A bi-static short-range elastic backscatter micro-lidar, named Colibri, has been developed for quantitative aerosol profiling with high range and temporal resolution within the first hundred meters. The geometric (i.e., overlap) and radiometric (i.e., lidar constant) calibrations were performed along with dark current and background noise characterizations. Results of a measurement campaign have demonstrated the capability of our system to characterize aerosol plumes with high range-resolution (<10 cm) in the short-range close to their emission sources (from 10 m). To this aim, fog-oil aerosol plumes were generated in a tunnel and characterized by using an optical particle counter. A forward inverse method without boundary conditions is presented for inverting short-range lidar profiles when no reference molecular zone is available. Lastly, we report the different retrieved lidar products, namely the distribution of aerosol layers, radiative properties (i.e., backscatter profiles), and the microphysical properties (i.e., number concentration profiles). For the validation of the proposed methodology, the lidar products were compared with measurements from the optical particle counter. Lastly, the impact of calibration errors on the lidar products is discussed through an uncertainty analysis.

In electromagnetic compatibility (EMC) context, we are interested in developing new ac- curate methods to solve efficiently and accurately Maxwell’s equations in the time domain. Indeed, usual methods such as FDTD or FVTD present im- portant dissipative and/or dispersive errors which prevent to obtain a good numerical approximation of the physical solution for a given industrial scene unless we use a mesh with a very small cell size. To avoid this problem, schemes like the Discontinuous Galerkin (DG) method, based on higher order spa- tial approximations, have been introduced and stud- ied on unstructured meshes. However the cost of this kind of method can become prohibitive accord- ing to the mesh used. In this paper, we first present a higher order spatial approximation method on carte- sian meshes. It is based on a finite element ap- proach and recovers at the order 1 the well-known Yee’s schema. Next, to deal with EMC problem, a non-oriented thin wire formalism is proposed for this method. Finally, several examples are given to present the benefits of this new method by compar- ison with both Yee’s schema and DG approaches.

Enforcing Gauss' law in numerical simulations of Maxwell's equations, specially in plasma physics, is a well-known key issue. Although the set of Maxwell's equations used for simulations do not include divergence laws, augmented systems which incorporates Gauss' law while retaining an overall hyperbolic form are frequently used to cope with charge conservation defects. Focusing on bounded domains and usual boundary conditions, existence and well-posedness of associated augmented systems have already been established. These extensions are non-unique and, among them, some surprisingly do not model properly the solutions of Maxwell's equations anymore. This matter is illustrated by a constructive example of waves propagating in a rectangular waveguide. A result providing both existence and uniqueness of an extension from Maxwell's equation to a proper augmented problem is proved by a perturbation argument. The main idea is that the solutions of Maxwell's equations must be a ground state, whenever charge conservation holds, for the solutions of any proper associated augmented system.