Development of the differential method associated with the Fast Fourier Factorization for the modelization of photonic device: from complex optical diffraction grating to guided integrated optic structure
Nowadays to design photonic devices, it is important to have reliable and efficient simulation tools. In fact, if exploiting the technological grids of the design parameters is considered possible for the simple devices, its cost in terms of number of tests becomes an obstacle to the optimization of the structures. Therefore, it is essential to develop fully vectorial simulations, with complex or/and real refractive indices materials, to guarantee that all the propagation modes (guided, radiated and evanescent modes) are taken into account. The simulations of the structures with high contrast refractive index (Silicon photonics for example) or structures using metallic layer and generating plasmonic modes or sub-wavelength structures like metamaterials are a set of examples that requires the use of these tools. These methods can be differentiated by their used calculation algorithm: calculation in the frequency domain by finite differences or finite elements, Fourier based methods, or calculation in the temporal domain with the finite difference method... For example, the FDTD has become in the recent years a reference tool in the domain of silicon photonics. However, almost all these methods are not necessarily optimal. They can be distinguishable by the required numerical resources, particularly in terms of the used memory, the execution time, the take into account of the boundary conditions, the discretization of the structure, or their workspace domain (spectral or spatial) ... Over the last fifteen years, the group involved with the development of electromagnetic tools in the laboratory (IMEP-Lahc), headed towards the development of RCWA based numerical tools to simulate and design the optical response of diffractive and guided optic structures. However, this last method as the FDTD can generate approximations inducing inaccuracies or an increase in the numerical resources used for certain configurations (memory, execution time...). The objective of this thesis is to develop a more general tool aiming to reduce these imperfections while retaining the possibility of using it on a multitude of photonics applications (diffractive optics, guided optics, etc.). My choice fell on the differential method which is widely used for the study of diffraction gratings. This method can be more efficient than the RCWA but it also has limitations especially for the simulation of periodic structures with complex profile in TM polarization. Since the 2000s, the association of a new module called FFF (Fast Fourier Factorization) has solved this problem and opened up new possibilities for this method. After a general introduction, the differential method associated with the FFF is presented in detail. Then, a simple and fast solution which makes the use of this method with metals having a purely real and negative permittivity is proposed and solve the problem of divergence faced before. Consequently, a complete study of a dielectric diffractive structure visual security applications is subsequently detailed. Moreover, the developed code of the DM-FFF is integrated in neural networks algorithm for optimal modeling and design of visual security structures. Finally, to meet the condition of generalizing the method for the different photonic structures (guided and diffractive), a coordinate transform inspired from the aperiodic FMM was implemented in the algorithm of the DM-FFF transforming the last one into an aperiodic method for the simulation of 2D integrated optical structures for complex, non-isotropic and non-magnetic materials. The decomposition of the propagation of eigenmode basis can provide access to information which are not directly provided by the FDTD for example (guided modes, radiated modes …). More precise, faster and more rigorous results were obtained compared to a-FMM especially in TM polarization with curvilinear profiles such as the case of cylindrical structures.
Pierre BENECH - Professor - Grenoble INP - IMEP-LAHC : CoSupervisor
Frédéric GARET - Professor - University Savoie Mont Blanc - IMEP-LAHC : Examiner
Nadège COURJAL - MCF- University of Franche-Comté, FEMTO-ST : Examiner
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Thesis prepared at the laboratoiry : UMR 5130 - IMEP-LaHC (Institut de Microélectronique, Electromagnétisme et Photonique - Laboratoire d'Hyperfréquences et de Caractérisation) supervised by MORAND Alain, supervisor and Pierre BENECH Cosupervisor.