Derivation of gain spectra of laser diodes from spontaneous emission measurements

The use of detailed balance relationships between absorption and emission to obtain a gain spectrum from a spontaneous emission spectrum is a relatively easy method of measuring the gain from a semiconductor laser. It has been shown that the usual theoretical gain and emission spectra do not satisfy these relationships casting doubt on the validity of the procedure. We show that this arises from the incorrect implementation of spectral broadening that leads to a situation where the carriers and photons are no longer in thermal equilibrium and the relationship between absorption and gain in the calculations breaks down. We show that with a more exact implementation of spectral broadening thermal equilibrium is preserved and that the relationship between absorption and emission remains valid. We discuss the accuracy of the measurements required to obtain a correct gain spectra