The Applied Computational Optics Group deals with the development of physical-optics-based approaches for modeling and design of optical systems. In our approach, light is represented by vectorial electromagnetic fields. And, from the source model on, it brings great advantages by enabling the representation of sophisticated light e.g. partially coherent diode laser, or ultrashort pulses. Setting off from the source, the physical-optics modeling of the optical system means to solve Maxwell's equations on the system level. Instead of employing a single solver for the whole system, we follow the concept of tearing and interconnection, i.e., to decompose the system into regions, apply regional Maxwell solvers in either rigorous manner or with certain mathematical approximations, and match the boundary values amongst regions to form the solution to the complete system. In particular, the regional solvers can be evaluate in different domains, e.g., spatial frequency domain, and by using the solvers in different domains in combination, the fast physical optics simulation of the system becomes feasible.

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Fig. 1: modeling of an exemplary system with field tracing techniques. The system is split into regions and various regional Maxwell solvers are applied. In this case, solvers for free space, SLM, prisms, lenses, and gratins are marked out. The solvers can be evaluated in different domains e.g. the spatial or the spatial frequency domain. With Fourier transform, fields in different domains can be connected, and the sequence of regional Maxwell solvers and Fourier transform to form the field tracing diagram. (rights: IAP)

In 2012, together with our colleagues at LightTrans GmbH, we were able to combine the mathematical concept of sparse tearing and interconnecting with our idea of non-sequential field tracing. That constitutes the basis of a new type of Maxwell's solver with high efficiency and numerical stability. We also introduced the parabasal field decomposition. This technique solves various problems in optical modeling, e.g., efficient propagation of non-paraxial harmonic fields, tracing scattered light through lens systems and tolerancing of optical systems. Furthermore we have developed rigorous semi-analytical methods for the efficient free-space propagation of non-paraxial fields. In laser resonator modeling we use advanced Eigenmode solver, to simulate the optical performance of stable and unstable active laser resonators. Here we use pseudospectral methods for the simulation of the field propagation through nonlinear active media.

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