Quantum cascade lasers are of great interest because of their working range and high
output power. Many investigations about these lasers are being done both experimentally
and theoretically and part of the experimental work is mainly concerned with the
confirmation of theoretical predictions. On the theory part, simulating the laser operation
demands many mathematical approximations and physical interpretations. To a very
good extent, results of the simulation conform to the experiment. Incorporating nonlinear
effects to the QC lasers makes them even more interesting as it becomes easier to go
beyond the level of performance and limitations dictated by the materials of the laser.
In this thesis, we tried to understand the effect of nonlinearity on propagation of a
pulse inside the medium of the laser. Specifically, we looked at saturable absorber (SA)
effect on the propagation of pulse. Saturable absorber is the basis of some other major
nonlinear effects as well. A finite difference approximation (up to second order
truncation error) was used to numerically solve the Maxwell-Bloch equations with SA
term and graphs were produced to compare the shape of the wave with and without the influence of SA.