4 ECTS credits
120 h study time
Offer 1 with catalog number 4012212ENR for all students in the 1st semester at a (E) Master - advanced level.
This course covers the main mathematical concepts required to fully understand photonic based systems and the physics of light-matter interaction. In particular, this course focuses on the following:
1- Complex analysis and calculus: after introducing complex functions and their properties, the course discusses so-called Residue Calculus and apply it to the calculation of real integrals using complex analysis. In this chapter, we will also see the importance of the kramers-kronig relation applied to the susceptibility of optical materials along with so-called conformal transformations.
2- The special functions that are Bessel functions and Hermite polynomials: what is their origin, their properties and why they are important in photonics.
3- Numerical techniques used in practice to simulate photonic systems: describing the main fundamental concepts of each, along with their advantages and drawbacks. The main goal here being to provide all information required to choose the most efficient method for a given problem considering its specificities.
4- The impact of symmetries and periodicities in photonic systems: detailing the effect of symmetries and periodicities on the system behaviour and how they could be exploited in practice e.g. in photonic crystals.
5- Dynamical behaviour of photonic systems: in this part, a short introduction to the much wider topic of nonlinear dynamics will be given. The course covers the basic concepts of dynamical systems, steady-states and periodic orbits first for 1D and 2D discrete maps before extending to continuous systems. Saddle points and chaos will also be quickly covered.
This course aims at introducing the main mathematical concepts that are encountered in the field of optics and photonics.
The goal is to provide the student with all the basic mathematical tools required to fully understand the main courses of the master in photonics. The student must be able 1/ to understand these concepts, and 2/ to use them in the context of photonics.
The expected learning outcomes for this course are:
- Master and apply advanced knowledge in the own field of engineering in case of complex problems
- Specify, design and test complex photonic components systems
- Be familiar with the basic elements of another master discipline which is relevant in combination with photonics
- Analyse complex problems and convert them into scientific questions
- Select and apply the proper models, methods and techniques
- Develop and validate mathematical models and methods
- Ability to talk about field of specialisation in English
- Report on technical or scientific subject orally, in writing and in graphics
- Act in an ethical, professional and social way
- Master the complexity of technical systems by the use of system and process models
- Dispose of enough knowledge and comprehension to control the results of complex calculations or make approximate estimates
- Pay attention to entire life-cycles of system machine and processes
- Choose the most appropriate design and test methods, including CAD methods for photonic components and system, understand their theoretical background and apply them accurately.
The final grade is composed based on the following categories:
Other Exam determines 100% of the final mark.
Within the Other Exam category, the following assignments need to be completed:
The evaluation is in two parts. The first part consists in a written, open book exam during which the student will have to solve different exercises using the mathematical concepts and calculation techniques developed during the course. Considering the complexity of the presented notions, the student must give detailed answers and explain how and why they proceed as they do. The written examination will account for 10 out of 20 points. The second part will be an oral, open-book examination without preparation time. The student receives a set of relatively simple questions which are to be answered concisely eventually by making quick drawings or calculations. If necessary the examiner will guide the students by giving some hint or ask intermediate questions leading to the answer. The oral examination will account for 10 out of 20 points.
The total score for the two parts of the examination yield a final score on a total of 20 points.
In addition to demonstrating that she/he understands the subject and mathematical concepts at stake, and that he/she is able to apply and explain them in a clear and structured way, the student must also:
- Know the requirements of the different theorems, lemma and formula presented
- Know advanced calculation techniques, and in particular but not limited to: derivation, integration, manipulation of sum and integrals, manipulation of matrices, determinant calculation, handling of complex phasors.
- Understand the connection between the mathematical concepts covered and known physical properties or mechanisms.
This offer is part of the following study plans:
Master of Photonics Engineering: On campus traject
Master of Photonics Engineering: Online/Digital traject