Modeling of the electromagnetic field and level populations in a waveguide amplifier: a multi-scale time problem

Alexandre Fafin (1) , Julien Cardin (1) , Christian Dufour (1) , Fabrice Gourbilleau (1)

1 CIMAP - UMR 6252 - Centre de recherche sur les Ions, les MAtériaux et la Photonique

A new algorithm based on auxiliary differential equation and finite difference time domain method (ADE-FDTD method) is presented to model a waveguide whose active layer is constituted of a silica matrix doped with rare-earth and silicon nanograins. The typical lifetime of rare-earth can be as large as some ms, whereas the electromagnetic field in a visible range and near-infrared is characterized by a period of the order of fs. Due to the large difference between these two characteristic times, the conventional ADE-FDTD method is not suited to treat such systems. A new algorithm is presented so that the steady state of rare earth and silicon nanograins electronic levels populations along with the electromagnetic field can be fully described. This algorithm is stable and applicable to a wide range of optical gain materials in which large differences of characteristic lifetimes are present.

Mots clés: Rare-earth- doped materials; Optical amplifiers; -wire and -dot devices; Computational electromagnetic methods; -wire and -dot devices.; Waveguides; Quantum-well

Domaines: Optique [physics.optics]; Physique Numérique [physics.comp-ph]; Science des matériaux [cond-mat.mtrl-sci]; Matière Condensée [cond-mat]; Electromagnétisme; Optique / photonique

Alexandre Fafin, Julien Cardin, Christian Dufour, Fabrice Gourbilleau. Modeling of the electromagnetic field and level populations in a waveguide amplifier: a multi-scale time problem. Optics Express, 2013, 21 (20), pp.24171-24184. ⟨10.1364/OE.21.024171⟩. ⟨hal-00927306⟩