Joseph Maubach

Aperiodic Fourier modal method in contrast-field formulation for simulation of scattering from finite structures

This paper extends the area of application of the Fourier modal method (FMM) from periodic structures to aperiodic ones, in particular for plane-wave illumination at arbitrary angles. This is achieved by placing perfectly matched layers at the lateral sides of the computational domain and reformulating the governing equations in terms of a contrast field that does not contain the incoming field. As a result of the reformulation, the homogeneous system of second-order ordinary differential equations from the original FMM becomes non-homogeneous. Its solution is derived analytically and used in the established FMM framework. The technique is demonstrated on a simple problem of planar scattering of TE-polarized light by a single rectangular line.

Orientation identification of the power spectrum

The image Fourier transform is widely used for defocus and astigmatism correction in electron microscopy. The shape of a power spectrum (the square of a modulus of image Fourier transform) is directly related to the three microscope controls, namely, defocus and twofold (two-parameter) astigmatism. We propose a new method for power-spectrum orientation identification. The method is based on the three measures that are related to the microscopes controls. The measures are derived from the mathematical moments of the power spectrum and is tested with the help of a Gaussian benchmark, as well as with the scanning electron microscopy experimental images. The method can be used as an assisting tool for increasing the capabilities of defocus and astigmatism correction a of nonexperienced scanning electron microscopy user, as well as a basis for automated application.

A Numerical Method for the Solution of Time‐Harmonic Maxwell Equations for Two‐Dimensional Scatterers

The Fourier modal method (FMM) is a method for efficiently solving Maxwell equations with periodic boundary conditions. In a recent paper [1] the extension of the FMM to non‐periodic structures has been demonstrated for a simple two‐dimensional rectangular scatterer illuminated by TE‐polarized light with a wavevector normal to the third (invariant) dimension. In this paper we present a generalized version of the aperiodic Fourier modal method in contrast‐field formulation (aFMM‐CFF) which allows arbitrary profiles of the scatterer as well as arbitrary angles of incidence of light.

Computation and Visualisation in the NumLab Numerical Laboratory

A large range of software environments addresses numerical simulation, interactive visualisation and computational steering. Most such environments are designed to cover a limited application domain, such as Finite Elements, Finite Differences, or image processing. Their software structure rarely provides a simple and extendible mathematical model for the underlying mathematics. Assembling numerical simulations from computational and visualisation blocks, as well as building such blocks is a difficult task.

An extended Fourier modal method for plane-wave scattering from finite structures

This paper extends the area of application of the Fourier modal method from periodic structures to aperiodic ones, in particular for plane-wave illumination at arbitrary angles. This is achieved by placing perfectly matched layers at the lateral sides of the computational domain and reformulating the governing equations in terms of a contrast field which does not contain the incoming field.