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

Introduction

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

Job Description

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. 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.

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. We have achieved this already for optical surfaces, i.e. mirrors and lenses (see Inverse freeform design in non-imaging optics (2025)), now it is time for F-GRINs.

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.

For more details, see Project_details_PEREGRINE.pdf.

Job Requirements

• A master’s degree (or an equivalent university degree) in mathematics or physics. Engineering master’s degree holders with a strong (and justifiable) inclination towards mathematics & physics are also encouraged to apply.
• An analytical mindset, familiarity with numerical methods and optimisation, or expertise in programming is solicited, preferably all three above. This could be substantiated by academic performance, research experience, MSc theses, industrial exposures, internships etc.
• A research-oriented attitude.
• Ability to work in an interdisciplinary team and interested in collaborating with industrial partners.
• Fluent in spoken and written English (C1 level).
  
  

Conditions of Employment

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. 

About us

Eindhoven University of Technology is a leading international university within the Brainport region where scientific curiosity meets a hands-on mindset. We work in an open and collaborative way with high-tech industries to tackle complex societal challenges. Our responsible and respectful approach ensures impact — today and in the future. TU/e is home to over 13,000 students and more than 7,000 staff, forming a diverse and vibrant academic community.

With over 110 (assistant, associate and full) professors, almost 300 PhD and EngD students, about 1500 Bachelor students and 1000 Master students, the Department of Mathematics and Computer Science (M&CS) is the largest department of the TU/e. By performing top-level fundamental and applied research, and maintaining strong ties with industry, M&CS aims to contribute to science and innovation in and beyond the region.

Curious to hear more about what it’s like as a PhD candidate at TU/e? Please view the video.

If you want to know more about our group and its research, click on this link.

Information

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.

Curious to hear more about what it’s like as a PhD candidate at TU/e? Please view the video.

Are you inspired and would like to know more about working at TU/e? Please visit our career page.

Application

We invite you to submit a complete application by using the apply button. The application should include a:

• Cover letter in which you describe your motivation and qualifications for the position.
• Curriculum vitae, including a list of your publications and the contact information of three references. Kindly note that we may reach out to references at any stage of the recruitment process. We recommend notifying your references upon submitting your application.

Ensure that you submit all the requested application documents. We give priority to complete applications.

We look forward to receiving your application and will screen it as soon as possible. The vacancy will remain open until the position is filled.

Please note

• You can apply online. We will not process applications sent by email and/or post. 
• A pre-employment screening (e.g. knowledge security check) can be part of the selection procedure. For more information on the knowledge security check, please consult the National Knowledge Security Guidelines.
• Please do not contact us for unsolicited services.