A vertical external cavity surface emitting laser (VECSEL) based system in a linear single cavity configuration is configured to deliver light in higher-order Hermite-Gaussian transverse modes with Watt-level output power. Simultaneous and independent lasing of spatially-restructurable multiple high-order transverse modes that are collinearly-propagating at the output of such laser cavity is facilitated with the use of an optical pumping scheme devised to control positions of location at which the gain medium of the system is pumped (e.g., locations of focal spots of multiple pump beams on the gain-medium chip). An external astigmatic mode converter is utilized to convert such high-order Hermite-Gaussian modes into corresponding Laguerre-Gaussian modes.