Numerical Approaches for the Analysis of Optical Devices

The research activity presented is focused on the study of numerical methods for electromagnetism and the development of simulation codes for integrated and fiber optics devices. The theoretical approach is mainly based on the finite element method (FEM). The developed codes permit both modal and propagative general-purpose analysis, suitable for the study of structures with arbitrary geometry, distribution or refractive index variation and media features. For modal analysis, mono- and bi-dimensional codes have been developed which are suitable for media that can also be anisotropic and nonlinear, both with and without losses. Both scalar and full-vectorial formulations have been developed. Propagative analysis has been performed with the development of beam propagation method (BPM) semi- and full-vectorial bi-dimensional cross-section codes. Moreover, formulations of propagators for finite-element frequency-domain (FEFD) and finite-element time-domain (FETD) analysis have also been implemented. Specific attention has been focused on the kind of base functions chosen to expand the unknown function (e.g. nodal functions or edge elements), on the different types of boundary conditions (absorbing, transparent or employing Perfectly Matched Layers, also called PML), on the most suitable solvers for algebraic problems capable of operating efficiently with sparse matrices of large size, and on the most efficient algorithms balancing execution speed and memory occupancy, in order to be able to process the meshes describing the structures under examination also on limited-resource machines. The codes are written in the C language for the Linux operating system and make use of high-efficiency solvers based on optimised mathematical libraries, such as the single- and multi-threaded BLAS libraries provided by the ATLAS project. Also, a simple graphical interface has been implemented in Tcl/Tk to set up and launch simulations. The developed numerical codes are efficient and rel- - iable, can work on simple personal computers also when examining structures of great complexity, which require large-sized meshes. These codes have been applied to the study of a wide array of devices, such as low-loss tapered coupling structures between photonic-crystal waveguides (PCWs) and standard wire waveguides of varying width. Another application example is the design of a small-sized polarization splitter based on the coupling of birefringent and non-birefringent cores in a square-lattice photonic-crystal fiber (PCF)