Theory of transverse modes in GaAs junction lasers

The resonant frequencies of a proposed laser model have been calculated and compared with high-resolution (0.1Å) spectral measurements. It is believed that for the first time a good agreement between theoretical and experimental results has been obtained for the frequency separation of transverse modes. The laser resonances are characterized by three mode numbers (
m, n, q
), where
m, n
are transverse mode numbers in the directions perpendicular and along the junction plane, respectively, and
q
is the longitudinal mode number. The output spectrum usually shows a number of "satellites" located adjacent to each longitudinal (Fabry-Perot) resonance. The observation of Hermite-Gaussian modes
H_{n},(\xi)\exp(-\xi^{2}/2})
along the junction plane has suggested that, for fixed
m
and
q
, each satellite may be associated with the mode numbers
n = 1, 2,
etc. This is supported by both theoretical and experimental results. The model includes the effects of a varying dielectric constant both perpendicular and along the junction plane. A parabolic profile of the dielectric constant is assumed along the junction plane as suggested by the presence of Hermite-Gaussian propagation. It is found from Maxwell's equations that the frequency separation between two modes (
m, n, q
) and (
m, n, +1, q
) is a function of the focusing given by the variation of the dielectric constant along the junction plane. More specifically, increased focusing is associated with larger frequency separations. A typical value for the amount of focusing was obtained by scanning a laser far field pattern along the junction plane. From this information the frequency separation calculated from the model was found to be of the order of 6.4 GHz (0.15 Å). This value includes the effects of dispersion and is in good agreement with frequency separations obtained experimentally from about 25 lasers that have been tested. This reproducibility, which has not been previously reported, is thought to be due to the use of diodes with stripe geometry metallic contacts.