PhD on Inverse methods for PEREGRINE (Performance Extremized Freeform-Gradient Index Optics)

Would you like to use mathematics to shed new light upon the world, literally?!! This project aims to develop a mathematical framework for design of freeform gradient-index (F-GRIN) optics. With industry, we will solve the forward problem involving differential systems, and perform PDE-constrained optimisation for designing novel optical elements

Context:The position is based on the PEREGRINE proposal, funded by the NWO (Dutch Research Council) - KIC call, with academic partners at Eindhoven and Delft Universities of Technology, and industrial partners at Anteryon, ASML, Demcon, JMO, and Signify. The vision of this project is to develop F-GRIN optical components described further below.

The Computational Illumination Optics (CIO) group from Eindhoven University of Technology will lead this project and will be responsible for the inverse design of the F-GRINs. CIO group is one of the few mathematics groups worldwide working on mathematical models of optical systems. We develop and analyze numerical methods to solve the resulting differential equations.

F-GRINs: Materials with a spatially-dependent distribution of the refractive index, known as freeform gradient index (F-GRIN) optics, is a modern development to control the colour-dependent (dispersive) distribution of light. Such an F-GRIN optic offers a large number of design parameters to transform the incident light distribution to a desired output distribution such as the image on the screen at the right in Figure 1. Thereby the device allows to perform a functionality relevant to our high-tech users and will bring sustainability benefits and new economic opportunities to the society. The image on the screen shows the peregrine falcon, the fastest animal on earth (during its high-speed dive of > 300 km/h) and namesake of our program.

Project Goal: The goal of this project is to establish the mathematical framework for the modelling, numerical simulation, and inverse design of the F-GRINs. Correspondingly it has the following goals and task divisions:

1. Mathematical modelling: Mathematically modelling the propagation of light energy through the gradient index optics. A challenge regarding this will be the modelling of scattering which will result in the generalised form of the radiative transfer equation.
2. Forward numerical solver: Based on the mathematical model derived, the goal would be to develop a numerical solver for the differential equations that is fast and robust. The main challenge here is the high dimensionality of the problem and the coupling with Hamiltonian optics.
3. Inverse problem (Optimsation): Upon solving the forward problem reliably and efficiently, the goal would be to prescribe a refractive index (RI) distribution for the F-GRIN that results in a target distribution of light from a given source distribution in a broadband optical range. This would require a PDE-constrained optimisation strategy and is a generalised optimal transport problem.

The end-goal would be to come up with a model-solve-design pipeline that our industrial and academic partners can use for practical applications.

Positioning: The project lies in the confluence of mathematical modelling, scientific computing, and optimisation. Moreover, it has deep ties with physics and technology with a promise to improve how optical elements are designed in industry, and how optimal transport problems are solved in general.

The full proposal can be found by clicking on this link.

A meaningful job in a dynamic and ambitious university, in an interdisciplinary setting and within an international network. You will work on a beautiful, green campus within walking distance of the central train station. In addition, we offer you:

• Full-time employment for four years, with an intermediate assessment after nine months. You will spend a minimum of 10% of your four-year employment on teaching tasks, with a maximum of 15% per year of your employment.
• Salary and benefits (such as a pension scheme, paid pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labour Agreement for Dutch Universities, scale P (min. € 3,059 - max. € 3,881).
• A year-end bonus of 8.3% and annual vacation pay of 8%.
• High-quality training programs and other support to grow into a self-aware, autonomous scientific researcher. At TU/e we challenge you to take charge of your own learning process.
• An excellent technical infrastructure, on-campus children's day care and sports facilities.
• An allowance for commuting, working from home and internet costs.
• A Staff Immigration Team and a tax compensation scheme (the 30% facility) for international candidates.

Do you recognize yourself in this profile and would you like to know more? Please contact the hiring manager Koondanibha Mitra, Assistant Professor, k.mitra@tue.nl.

Visit our website for more information about the application process or the conditions of employment. You can also contact Yvo Nooteboom, HR Advisor, y.f.j.nooteboom@tue.nl or +31 40 247 6340.

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