Domain Decomposition Method for Maxwell's Equations: Scattering off Periodic Structures

We present a domain decomposition approach for the computation of the electromagnetic field within periodic structures. We use a Schwarz method with transparent boundary conditions at the interfaces of the domains. Transparent boundary conditions are approximated by the perfectly matched layer method (PML). To cope with Wood anomalies appearing in periodic structures an adaptive strategy to determine optimal PML parameters is developed. We focus on the application to typical EUV lithography line masks. Light propagation within the multi-layer stack of the EUV mask is treated analytically. This results in a drastic reduction of the computational costs and allows for the simulation of next generation lithography masks on a standard personal computer.Comment: 24 page

Transparent Boundary Conditions for Time-Dependent Problems

A new approach to derive transparent boundary conditions (TBCs) for dispersive wave, Schrödinger, heat, and drift-diffusion equations is presented. It relies on the pole condition and distinguishes between physically reasonable and unreasonable solutions by the location of the singularities of the Laplace transform of the exterior solution. Here the Laplace transform is taken with respect to a generalized radial variable. To obtain a numerical algorithm, a Möbius transform is applied to map the Laplace transform onto the unit disc. In the transformed coordinate the solution is expanded into a power series. Finally, equations for the coefficients of the power series are derived. These are coupled to the equation in the interior and yield transparent boundary conditions. Numerical results are presented in the last section, showing that the error introduced by the new approximate TBCs decays exponentially in the number of coefficients

Resonant Plasmonic–Biomolecular Chiral Interactions in the Far-Ultraviolet: Enantiomeric Discrimination of sub-10 nm Amino Acid Films

Resonant plasmonic–molecular chiral interactions are a promising route to enhanced biosensing. However, biomolecular optical activity primarily exists in the far-ultraviolet regime, posing significant challenges for spectral overlap with current nano-optical platforms. We demonstrate experimentally and computationally the enhanced chiral sensing of a resonant plasmonic–biomolecular system operating in the far-UV. We develop a full-wave model of biomolecular films on Al gammadion arrays using experimentally derived chirality parameters. Our calculations show that detectable enhancements in the chiroptical signals from small amounts of biomolecules are possible only when tight spectral overlap exists between the plasmonic and biomolecular chiral responses. We support this conclusion experimentally by using Al gammadion arrays to enantiomerically discriminate ultrathin (\u3c10 nm thick) films of tyrosine. Notably, the chiroptical signals of the bare films were within instrumental noise. Our results demonstrate the importance of using far-UV active metasurfaces for enhancing natural optical activity