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Journal of Electromagnetic Waves and Applications

The Nonlinear Absorption Coefficient of a Strong Electromagnetic Wave by Confined Electrons in Quantum Wells Under the Influences of Confined Phonons

Nguyen Quang Bau, Le Thai Hung, N. D. Nam

Published Jan 1, 2010• 14 citations
Publisher

Abstract

The nonlinear absorption coefficient (NAC) of a strong electromagnetic wave (EMW) by confined electrons in quantum wells under the influences of confined phonons is theoretically studied by using the quantum transport equation for electrons. In comparison with the case of unconfined phonons, the dependence of the NAC on the energy (ħΩ), the amplitude (Eo) of external strong EMW, the width of quantum wells (L) and the temperature (T) of the system in both cases of confined and unconfined phonons is obtained. Two limited cases for the absorption: close to the absorption threshold (|kħΩ – ħω0| « ε) and far away from the absorption threshold (|kħΩ – ħωo| » ε) (k = 0,±1,±2,...,ωo and ε are the frequency of optical phonon and the average energy of electron, respectively) are considered. The formula of the NAC contains the quantum number m characterizing confined phonons and is easy to come back to the case of unconfined phonons and linear absorption. The analytic expressions are numerically evaluated, plotted and discussed for a specific case of the GaAs/GaAsAl quantum well. Results show that there are more resonant peaks of the NAC which appear in the case of confined phonons when Ω > ω 0 than in that of unconfined phonons. The spectrums of the NAC are very different from the linear absorption and strongly depend on m.

DOI
10.1163/156939310792486674

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Chinese Journal of Luminescence•Jan 1, 2006•0 citations
The nonlinear absorption coefficient (NAC) of a strong electromagnetic wave (EMW) by confined electrons in quantum wells under the influences of confined phonons is theoretically studied by using the quantum transport equation for electrons. In comparison with the case of unconfined phonons, the dependence of the NAC on the energy (ħΩ), the amplitude (Eo) of external strong EMW, the width of quantum wells (L) and the temperature (T) of the system in both cases of confined and unconfined phonons is obtained. Two limited cases for the absorption: close to the absorption threshold (|kħΩ – ħω0| « ε) and far away from the absorption threshold (|kħΩ – ħωo| » ε) (k = 0,±1,±2,...,ωo and ε are the frequency of optical phonon and the average energy of electron, respectively) are considered. The formula of the NAC contains the quantum number m characterizing confined phonons and is easy to come back to the case of unconfined phonons and linear absorption. The analytic expressions are numerically evaluated, plotted and discussed for a specific case of the GaAs/GaAsAl quantum well. Results show that there are more resonant peaks of the NAC which appear in the case of confined phonons when Ω > ω 0 than in that of unconfined phonons. The spectrums of the NAC are very different from the linear absorption and strongly depend on m.
Theoretical study on the nonlinear absorption of a strong electromagnetic waves in infinite semi-parabolic plus semi-inverse Squared Quantum Wells (ISPPSISQW) by using quantum kinetic equations for electron in the case of electron-acoustic phonon scattering. Analytical expressions for the nonlinear multi-photon absorption coefficient in the ISPPSISQW are obtained for a specific GaAs/GaAsAl in the case off the absence and the case of the presence of an external magnetic field B. A second- order multi-photon process is included in the result. The dependence of the nonlinear multi-photon absorption coefficient on the intensity (E0)(E_0)(E0​) and the frequency (Ω)(\Omega)(Ω) of a strong electromagnetic wave, confinement frequency of ISPPSISQW (Ω)(\Omega)(Ω) and the temperature investigated. The numerical computations for a specific ISPPSISQW GaAs/GaAsAl show that the nonlinear multi-photon absorption coefficient decreases rapidly with increasing ωz\omega_zωz​ or Ω\OmegaΩ and the nonlinear multi-photon absorption coefficient increases rapidly E0E_0E0​ or T. In the case of the presence of an external magnetic field B, numerical calculations indicate the occurrence of magneto-photon-phonon resonances when the resonance conditions are met. As the photon energy changes, the resonance peaks tend to increase with the increase in photon energy.
The electron-phonon interaction influences on linear and nonlinear optical absorption in cylindrical quantum wires (CQW) with an infinite confining potential are investigated. The optical absorption coefficients are obtained by using the compact-density-matrix approach and iterative method, and the numerical results are presented for GaAs CQW. The results show that the electron-phonon interaction makes a distinct influence on optical absorption in CQW. The electron-phonon interaction on the wave functions of electron dominates the values of absorption coefficients and the correction of the electron-phonon effect on the energies of the electron makes the absorption peaks blue shift and become wider. Moreover, the electron-phonon interaction influence on optical absorption with an infinite confining potential is different from that with a finite confining potential.
The optical absorptions coefficients with considering the electron-phonon interaction were theoretically studied in square tangent quantum wells.The wave functions and energy levels are described in square tangent quantum wells by perturbation theory when the polaron effects were considered,and analytic expression for the linear and the third-order nonlinear optical absorption coefficients was obtained by the compact density-matrix method and the iterative procedure.The numerical results for typical GaAs/AlGaAs material showed that the electron-phonon interaction had great influence on the linear,nonlinear and total optical absorption,meanwhile the absorption saturation phenomenon was more obvious than the one without considering the polaron effects.Moreover,the changes of the total optical absorptions increased with the well width b decreasing or the well depth V0 increasing when the electron-phonon interaction was considered.
By using the compact density matrix approach and iterative procedure, a detailed procedure for the calculation of the linear and nonlinear optical absorption coefficients was given in the electric-field-biased semi parabolic quantum wells(QWs). The simple analytical formulas for the linear and nonlinear optical absorption coefficients in the systems are also deduced. Numerical result on typical GaAs materials shows that,the linear and nonlinear optical absorption coefficients sensitively depend on the applied electric field and the confined potential frequency of the semiparabolic QWs systems as well as the incident optics beam intensity.
In this study, the effects of the external fields (electric and tilted magnetic fields) and well parameters on the optical absorption coefficients in GaAs/GaAlAs multiple (five) quantum wells under the applied electric and tilted magnetic fields has been investigated theoretically. Firstly, the energy eigenvalues and eigen functions of an electron confined in multiple quantum wells are calculated by analytically from Schrödinger equation using the transfer matrix method within the effective mass approximation, Secondly, the linear, nonlinear and total intersubband optical absorptions in GaAs/GaAlAs multiple quantum wells system are studied within the compact density-matrix approach. It is shown that the parameters such as strenghts of the external fields and θ-tilted angle values not only shift the peak positions in absorption spectrum but also considerably modify their potential heights. In generally, electronic and optical properties of the quantum wells are very sensitive to the applied external fields and well parameters. Therefore, we can conclude that the effect of the external fields can be used to tune and control the optical properties of interest in the range of the far-infrared electromagnetic spectrum.
In the past few years advance in nanofabrication techniques have made it possible to make well-like compound semiconductor structures of low nanometer size.In these structures,the state of the electron in the direction perpendicular to the length of the well is quantized with sufficiently large separation in energy levels and the motion of the electron parallel to the length is that of a quasi-free electron.One of the most remarkable properties of these one-dimensional electron system is that the optical transitions between the size-quantized subbands are feasible.The result shows there is a large optical nonlinearities in asymmetric quantum wells.The problem of optical saturation of intersubband absorption has recently attracted considerable attention.The problem is very important to the development of superlattice devices such as fast infrared detectors and(modulators) because one needs to know the range of input optical intensities for which linear operation is(possible.) The analytical expression of the linear and the third-order nonlinear optical intersubband absorption coefficients are obtained in Pschl-Teller wells using the density matrix formalism taking into account the(intrasubband) relaxation.Since there are two adjustable parameters κ and λ in Pschl-Teller wells,the shapes of the wells will change with the change of the parameters κ and λ,accordingly the linear and the third-order nonlinear optical absorption coefficients will change with the parameters κ and λ.It is shown that the optical absorption coefficient depends on the parameter,and the optical intensity strongly. The absorption saturation will occur with I increase.Numerical results are presented for a typical AlGaAs/GaAs Pschl-Teller well.