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Three-Dimensional Discontinuous Galerkin Method for the Analysis of Nano-Optical Electromagnetic Systems using Highly Accurate Boundary Integrals for Mesh Truncation

Applicant Oswald Benedikt
Number 126843
Funding scheme Project funding (Div. I-III)
Research institution Paul Scherrer Institut
Institution of higher education Paul Scherrer Institute - PSI
Main discipline Electrical Engineering
Start/End 01.05.2010 - 30.04.2012
Approved amount 196'230.00
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Keywords (12)

Finite Element Boundary Integral; Discontinuous Galerkin; Electromagnetic Near Field; Explicit Time Domain Schemes; Higher Order Interpolation; DG; Nano-Optics; Computational Electrodynamics; Boundary Integral; Transparent Boundary Condition; Dispersive Dielectric Materials; Metals in the Optical Region of the

Lay Summary (English)

Lead
Lay summary
Increasingly, computational electromagnetics has been challenged to provide the capability for modeling configurations with nanometer structure sizes in the optical region of the spectrum. When exploring the electromagnetics of time-dependent physics it is advantageous to also model the electromagnetics in the time domain: e.g. for spectroscopy and microscopy using ultra-short laser pulses and laser assisted field emission for electron sources in accelerators. Principal applications are in the near-field electromagnetic regime where laser light interacts with metallic objects of micrometer size, but with physically relevant features down to the nanometer scale. To be of relevance analysis in this regime must be undertaken in 3-dimensional space. Nano-optical systems have characteristic length scales on the order of on hundredth of the wavelength or smaller. The complete, uniform discretization of geometry of such fine detail quickly renders the problem intractable; on the other hand, using a coarser mesh will miss physical effects caused by deep sub-wavelength sized features. In order to resolve the relevant physics on this wide span of length scales, the numerical method must be able to handle a varying level of detail (LoD). This is often achieved by finite element (FE) methods. They tessellate the geometry into a tetrahedral mesh whose elements then vary continuously in size and seamlessly model both large and small features. Also, tetrahedra effortlessly model curved geometry. Still, realistic problems require ultra-large meshes whose number of elements may quickly reach several tens of millions. It is therefore imperative to devise techniques that can reduce the size of the computational mesh significantly. Recently, a new class of Discontinuous Galerkin (DG) methods has emerged which can be formulated on unstructured, tetrahedral meshes and lead to fully explicit time stepping schemes, using an element-wise multiply-and-add approach, thus providing level of detail modeling combined with fast time stepping. DG methods also discretize the volume of the computational domain and therefore need schemes to truncate the tessellation of space so that outgoing electromagnetic waves are not reflected; these schemes are broadly classified into: absorbing boundary conditions (ABC), perfectly matched layers (PML) and boundary integral (BI) techniques. Accurate and flexible boundary truncation schemes are particularly important in the analysis of near-field electromagnetic problems because there the distance between scattering objects and the boundary of the computational mesh would ideally be a very small fraction of the wavelength.
Direct link to Lay Summary Last update: 21.02.2013

Responsible applicant and co-applicants

Employees

Publications

Publication
The element level time domain (ELTD) method for the analysis of nano-optical systems: I. Nondispersive media
Fallahi Arya, Oswald Benedikt, Leidenberger Patrick (2012), The element level time domain (ELTD) method for the analysis of nano-optical systems: I. Nondispersive media, in Photonics and Nanostructures - Fundamentals and Applications, 10(2), 207-222.
The element level time domain (ELTD) method for the analysis of nano-optical systems: II. Dispersive media
Fallahi Arya, Oswald Benedikt (2012), The element level time domain (ELTD) method for the analysis of nano-optical systems: II. Dispersive media, in Photonics and Nanostructures - Fundamentals and Applications, 10(2), 223-235.
3-Dimensional Time-Domain Full-Wave Analysis of Optical Array Antennas
Oswald B., Fomins A., Fallahi A., Leidenberger P., Bastian P. (2011), 3-Dimensional Time-Domain Full-Wave Analysis of Optical Array Antennas, in J. Comput. Theor. Nanosci., 8(8), 1573-1589.
On the computation of electromagnetic dyadic Green's Functions in Spherically Multilayered Media
Fallahi A., Oswald B. (2011), On the computation of electromagnetic dyadic Green's Functions in Spherically Multilayered Media, in IEEE Transactions on Microwave Theory and Techniques, 59(6), 1433-1440.

Scientific events

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Title Type of contribution Title of article or contribution Date Place Persons involved


Associated projects

Number Title Start Funding scheme
125084 Femtosecond electron dynamics and nano-optic enhancement in laser-assisted field-emission from metallic nano-tip arrays with controlled apex-sizes 01.12.2009 Project funding (Div. I-III)

Abstract

Increasingly, computational electromagnetics has been challenged to provide the capability for modeling configurations with nanometer structure sizes in the optical region of the spectrum. When exploring the electromagnetics of time-dependent physics it is advantageous to also model the electromagnetics in the time domain: e.g. for spectroscopy using ultra-short laser pulses and laser assisted field emission for ultra-fast time resolved electron microscopy. Principal applications are in fields where laser light interacts with metallic objects of micrometer size but with physically relevant feature sizes down to the nanometer scale. Such problems are dubbed near-field electromagnetic problems. To be relevant, such problems must be analyzed in 3-dimensional space. Nano-optical systems have characteristic length scales on the order of (lambda / 100) or smaller, where lambda is the wavelength.The complete discretization of geometry of such fine detail quickly renders the problem intractable; on the other hand, using a coarser mesh will miss important physical effects caused by deep sub-wavelength feature size. To still resolve the relevant physics on this wide span of length scales the numerical method must be able to handle a varying level of detail (LoD). This is often achieved by finite element (FE) methods. They tessellate the geometry into a tetrahedral mesh whose elements then vary continuously in size and seamlessly model both large and small features. Another advantage of tetrahedra is their inherent ability to model curved geometry in an effortless manner. Still, realistic problems require ultra-large meshes whose number of elements quickly may reach several tens of millions. It is therefore imperative to devise techniques that can reduce the size of the computational mesh significantly. Eventually, a wide span of length scales can be accommodated efficiently, resolving the physics associated with sub-wavelength feature sizes while simultaneously modeling considerably larger geometries. Because FE methods discretize the volume of the computational domain, they need procedures to truncate the tessellation of space so that outgoing electromagnetic waves are not reflected when they hit the encounter the boundary of the mesh. Considerable effort has been invested to explore boundary condition schemes that are both accurate and efficient; these schemes are, broadly, classified into: absorbing boundary conditions (ABC), perfectly matched layers (PML) and boundary integral (BI) techniques. Accurate and flexible boundary truncation schemes are particularly important in the analysis of near-field electromagnetic problems because there the distance between scattering objects and the boundary of the computational mesh would ideally be a very small fraction of the wavelength. At present only the BI approach can be placed that close to scattering objects. It has the undeniable advantage that it is an exact truncation scheme, however its practical realization is particularly challenging in the time domain and reports of its successful application are scarce. Still, for the analysis of near-field electromagnetic problems a mesh truncation scheme that can be placed extremely close to the scatterers is urgently required. Finite element time domain (FETD) methods to solve Maxwell's equations have existed for some years,yet they have suffered from the fact that at every time step a large system of linear equations must be solved, therefore putting an additional computational burden onto the method. Relatively recently, the new class of Discontinuous Galerkin (DG) methods has emerged. The DG methods can be formulated on unstructured, tetrahedral meshes and lead to fully explicit time stepping schemes, using an element-wise multiply-and-add approach, thus providing level of detail modeling and yet a fast time domain method. These features render the DG approach attractive to explore electromagnetic near-field problems. At present, it is not known if the DG approach is also capable of accurately solving near-fieldelectromagnetic problems in 3-dimensional space. There is evidence that it can be used in 2-dimensional setups. A combination of the efficient DG electromagnetic time-domain method with an exact boundaryintegral mesh truncation scheme has enormous potential for the analysis of realistic electromagnetic near-field problems. The objectives are: (i) to investigate a 3-dimensional DG scheme for the analysis of scientifically relevant electromagnetic near-field problems and (ii) to truncate the computational mesh with a boundary integral procedure that can be placed in very close proximity to scattering objects. The proposed research will be undertaken at the Paul Scherrer Institut in the Large Research Facilities Division (GFA) supervised by Benedikt Oswald. Because the subject of this research is rather challenging, it is proposed that is investigated by a post-doctoral researcher who has the necessary experience and expertise to successfully accomplish the project.
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