Benjamin Vial

Quasimodal expansion of electromagnetic fields in open two-dimensional structures

A quasimodal expansion method (QMEM) is developed to model and understand the scattering properties of arbitrary shaped two-dimensional (2-D) open structures. In contrast with the bounded case which have only discrete spectrum (real in the lossless media case), open resonators show a continuous spectrum composed of radiation modes and may also be characterized by resonances associated to complex eigenvalues (quasimodes). The use of a complex change of coordinates to build Perfectly Matched Layers (PMLs) allows the numerical computation of those quasimodes and of approximate radiation modes. Unfortunately, the transformed operator at stake is no longer self-adjoint, and classical modal expansion fails. To cope with this issue, we consider an adjoint eigenvalue problem which eigenvectors are bi-orthogonal to the eigenvectors of the initial problem. The scattered field is expanded on this complete set of modes leading to a reduced order model of the initial problem. The different contributions of the eigenmodes to the scattered field unambiguously appears through the modal coefficients, allowing us to analyze how a given mode is excited when changing incidence parameters. This gives new physical insights to the spectral properties of different open structures such as nanoparticles and diffraction gratings. Moreover, the QMEM proves to be extremely efficient for the computation of Local Density Of States (LDOS).

Postseismic pressure solution creep: Evidence and time‐dependent change from dynamic indenting experiments

Active faults in the Earths upper crust can slide either steadily by aseismic creep or abruptly causing earthquakes. Seismic and aseismic processes are closely related: earthquakes are often followed by transient afterslip creep. Postseismic displacement rates progressively decrease with time over a period of years or decades. So seismic fracturing activates the creep rate, and various healing processes progressively reduce it. This article presents pressure solution indenter experiments on halite, calcite, and plaster that show how fracturing and comminution processes induced by dynamic stress loading (applied by dropping steel balls) drastically accelerate the displacement rates accommodated by pressure solution creep by decreasing the dissolution contact area and the diffusive mass transfer distance along this contact. However, as fractures progressively heal and dissolution contacts flatten, these effects disappear, and the displacement rates slow down. The time-dependent change in indenter displacement after dynamic stress loading has been measured and is best fitted by power laws with exponents that change with time from 0.3 to 1 when healing is achieved. Natural postseismic (afterslip) displacement/time relationships have been analyzed and also show a power law change with a power law exponent in the range of 0.25–0.4. It is proposed that the variation in power law exponent with time is related to the change in morphology of the dissolution contact that is fractured or comminuted during the dynamic event and is then progressively healed and smoothed. In natural faults, monitoring the power law parameters could give access to the characteristic healing time in the fault.

Adaptive perfectly matched layer for Wood’s anomalies in diffraction gratings

We propose an Adaptive Perfectly Matched Layer (APML) to be used in diffraction grating modeling. With a properly tailored co-ordinate stretching depending both on the incident field and on grating parameters, the APML may efficiently absorb diffracted orders near grazing angles (the so-called Woods anomalies). The new design is implemented in a finite element method (FEM) scheme and applied on a numerical example of a dielectric slit grating. Its performances are compared with classical PML with constant stretching coefficient.

Resonances determination in microstructured films embedded in multilayered stacks

Our approach consists in finding the eigenmodes and the complex eigenfrequencies of structures using a finite element method (FEM), that allows us to study mono- or bi-periodic gratings with a maximum versatility : complex shaped patterns, with anisotropic and graded index material, under oblique incidence and arbitrary polarization. In order to validate our method, we illustrate an example of a four layer dielectric slab, and compare the results with a specific method that we have called tetrachotomy, which gives us numerically the poles of the reflection coefficient (which corresponds to the eigenfrequencies of the structure). To illustrate our method, we show the eigenvalues of one- and two-dimensional gratings.

Transformation optics PML and quasi-mode analysis: Application to diffraction gratings

This paper presents the Perfectly Matched Layers (PMLs) in the framework of transformation optics as a complexvalued change of coordinates. PMLs provide the suitable operator extensions required for the leaky mode computation of open waveguides and the quasi-mode computation of scattering problems. Quasi-modes of diffraction gratings are considered here together with a numerical use of this spectral analysis.