Editing Laser diode rate equations (section)

==Gain Compression==

The gain term, <math>G</math>, cannot be independent of the high power densities found in
semiconductor laser diodes.  There are several phenomena which cause the gain to
'compress' which are dependent upon optical power.  The two main phenomena are
[[spatial hole burning]] and [[spectral hole burning]].

Spatial hole burning occurs as a result of the standing wave nature of the optical
modes.  Increased lasing power results in decreased carrier diffusion efficiency which
means that the stimulated recombination time becomes shorter relative to the carrier
diffusion time.  Carriers are therefore depleted faster at the crest of the wave causing a
decrease in the modal gain.

Spectral hole burning is related to the gain profile broadening mechanisms such
as short intraband scattering which is related to power density.

To account for gain compression due to the high power densities in semiconductor lasers, the gain equation is modified such that it becomes related to the inverse of the optical power.  Hence, the following term in the denominator of the gain equation :

:<math>1 + \epsilon \sum_{\mu=1}^{\mu=M}P_\mu</math>