Optical rectification in quantum wells within different confinement and nonlinearity regimes

In this paper, we study the effect of conduction band non-parabolicity on optical rectification coefficients (ORCs) of quantum well systems by using compact density matrix approach. To investigate the non-parabolicity effect, we include a fourth derivative of the wave function in the Schrödinger equation. Our calculations are based on high accuracy 3, 5, 13 and 15 points finite difference methods that are developed by an interpolation approach. We show that, in some situations, the conduction band non-parabolicity can considerably affect the optical properties. Thus, it is necessary to include the conduction band non-parabolicity effects. We compare three different structures GaAs/AlxGa1-xAs (weak confinement & medium nonlinearity), GaN/AlN (strong confinement & weak nonlinearity) and InSb/GaSb (medium confinement & strong nonlinearity). We show that the non-parabolicity is very important for systems with smaller system lengths. For fixed geometrical parameters, the ORC of Al0.3Ga0.7As/GaAS quantum wells is greater than that of GaN/AlN quantum wells and the ORC of GaN/AlN quantum wells is greater than that of InSb/GaSb quantum wells. The behavior of the ORC under the influence of the applied electric field is different for the three above-mentioned quantum well systems. The red or blue shift of the ORC peak positions is more observable for systems with larger Leff.