Optical Properties of Energy-Dependent Effective Mass GaAs/Ga x In1−x As and GaAs/Al x Ga1−x As Quantum Well Systems: A Shooting Method Study

In this paper, we study the effect of energy-dependent effective mass on optical properties of GaAs/GaxIn1−xAs and GaAs/AlxGa1−xAs quantum well systems through the compact density matrix approach. We solved the resulting nonlinear Schrödinger equation by a simple shooting method and present the algorithm. We show that the energy-dependent effective mass effect is more important for systems with narrower quantum well systems. By an energy-dependent effective mass assumption, absorption coefficient peak height increases with increasing the total system length L while in the constant effective mass limit, absorption coefficient peak heights have not been influenced by changing L. In the GaAs/AlxGa1−xAs system, by increasing the number of wells, the linear absorption coefficient amplitude at first increases and then decreases in the fixed effective mass approximation and monotonically decreases in the energy-dependent effective mass case. By increasing the number of wells, the linear absorption coefficient peak position at first shows a blue shift and then shows a redshift. In the GaAs/GaxIn1−xAs system, the situation is more complicated and it is described in more detail in the text. However, GaAs/GaxIn1−xAs quantum well systems have larger values of absorption coefficient peak heights than GaAs/AlxGa1−xAs ones.