Design and optimization of a multi-cores photonic crystal fiber for spatial flat in-phase supermode laser output

• Flat supermode was obtained by optimizing doped concentration and geometric structure.
• Doped concentration-ratio tolerance is 4% for only optimizing doped concentration.
• The diameter-ratio tolerance is 0.74% for only optimizing geometrical structure.
• Both Δρr and Δdr are 7.6% for synchronously optimizing ρr and dr.

We report a new recipe, which is combinatorially optimizing distribution of Yb3+-doped concentration and geometrical structure of the multi-cores photonic crystal fiber (MCPCF) to obtain the equal amplitude distribution of the in-phase supermode. We present theoretical model based on the perturbation theory of coupled modes and vector finite element method (VFEM). Furthermore, a 7-cores PCF is designed. The equal amplitude distribution can be obtained through only optimizing distribution of Yb3+-doped concentration or geometrical structure, which is studied in detail. The results show that the doped concentration-ratio tolerance is 4% for only optimizing doped concentration and the air-hole diameter ratio tolerance is 0.74% for only optimizing geometrical structure. For simultaneously optimizing them, both the doped concentration-ratio tolerance and the air-hole diameter ratio tolerance are 7.6%, which is larger than 4% and 0.74%. So, in order to obtain spatially flat in-phase supermode, we simultaneously adjust the doped concentration ratio and the air-hole diameter ratio, which will facilely implement in experimental operation.