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
- 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
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
- 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.
