Effect of transient susceptibility on femtosecond pulse propagation in semiconductor quantum well waveguide

Ultra fast pulse evolution in a semiconductor quantum well structure (QWS) is theoretically analyzed. The polarization induced in the medium due to an incident Gaussian electromagnetic beam has been obtained using the semiconductor Bloch equations. The non-linear Schrodinger equation is used to analyze the effect of the induced polarization on the pulse. An interesting manifestation of the intensity dependence of the refractive index in non-linear media occurs through self-phase modulation (SPM), a phenomenon that leads to spectral broadening of the optical pulses. In doing the miniaturization of the device, we use semiconductor nanostructures in which the non-linearity is very large as compared to their bulk counterparts. Consequently, the phenomenon of SPM becomes significant at lower length scale leading to the limitations of the device. Numerical analysis was performed for a 150 fs Ti:sapphire laser radiation propagating along the transverse plane of a GaAs/AlGaAs QWS with realistic material parameters reveals asymmetric spectral broadening of the pulse due to SPM. The results agree qualitatively well with those available in the literature.