Site Personnel de Stéphane Balac - Enseignant Chercheur à l'Université de Rennes 1

Mathematical modelling and numerical simulation in optronics and optical telecommunications

Mathematical modelling and numerical simulation of nonlinear optical phenomena in resonant microstructures

Whispering Gallery Mode (WGM) optical micro-resonators are optical resonator devices capable of confining light in very small modal volumes and for long periods of time.These devices are constituted of an access waveguide and a dielectric micro-cavity (with a spherical or cylindrical geometry with a radius ranging from 10 to 20 microns) where the light propagates along the surrounding interface of the cavity via total internal reflection. Over the last two decades, WGM micro-resonators have attracted much interest for fundamental research in quantum and nonlinear optics for applications e.g. in lasing, optical sensing or optical telecommunications.The theoretical study of WGM micro-resonators in order to improve their characteristics (such as their quality factor) or to broaden their field of applications (e.g. for use as bio-sensors for medical analysis) is currently limited by the weakness of the mathematical approaches used to model these devices and by the lack of efficient numerical simulation tools. Our aim is to develop mathematical models for WGM micro-resonators and to implement numerical simulation tools to improve their theoretical study.

This work is carried out in the framework of a multidisciplinary collaboration involving members of the Lasers & Telecoms Group at FOTON laboratory (UMR CNRS 6082, Lannion / Rennes), the Numerical Analysis team of the Mathematics Research Institute of Rennes (IRMAR, UMR 5525) and the MOST group at LAAS CNRS in Toulouse. It is granted by the ANR project ORA (optical resonators and their applications, ANR program Blanc 2010), the CNES project SHYRO and through the RTR Siscom project ROSE (2013).

Description of ORA project.
Description of SHYRO project.
Description of ROSE project.
Publications related to this research topic

Numerical simulation of incoherent optical wave propagation in non-linear fibres

This research activity concerns the study of pulsed laser systems containing a fibre amplifier for boosting the output power such as MOPFA systems (a master oscillator coupled with fibre amplifier, usually a cladding-pumped high-power amplifier often based on an ytterbium-doped fibre). An experimental study has established that the observed non-linear effects (such as Kerr effect, four waves mixing, Raman effect) could behave very differently depending on the characteristics of the optical source emitted by the master laser. However, it has not been possible to determine from the experimental data if the "statistics" of the photons is alone responsible for the various nonlinear scenarios observed. Therefore, we have developed a computer program for solving the generalized nonlinear Schrödinger (GNLS) equation with a stochastic source term in order to validate the hypothesis that the coherence properties of the master laser are mainly liable for the behaviour of the observed nonlinear effects.

The numerical method used to solve the GNLS equation is the ?Interaction Picture (IP) method? a variant of the Symmetric Split-Step method using an exponential integrator. The IP method has been developed by the Bose-Einstein condensate theory group of R. Ballagh from the Jack Dodd Centre at the University of Otago in the 90?s for solving the Gross-Pitaevskii equation which is ubiquitous in Bose condensation. We have study the IP method from a mathematical point of view and have compared it to the Symmetric Split-Step method. We also have developed dedicated local error estimate methods for adaptive step-size control in the IP method where the non-linear problem is solved by Embedded Runge-Kutta schemes.

  This work is achieved in collaboration with A. Fernandez, T. Chartier (Foton)  and F. Mahé, F. Méhat and R. Texier-Picard (IRMAR). It is supported by the Conseil Régional de Bretagne in the framework of the Green Laser project and in connection with Quantel Lannion R&D department.

Description of GreenLaser project.

Publications related to this research topic
| UFR de mathématiques | IRMAR | Université de Rennes 1 |