# Mathematical modeling in optics and photonics

Duration: 25h allocated as follows : 8h (lectures) + 19h (project work)

Who should attend?

The course is aimed at

- Master level students or PhD students in Physics
- Master level students in Mathematics

who intend to use mathematical models in linear or nonlinear optics for numerical simulation purposes.

Prerequisites:

Differential and integral calculus for functions of several variables, partial differential equations at undergraduate level.

Course objectives

As a result of this course, you will:- Understand the fundamental principles underlying linear and nonlinear optics
- Understand how various popular mathematical models in optics are derived from Maxwell's equations

Description

This course will present some key mathematical models in optics, providing a general framework for the study of various problems in this field. We shall consider the propagation of electromagnetic waves governed by Maxwell's equations, coupled with constitutive relations to model the interaction of electromagnetic fields with matter. Two cases will be considered: linear for moderate field amplitudes and non-linear for high intensity field such as lasers. Important methods and popular mathematical models will be illustrated by problems involving optical waveguides, laser beam propagation, crystal optics,

This course is intended to serve as an introduction to popular mathematical models in linear and nonlinear optics. We will tackle only a few basic problems (optical waveguides, laser beam propagation, crystal optics ...), with however the aim of giving methods and landmarks in the theory.

Course topics:

- Maxwell's equations
- Linear and nonlinear polarization
- Mathematical modelling of optical waveguides
- The Nonlinear Schrödinger Equation in optics

Main lecturer : Stéphane Balac, Ph.D from University of Rennes 1
(France),
is Assistant Professor in Numerical Analysis at the Mathematics
Institute of Rennes and FOTON Laboratory. His research areas are related to mathematical
modeling and numerical simulation in photonics and optical
telecommunications. |

Lecturers : Eric Darrigrand, Yvon Lafranche, Fabrice Mahé