Anthony Gourdin | Searcharxiv

arXiv2024

A single layer representation of the scattered field for multiple scattering problems

The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series expansion over spherical harmonics and spherical Bessel functions for spherical geometries. More precisely, given a set of scatterers, the field scattered by any subset can be expressed as an integral over any smooth surface enclosing the given subset alone. It is then possible to solve the multiple scattering problem by using this integral representation instead of an expansion over spherical harmonics. This result is used to develop an extension of the Fast Multipole Method in order to deal with subsets that are not enclosed within non-intersecting balls.

math-ph↗

arXiv2024

Investigation of the anatase-to-rutile transition for TiO$_2$ sol-gel coatings with refractive index up to 2.7

This work describes the elaboration of rutile titanium dioxide films with high refractive indices and low scattering by sol-gel process and controlled crystallization. The evolutions of the optical properties and crystalline structure of sol-gel processed titania coatings on fused silica were investigated for different thermal budgets of the annealing post-treatment using ellipsometry, spectrophotometry, X-ray diffraction and electronic microscopy. It reveals that anatase and rutile coatings with refractive indices of 2.5 and 2.7 can be prepared with associated optical loss of 0.5% and 1%, respectively, which are excellent compromise for applications in integrated photonics. These evolutions are associated to the thermally induced mass transfer and phase transitions occurring during thermal annealing that involves first the nucleation growth and sintering of anatase polyoriented nanocrystals, followed by the transformation into rutile polyoriented nanocrystals. Concomitantly, rutile crystals with (110) faces parallel to the surface consume surrounding anatase and rutile nanocrystals by diffusive sintering to yield micron-size rutile monocrystalline and monooriented platelets patchwork, exhibiting refractive index of 2.73 and 1.2% optical loss. The formation of these platelets is governed by surface energies and is responsible for the increase in optical loss.

physics.optics↗