Ability to increase a weak electromagnetic wave by confined electrons in doped superlattices in the presence of laser radiation modulated by amplitude

The analytic expressions for the absorption coefficient (ACF) of a weak electromagnetic wave (EMW) caused by confined electrons in the presence of laser radiation modulated by amplitude in doped superlattices (DSL) are obtained by using the quantum kinetic equation for electrons in the case of electron–optical phonon scattering.
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Ability to increase a weak electromagnetic wave by confined electrons in doped superlattices in the presence of laser radiation modulated by amplitude JOURNAL OF SCIENCE OF HNUE Mathematical and Physical Sci., 2012, Vol. 57, No. 7, pp. 113-123 This paper is available online at http://stdb.hnue.edu.vn ABILITY TO INCREASE A WEAK ELECTROMAGNETIC WAVE BY CONFINED ELECTRONS IN DOPED SUPERLATTICES IN THE PRESENCE OF LASER RADIATION MODULATED BY AMPLITUDE Nguyen Thi Thanh Nhan1, Nguyen Vu Nhan2 and Nguyen Quang Bau1 1 Faculty of Physics, College of Natural Sciences, Hanoi National University 2 Faculty of Physics, Academy of Defence force - Air force Abstract. The analytic expressions for the absorption coefficient (ACF) of a weak electromagnetic wave (EMW) caused by confined electrons in the presence of laser radiation modulated by amplitude in doped superlattices (DSL) are obtained by using the quantum kinetic equation for electrons in the case of electron–optical phonon scattering. The dependence of the ACF of a weak EMW on the temperature, frequency and superlattice parameters is analyzed. The results are numerically calculated, plotted and discussed for n-GaAs/p-GaAs DSL. The numerical results show that ACF of a weak EMW in a DSL can get negative values. So, by the presence of laser radiation modulated by amplitude, in some conditions, the weak EMW is increased. The results also show that in some conditions, the ability to increase a weak EMW can be enhanced in comparison with the use of non-modulated laser radiation. This is different from the case of the absence of laser radiation modulated by amplitude. Keywords: Absorption coefficient, doped superlattices, weak electromagnetic wave, laser radiation.1. Introduction In recent times, there has been a growing interest in studying and discovering thebehavior of low-dimensional systems, in particular, DSL. The confinement of electronsin these systems considerably enhances electron mobility and leads to their unusualbehaviors under external stimuli. As a result, the properties of low-dimensional systems,especially the optical properties, are very different in comparison with those of normalReceived September 25, 2012. Accepted October 4, 2012.Physics Subject Classification: 62 44 01 03.Contact Nguyen Thi Thanh Nhan, e-mail address: nhan_khtn@yahoo.com.vn 113 Nguyen Thi Thanh Nhan, Nguyen Vu Nhan and Nguyen Quang Baubulk semiconductors [1, 2]. The linear absorption of a weak EMW by confined electronsin low-dimensional systems has been investigated using the Kubo-Mori method [3, 4]and the nonlinear absorption of a strong EMW by confined electrons in low-dimensionalsystems has been studied by using the quantum kinetic equation method [5, 6]. Theinfluence of laser radiation on the absorption of a weak EMW by free electrons in normalbulk semiconductors has been investigated using the quantum kinetic equation method[7, 8] and the presence of laser radiation and, in some conditions, the weak EMW isincreased. The influence of laser radiation (non-modulated and modulated by amplitude)on the absorption of a weak EMW in compositional superlattices has been investigatedusing the Kubo-Mori method [9]. The influence of laser radiation on the absorption of aweak EMW in quantum wells has been investigated using the quantum kinetic equationmethod [10]. However, the influence of laser radiation modulated by amplitude on theabsorption of a weak EMW in DSL is still open for study. Researching the influence oflaser radiation on the absorption of a weak EMW plays an important role in experimentsbecause it is difficult to directly measure the ACF of strong EMW (laser radiation) byexperimental means. Therefore, in this paper, we study the ability to increase a weak EMWby confined electrons in DSL in the presence of laser radiation modulated by amplitude.The electron-optical phonon scattering mechanism is considered. The ACF of a weakEMW in the presence of a laser radiation field modulated by amplitude are obtained usingquantum kinetic equation for electrons in a DSL. We then estimate numerical values forthe specific n-GaAs/p-GaAs DSL to clarify our results.2. Content2.1. The absorption coefficient of a weak EMW in the presence of a laser radiation field modulated by amplitude in a DSL2.1.1. The laser radiation field modulated by amplitude As in [9], here we also assume that the strong EMW (laser radiation) modulated byamplitude has the form: F~ (t) = F~1 (t) + F~2 (t) = F~1 sin (Ω1 t + α1 ) + F~2 sin (Ω2 t + α2 ) (2.1)where, F~1 and F~2 has same direction, Ω1 and Ω2 are a bit different from each other orΩ1 ≈ Ω2 ; |∆Ω| = |Ω1 − Ω2 | ≪ Ω1 , Ω2 . After some transformations, we obtain: F~ (t) = E ~ 01 sin (Ωt + ϕ1 ) (2.2) pwith E01 = F12 + F22 + 2F1 F2 cos(∆Ωt + ∆α), ∆Ω = Ω1 − Ω2 , ∆α = α1 − α2 , Ω1 + Ω2 ′ α1 + α2 ′ F1 − F2 ∆Ω ∆α Ω= , ϕ1 = α + α , α = , tgα = tg t+ 2 . 2 2 F1 + F2 2114 Ability to increase a weak electromagnetic wave by confined electrons in doped superlattices...here, Ω is the reduced frequency (or the frequency of the laser radiation modulated byamplitude) and |∆Ω| is the modulated frequency. E ~ 01 is the intensity of the laser radiationmodulated by amplitude. ...