Single-photon acquisition probability is deduced from TEM_ 10 and TEM_ 01 mode Hermite-Gaussian beams of optical electromagnetic field equation. Single-photon acquisition is analyzed for the laser links between a ground station and a satellite in a low earth orbit. The theoretical study shows that it is feasible for quantum key distribution between a ground station and a satellite in a low earth orbit to use highly attenuated laser pulses based on TEM_ 10 and TEM_ 01 mode Hermite-Gaussian beams as single-photon sources.