Effect of Magnetic Field on Nonlinear Absorption of a Strong Electromagnetic Wave in Low-dimensional Systems

Abstract

Recently, there are more and more interests in studying and discovering the behavior of low-dimensional system, such as compositional superlattices, doped superlattices, quantum wells, quantum wires and quantum dots. The confinement of electrons and phonons in lowdimensional systems considerably enhances the electron mobility and leads to unusual behaviors under external stimuli. Many attempts have conducted dealing with these behaviors, for examples, electron-phonon interaction effects in two-dimensional electron gases (graphene, surfaces, quantum wells) (Ruker et al., 1992; Richter et al., 2009; Butscher et al., 2006). The dc electrical conductivity (Vasilopoulos et al., 1987; Suzuki, 1992), the electronic structure (Sager et al., 2007), the wavefunction distribution (Samuel et al., 2008) and the electron subband (Flores, 2008) in quantum wells have been calculated and analyzed. The problems of the absorption coefficient for a weak electromagnetic wave in quantum wells (Bau&Phong, 1998), in doped superlattices (Bau et al., 2002) and in quantum wires (Bau et al., 2007) have also been investigated and resulted by using Kubo-Mori method. The nonlinear absorption of a strong electromagnetic wave in low-dimensional systems have been studied by using the quantum transport equation for electrons (Bau&Trien, 2011). However, the nonlinear absorption of a strong electromagnetic wave in low-dimensional systems in the presence of an external magnetic field with influences of confined phonons is stills open to study. In this chapter, we consider quantum theories of the nonlinear absorption of a strong electromagnetic wave caused by confined electrons in the presence of an external magnetic field in low dimensional systems which considered the effect of confined phonons. The problem is considered for the case of electron-optical phonon scattering. Analytic expressions of the nonlinear absorption coefficient of a strong electromagnetic wave caused by confined electrons in the presence of an external magnetic field in low-dimensional systems are obtained. The analytic expressions are numerically calculated and discussed to show the differences in comparison with the case of absence of an external magnetic with a specific AlAs/GaAs/AlAs quantum well, a compensated n-p n-GaAs/p-GaAs doped superlattices and a specific GaAs/GaAsAl quantum wire. This book chapter is organized as follows: In section 2, effect of magnetic field on nonlinear absorption of a strong electromagnetic wave in a quantum well. Section 3 presents the effect