Machine Learning and Time Domain Methods for Simulations in Nonlinear Optics

Supervisors: Prof. Franz Kärtner (DESY/UHH), Prof. Markus Bause (HSU)

Nonlinear optical processes often rely on the slowly-varying envelope approximation assuming only narrowband optical signals that interact with each other over perturbative optical nonlinearities. However, many modern optical processes such as continuum generation in nonlinear waveguides or THz generation easily cover multiple octaves of bandwidth. This asks for the direct simulation of the electric field including the carrier wave. It becomes even more demanding when carrier-envelope phase sensitive effects are important. One such process is continuum generation as well as THz generation in periodically poled Lithium Niobate, which can generate spectra ranging from 400 nm to 4000 nm. Even though significant progress has been made in the numerical simulation of nonlinear optical processes, substantial progress in multiscale simulation techniques is required for optimization of such processes. Data science, in particular machine learning, offers the potential to accelerate computations, such that a real breakthrough becomes feasible, by inferring knowledge from data bases instead of computing all physical quantities of the system on sufficiently fine spatial and temporal scales.
By combining the expertise of groups from physics and mathematics and building upon their previous joint research, the long-term goal is to achieve the simulations only by providing the physics and geometry of the problem, consequently reducing the mesh and solver parameters setup time to almost zero and eliminating the need of expertise. These cost-effective simulations of such processes will enable the desired progress in elucidation, design and implementation of ultrabroadband optical systems, such as single-cycle pulse generation. We are looking for one PhD student working under joint supervision of the PIs from physics and mathematics.