Antihydrogen can be synthesized by mixing antiprotons and positrons in a Penning trap environment. Here an experiment to stimulate the formation of antihydrogen in the n = 11 quantum state by the introduction of light from a CO2 continuous wave laser is described. An overall upper limit of 0.8% with 90% C.L. on the laser-induced enhancement of the recombination has been found. This result strongly suggests that radiative recombination contributes negligibly to the antihydrogen formed in the experimental conditions used by the ATHENA Collaboration.