The Nonlinear Absorption of a Strong Electromagnetic Wave in Low-dimensional Systems

Abstract

It is well known that in low-dimensional systems, the motion of electrons is restricted. The confinement of electron in these systems has changed the electron mobility remarkably. This has resulted in a number of new phenomena, which concern a reduction of sample dimensions. These effects differ from those in bulk semiconductors, for example, electronphonon interaction effects in two-dimensional electron gases (Mori & Ando, 1989; Rucker et al., 1992; Butscher & Knorr, 2006), electron-phonon interaction and scattering rates in one-dimensional systems (Antonyuk et al., 2004; Kim et al., 1991) and dc electrical conductivity (Vasilopoulos et al., 1987; Suzuki, 1992), the electronic structure (Gaggero-Sager et al., 2007), the wave function distribution (Samuel & Patil, 2008) and electron subband structure and mobility trends in quantum wells (Ariza-Flores & Rodriguez-Vargas, 2008). The absorption of electromagnetic wave in bulk semiconductors, as well as low dimensional systems has also been investigated (Shmelev et al., 1978; Bau & Phong, 1998; Bau et al., 2002; 2007). However, in these articles, the author was only interested in linear absorption, namely the linear absorption of a weak electromagnetic wave has been considered in normal bulk semiconductors (Shmelev et al., 1978), the absorption coefficient of a weak electromagnetic wave by free carriers for the case of electron-optical phonon scattering in quantum wells are calculated by the Kubo-Mori method in quantum wells (Bau & Phong, 1998) and in doped superlattices (Bau et al., 2002), and the quantum theory of the absorption of weak electromagnetic waves caused by confined electrons in quantumwires has been studied based on Kubo’s linear response theory andMori’s projection operator method (Bau et al., 2007); the nonlinear absorption of a strong electromagnetic wave by free electrons in the normal bulk semiconductors has been studied by using the quantum kinetic equation method (Pavlovich & Epshtein, 1977). However, the nonlinear absorption problem of an electromagnetic wave, which has strong intensity and high frequency, in low dimensional systems is still open for study. In this book chapter, we study the nonlinear absorption of a strong electromagnetic wave in low dimensional systems (quantumwells, doped superlattices, cylindrical quantumwires and rectangular quantum wires) by using the quantum kinetic equation method. Starting from the kinetic equation for electrons, we calculate to obtain the electron distribution functions in low dimensional systems. Then we find the expression for current density vector and the nonlinear absorption coefficient of a strong electromagnetic wave in low dimensional The Nonlinear Absorption of a Strong Electromagnetic Wave in Low-dimensional Systems