PhD project Scientific Computing / Illuminations Optics Freeform light guides for homogeneous illumination

The Department of Mathematics and Computer Science of Eindhoven University of Technology has a vacancy for a PhD-student in its Centre for Analysis, Scientific computing and Applications (CASA). CASA comprises the chairs Scientific Computing (SC) and Applied Analysis (TA). Its major research objective is to develop new and to improve existing mathematical (both analytical and numerical) methods for a wide range of applications in science and engineering.

Background

Illumination optics plays an important role in modern society. Products like mobile phones, lamps, car headlights, road lighting and even satellites all utilize illumination optics. A good optical design determines, for example, the energy efficiency of illumination devices, the minimization of light pollution or the sensitivity of sensors in satellites. The design of novel, sophisticated optical systems requires advances in the mathematical description and numerical simulation methods for these systems.

The optics applied in illumination is nonimaging, in contrast to for example a camera lens which is imaging. In nonimaging optics we study the transfer of light from a source to a target. The key problem is to design optical systems that convert a given source intensity into a desired target intensity.

A modern trend in illumination optics is to use scattering elements in addition to commonly used refractive (lenses) or reflective (mirrors) optical components. For example, in LED lighting systems scattering surfaces are used to hide too bright light sources and to redistribute the light. The physical description of scattering surfaces, on the one hand, and refractive/reflective surfaces, on the other hand, is quite different.

To bridge the gap between the corresponding subdisciplines scattering and geometrical optics, an NWO/TTW perspectief project was proposed by UT, TU Delft and TU/e, called Free-Form Scattering Optics. This proposal is supported by leading parties in the illumination industry: TNO, ASML, Signify, Lumileds, Demcon and Schott. In this project 12 PhD students work on different topics related to a) the fundamentals of scattering, b) the fundamentals of free-form optics, c) homogenization and diffusion and d) control the direction of light by interference.

This PhD project relates to the work package c) homogenization and diffusion.

Project Description

An alternative description of the propagation of light in an optical system is based on the phase space representation of the system. In this representation, each ray is defined by one or two space and direction coordinates, thus constituting a two or four dimensional phase space. The propagation of one ray can be described by the movement of a point in phase space, and the propagation of an entire beam can be interpreted as a 'flow' in phase space. This flow is governed by Liouville's equation, which is a first order hyperbolic conservation law. Sophisticated solution methods for the two-dimensional equation exist. 

The purpose of this research project is to extend the solution methods to the fourdimensional Liouville equation and to apply these methods to wave guides. More specifically, the Liouville solvers should be combined with methods from optimal control to design wave guides that create a homogeneous light output.

As a PhD student your tasks are the following:

Perform scientific research in the described domain;

Present results at international conferences;

Publish results in scientific journals;

Participate in activities of the group and the department;

Assist SC-staff in teaching undergraduate and graduate courses (at most 20 % of the time).

Requirements

We are looking for talented, enthusiastic PhD candidates who meet the following requirements:

A MSc in (applied) mathematics, physics or a related discipline with a strong background in computational physics;

Experience with Matlab and preferably C or C++;

Creative, pro-active team player with good analytical skills;

Good communicative skills in English, both written and oral.

Appointment and salary

We offer:

A full-time appointment for a period of four years, with an intermediate evaluation after nine months;

A gross salary of Euros 2,266 per month in the first year increasing up to Euros 2,897 per month in the fourth year;

Support for your personal development and career planning including courses, summer schools, conference visits, etc.;

A research position in an enthusiastic and internationally renowned research group;

A broad package of fringe benefits (e.g. excellent technical infrastructure, saving schemes, excellent sport facilities, and child daycare).