Deconvolution of optical broadening in semiconductors

Gain spectra in semiconductors have often been measured by using Henry's formula in which directly measurable spontaneous emission spectra are transformed to gain spectra, but optical broadening is neglected. We have studied the effect of the optical broadening to the Henry's formula and have derived a more general relation by deconvolution of the optical broadening using Fourier transformation. Lorentz, Gauss and sech-lineshape optical broadening have been examined in detail. Numerical examples for a 50Å GaN/Al0.2 Ga0.8N quantum well have been used to transform the spontaneous emission to the gain spectrum using the general relation for the case of the sech-lineshape broadening. We have also derived a rather simple formula similar to the Henry's formula for the Gaussian broadening mechanism