Hermite-Gaussian multi-mode excitation in spatial gain shaping approaches for laser resonators

Abstract

This study explores the excitation of transverse laser modes through spatial gain shaping, while focusing on the boundary between selective single-mode and multi-mode lasing. By deliberately reducing the similarity between intensity distributions of pump and laser mode, it was studied, if and which other modes are excited besides the target mode, and how the modes compete for the spatially distributed gain. Analysis of the usually unwanted multi-mode lasing revealed characteristic properties of pump distributions adapted to Hermite-Gaussian $\text{HG}_{m,0}$ modes: a center-heavy pump distribution at first distinctly excites the target mode and eventually low-order modes, whereas an eccentric pump distribution reduces the lasing threshold at the expense of distinction to the neighboring modes. By understanding why certain gain distributions do not excite a single mode, we infer guidelines for the design of pump patterns in spatial gain shaping approaches.