Emission Power

In the active zone of a laser diode, since the mobility of the electrons (n) is much higher than that of the holes (p), the total current density is nearly equal to that of the electrons following :

On the other hand, the variation in the electrons' density in comparison with the time is equal to the difference between the electrons' contribution

and the rate of the recombining of the electrons with q being the electrons' charge,  being the rate of the recombing of the electrons by the stimulated emission of photons (resp. non-radiating and photon spontaneity).

In hypothesizing that the active zone is homogenous and that all of the electrons recombine there, the electron contribution becomes simply :

Where d is the width of the active zone.

The evolution of the density of extra electrons in the active zone of a monomode laser diode is thus given by the “continuity equation”.

Where  is the density of electrons supplementary to the diode without feedback,  is the density of photons of the diode without feedback produced by stimulated emission, is the life time of an electron, and   is the coefficient of stimulated emission dependent upon  and accounting for the optical confinement factor.

The evolution of luminous flux I(z) in the interior of the laser diode, which is proportional to the density of photons, is given by : In noticing that

with being the time for a return-trip to the interior of the laser cavity, one obtains for the written expression of the stimulated emission coefficient :

Where  is the group speed in the active environment of the laser diode.

Under the conditions of spontaneous emission, since the density of photons could be considered as negligible, the rise of the injection current allows for the build-up of the density of electrons and thus of the gain . When for a threshold current density without feedback , this gain reaches the threshold value of , the laser emission condition is satisfied. The stimulated emission thus becomes predominant to the spontaneous emission and the density of photons is no longer negligible. For a current density  superior to the threshold value, the laser emission condition must always be verified, meaning that the gain and, as a result, the density of electrons no longer differ in their threshold values demonstrating the relationship  . Here's how the continuity equation allows us to express the density of photons contingent upon the current densities  :

The emission power without feedback  being proportional to the density of photons in the cavity, is thus expressed according to the injection current and to the injection current without feedback iths by the relationship :

Where  is a proportionality coefficient between the density of photons and the luminous emission power, the active volume, and the external quantum yield called the slope efficiency by laser diode manufactures.

This relationship demonstrates a linear variation of the emission power in the case of a slow modulation of the injection current above the threshold current.