Computational Optics
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Computer-based models and simulations enable an economic and fast insight into the functionality of optical systems as well as a fast prototyping thereof. Thus, complex design problems and analyses can be treated efficiently and with high precision while accounting for the relevant physical properties.
The Computational Optics group performs research on various numerical approaches in photonics. Among others, these are the design of freeform optics, the computation of application specific intensity distributions in laser materials processing as well as the design of optical neural networks for beam shaping. To this end, numerous software development tools and strategies are used, while several high-performance computers are available.
Design of highly efficient freeform optics
Refracting and reflecting surfaces that strongly depart from spherical and aspherical shapes are referred to as freeform optics. Here, the techniques of classical optics design can no longer be applied, and new algorithms need to be developed, focusing on the efficient redistribution of energy to tailor irradiance or intensity distributions. This principally enables the generation of very complex illuminance distributions, which is only constrained through physical limitations as e.g. high etendue or low beam quality. Freeform optics are used in high-efficiency luminaires, to reduce energy consumption and operating costs for a given illumination setup. A novel application area of freeform optics is the realization of application specific intensity distributions for laser materials processing.
The Computational Optics group develops freeform optics tailored to non-imaging applications for industrial and research customers. Current research topics include the development of design algorithms for various types of light sources as well as the Fresnelization of freeform optics for space reduction. In the development of such design algorithms, we apply state-of-the-art methods from the fields of differential geometry, computer graphics as well as nonlinear optics.
Collaborating with local manufacturers, we provide virtual prototypes with a production-ready design and we perform the characterization of the manufactured optics.
Solution of the Inverse Heat Conduction Problem in Laser Materials Processing
In the numerous methods of laser materials processing, the applied laser beam induces a temporal and spatial varying temperature profile within the treated material, which in the end determines the processing quality as well as efficiency. As this temperature profile is influenced significantly by the laser beam’s intensity distribution, the purposeful realization of temperature profiles is enabled by application specific beam shaping. To this end, it is necessary to deduce the intensity (i.e. the cause) from the prescribed temperature (i.e. the effect) which constitutes an inverse heat conduction problem that is a mathematically ill-posed problem.
The group Computational Optics develops efficient numerical algorithms for the solution of this inverse heat conduction problem which enables the calculation of specific intensity distributions for a broad range of application. Especially temperature dependent thermophysical and optical material properties as well as complex geometries are taken into account.
Our close cooperation with the Fraunhofer Institute for Laser Technology guarantees an application-oriented realization. Thus, the developed methods have already been validated experimentally for the applications of laser hardening or laser-based softening of high-strength steels.
Development of Diffractive Neural Networks for Laser Beam Shaping
Diffractive neural networks (DNNs) are a physical implementation of artificial neural networks. Light acts as information while so-called diffractive optical elements (DOEs) represent the layers of the network. Each pixel on each DOE is a trainable parameter in a DNN, emulating a neuron, which manipulates the phase of an incoming electromagnetic field. Such networks are trained in a computer and afterwards realized experimentally in order to fulfill e.g. image classification tasks at the speed of light.
The Computational Optics group has its own training architecture for DNNs for designing optical systems for laser beam shaping. These DNN-based systems have several functionalities that are difficult or impossible to achieve with other systems:
- Simultaneous control of amplitude and phase: The phase of the field in the target plane can be treated as an additional optimization goal to achieve a higher depth of field.
- Multiple target planes: DNNs can be trained with multiple simultaneous target planes for effectively creating three-dimensional beam shaping.
- Alignment robustness: DNNs can be trained with variations of the incoming beam (e.g. displacement or tilt) to automatically compensate such deviations in the experiment.
These features make DNNs promising systems for laser materials processing. Current research topics are expansions to the training architecture and experimental confirmation of the calculated systems.
Diode Laser Simulation for High-Power Applications and for Quantum Technology
Another topic within the Computational Optics group is the simulation of diode lasers with a focus on the interaction between the gain chips and external cavities. To this end, the software SEMSIS (Semiconductor Laser Simulation Software) which has been developed in cooperation with Fraunhofer ILT as well as the Chair for Laser Technology of RWTH Aachen University is applied and further engineered to create a deeper understanding of the physical processes inside edge or surface emitters. The software can for example be used for calculating the eigenmodes of a waveguide, but also to propagate initial values of the electric field through the waveguide using the Beam Propagation Method (BPM). Additionally, electrical, thermal, mechanical as well as quantum mechanical models can be coupled to the optical one and the complete model is solved self-consistently.
Application areas of the SEMSIS tool are the development of high-power diode lasers as well as shot-noise limited lasers for quantum communication.
Further research interests
Additional research topics of the Computational Optics group are:
- the realization of an algorithmic resolution increase in imaging applications through Fourier ptychography
- the development of wave-optical simulation tools
- the evaluation of quantum algorithms for problems in optics design and photonic production.