generation computers. Moreover, global economic progress demands new and sustainable energy resources and one option is to make use of the power stored in optical radiation from the sun. Additionally, understanding fundamental physics such as the optical properties of asymmetric, or chiral, structures could promote future innovations in engineering. In order to understand and manipulate these kinds of processes, physics provides a well established model: the so-called Maxwell’s equations. Stated by James Clerk Maxwell in 1862, this description of the interaction of light and matter still provides a profound basis for the analysis of electromagnetic phenomena. However, real world problems cannot be calculated using simple mathematics. Rather, computer simulations are needed to obtain solutions of the physical model. Finding suitable methods to solve these problems opens up a wide variety of possibilities. On the one hand, there are methods which require long computing times. On the other hand, some algorithms depend on high memory usage. That is why the field of numerics deals with the question which method is optimally suited for specific problems. The aim of this work is to investigate the applicability of the so-called Fourier Modal Method (FMM) to nano-optical scattering problems in general. Since simple analytical solutions are non-existent for most recent physical problems, we use the Finite Element Method (FEM) to double-check performance of the FMM. Mathematics provide reliable procedures to control the errors of numerics using the FEM. Yet up to now it has not been possible to rigorously classify the quality of the Fourier Modal Method’s results. It is not fully understood whether the process of investing more and more computing resources yields more accurate results. So, we have to ask ourselves: does the numerical method invariably converge? In spite of this uncertainty when using the FMM, it is a well established method dating back to the 1980s. This numerical method has recently been used to optimize performance of solar cells [19] as well as to improve the optical properties of so-called single-photon sources [41] which are essential for quantum cryptography. The latter is a promising candidate to increase digital security and revolutionise cryptography techniques. Furthermore, with the help of the Fourier Modal Method an important issue in optics has been partly resolved: angular filtering of light was made possible by using a mirror which becomes transparent at a certain viewing angle [77]. In addition, an improved numerical technique to design so-called Photonic Crystal waveguides based on the FMM was developed recently [15]. Photonic Crystals are used in the fields of optical bio-sensing and for the construction of novel semiconductor devices. Moreover, approaches to link the FMM and the FEM try to combine advantages of both methods to obtain fast and accurate results [81]. These ideas are closely linked to the well-known concept of Domain Decomposition within the FEM [88]. Here, one possibility to couple domains is to use the scattering matrix formalism as it is done in the FMM. In the scope of this convergence study, we state Maxwell’s equations, particularly for periodic geometries. We describe two physical phenomena of nano-optics, namely chirality and opto-electrical coupling, and define the errors of our simulations. Afterwards, the two investigated methods are analysed with respect to their general properties and a way to unify modelling physics when using both algorithms is presented. With the help of various numerical experiments, we explore convergence characteristics of the FMM and draw conclusions about the ability of this approach to provide accurate results and, consequently, its potential for research on technological innovations. KW - Nano-optics KW - Fourier Modal Method (FMM) KW - Rigorous Coupled Wave Analysis (RCWA) KW - Finite Element Method (FEM) Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-56084 ER -