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

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.

- A. Rasoloniaina, V. Huet, M. Thual, S. Balac, P. Féron, and Y. Dumeige. Analysis of third-order nonlinearity effects in very high-Q WGM resonator cavity ringdown spectroscopy. Journal of the Optical Society of America B (32(3),370-378 (2015))
- S. Balac and P. Féron. Whispering gallery modes volume computation in optical micro-spheres. Rapport de recherche du laboratoire FOTON, 2014

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.

- S. Balac and A. Fernandez. SPIP: A computer program implementing the Interaction Picture method for simulation of light-wave propagation in optical fibre. Computer Physics Communications, 2015 (DOI : 10.1016/j.cpc.2015.10.012)
- S. Balac and F. Mahé. An Embedded Split-Step method for solving the nonlinear Schrödinger equation in optics. Journal of Computatiional Physics (280, 295-305 (2015))
- S. Balac and A. Fernandez. Mathematical analysis of adaptive
step-size techniques when solving the nonlinear Schrödinger equation
for simulating light-wave propagation in optical fibers. Optics
Communications (329, 1-9 (2014))

- S. Balac, A. Fernandez, F. Mahé, F. Méhats and R. Texier-Picard. The
Interaction Picture method for solving the generalized nonlinear
Schrödinger equation in optics. Submitted to M2AN (2014)

- S. Balac. High order embedded Runge-Kutta scheme for step-size control in the Interaction Picture method. J. KSIAM (Journal of the Korean Society for Industrial and Applied Mathematics) (17(4) : 238?266 (2013))
- S. Balac and F. Mahé. Embedded Runge-Kutta scheme for step-size
control in the Interaction Picture method
*. Computer Physics Communications*(184(4) : 1211-1219 (2013)) - A. Fernandez, S. Balac, A. Mugnier, F. Mahé, R. Texier-Picard, T. Chartier and D. Pureur. Numerical simulation of incoherent optical wave propagation in nonlinear fibres. European Physical Journal - Applied Physics, (64(2): 24506, (2013))
- S. Balac and A. Fernandez. Comparison of adaptive step-size control strategies for solving the Generalised Non-Linear Schrodinger Equation in optics by the Interaction Picture method. Rapport de recherche du laboratoire FOTON, 2012.