From these equations, it is possible to derive a set of steady state and small signal equations to help in further understanding the static and dynamic characteristics of semiconductor lasers.

Note that these equations can be cast in many different forms, this is one example of them.

Table of contents |

2 Gain Compression 3 Spectral Shift |

N and P are carrier and photon densities respectively. I is the injected current and e the electronic charge.τ_{n} and τ_{p} are carrier and photon lifetimes respectively. M is the number of modes modelled. V is the active region volume which can be omitted if the
equations are to be interpreted in terms of carrier and photon numbers as opposed to densities. Γ is the mode confinement factor which describes how much of the mode is confined in the active region. μ is the mode number.β_{mu} is the spontaneous emission factor.

G_{μ} is the gain of the μ^{th} mode and can be modelled by a parabolic dependence of gain
on wavelength as follows:

β_{μ} is given by

β_{0} is the spontaneous emission factor, λ_{s} is the centre wavelength for spontaneous emission and δλ_{s} is the spontaneous emission FWHM. Finally, λ_{mu} is the wavelength of the μ^{th} mode and is given by

The gain term, G, 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 :

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. A complete analysis of spectral shift during direct modulation found that the refractive index of the active region varies proportionally to carrier density and hence the wavelength varies proportionally to injected current.

Experimentally, a good fit for the shift in wavelength is given by: