This system of ordinary differential equations relates the number or density of photons and charge carriers (electrons) in the device to the injection current and to device and material parameters such as carrier lifetime, photon lifetime, and the optical gain.
The rate equations may be solved by numerical integration to obtain a time-domain solution, or used to derive a set of steady state or small signal equations to help in further understanding the static and dynamic characteristics of semiconductor lasers.
In the multimode formulation, the rate equations[1] model a laser with multiple optical modes.
) and the third term is the carrier depletion due to stimulated recombination, which is proportional to the photon density and medium gain.
and the third term is the contribution of spontaneous emission from the carrier radiative recombination into the laser mode.
The gain term, G, cannot be independent of the high power densities found in semiconductor laser diodes.
Spatial hole burning occurs as a result of the standing wave nature of the optical modes.
Carriers are therefore depleted faster at the crest of the wave causing a decrease in the modal gain.
Hence, the following term in the denominator of the gain equation : Dynamic wavelength shift in semiconductor lasers occurs as a result of the change in refractive index in the active region during intensity modulation.
It is possible to evaluate the shift in wavelength by determining the refractive index change of the active region as a result of carrier injection.