We investigate the conversion between transverse mode structures in four-wave mixing in a heated rubidium vapour. While angular momentum conservation in this nonlinear process dictates the selection rules for the angular quantum number, the role of the radial quantum number is more esoteric. We demonstrate experimentally that a clean Laguerre-Gauss mode LG p =LG 0 1 can be generated by converting LG 1 0 and LG −1 0 near-infrared pump beams -but only if the length of the atomic medium exceeds the Rayleigh range. In the same regime we also observe a direct transfer of the total radial quantum number from input to generated light modes.

External-cavity diode lasers are ubiquitous in atomic physics and a wide variety of other scientific disciplines, due to their excellent affordability, coherence length and versatility. However, for higher power applications, the combination of seed lasers, injection-locking and amplifiers can rapidly become expensive and complex. Here we present a high-power, single-diode laser design with specifications: >210 mW, 100 ms-linewidth (427 ± 7) kHz, >99% mode purity, 10 GHz mode-hop-free tuning range and 12 nm coarse tuning. Simple methods are outlined to determine the spectral purity and linewidth with minimal additional infrastructure. The laser has sufficient power to collect 10 10 87 Rb atoms in a single-chamber vapourloaded magneto-optical trap. With appropriate diodes and feedback, the system could be easily adapted to other atomic species and diode laser architectures.