Jérémy ITIER will defend his Ph.D. Thesis entitled “Numerical Modeling of Nonlinear Light Scattering: Theory and Simulation of Polarization-Dependent Interactions in Structured Media” on Thursday 26th of November at 02:00 p.m. in the Rouard Lecture hall, Campus St Jerome, Marseille.
The talk will be in French, but the slides will be in English.
Composition of the Jury:
– Anne-Sophie BONNET-BEN DHIA, President
– Christophe GEUZAINE, Reviewer
– Benoît BOULANGER, Reviewer
– Sophie BRASSELET, Examinator
– Frédéric ZOLLA, Thesis Supervisor
– Gilles RENVERSEZ , Thesis Co-supervisor
Abstract: This thesis focuses on the development of numerical models for simulating light scattering by nonlinear materials. The emergence of complex photonic structures, such as metasurfaces and photonic crystals, has opened new possibilities for controlling and enhancing nonlinear optical effects. However, their geometrical and material complexity also raises new challenges for predicting their behavior and requires the development of numerical methods capable of modelling them accurately. Starting from Maxwell’s equations, we first recall the derivation, in the harmonic regime, of the equations governing light scattering by nonlinear materials. The resulting problem takes the form of a coupled system of nonlinear partial differential equations. The objective of this thesis is to propose, from these equations, new numerical methods for solving nonlinear scattering problems in complex geometries. As a first step, we establish a numerical model for the linear scattering problem based on the finite element method, which is particularly well suited to arbitrary geometries. Comparisons with analytical solutions for a slab and an infinite cylinder are used to validate the formulation and study its numerical convergence. In particular, these results highlight the benefits of higher-order elements and curved meshes. The model is then extended to nonlinear problems. The resulting coupled system is solved self-consistently using several iterative algorithms based on Picard and Newton-Raphson schemes. Slab and cylinder geometries are subsequently used to illustrate the capabilities of the model, investigate its convergence, validate it using an energy criterion, and identify the algorithms providing the best compromise between robustness and computational cost. The numerical framework is used, in particular, to recover the classical influence of phase matching on second-harmonic generation and to show how symmetries of the material constitutive properties determine whether nonlinear interactions lead to an active or passive behavior. Finally, we introduce an alternative approach for solving the nonlinear system without relying on iterative algorithms, which can be computationally expensive and more complex to implement. This method is based on a perturbative expansion of the electric field, transforming the nonlinear problem into a sequence of linear problems that can be solved successively. We evaluate the error introduced by this approximation, determine the domain of validity of the method, and demonstrate that it significantly reduces the computational cost compared with the iterative approach. The perturbative formulation also enables analytical solutions to be derived for slab and cylinder geometries, providing further insight into the underlying nonlinear interactions. Overall, this thesis provides a general numerical framework for modelling nonlinear electromag-netic interactions in complex geometries without relying on the propagation approximations commonly employed in homogeneous media.
