We studied the optical reflectivity of a specially grown double quantum well ͑DQW͒ structure characterized by a rectangular shape and a high electron density at room temperature. Assuming that the QWs depth is known, reflectivity spectra in the mid-IR range allow to carry out the precise measurements of the SAS-gap values ͑the energy gap between the symmetric and anti-symmetric states͒ and the absolute energies of both symmetric and antisymmetric electron states. The results of our experiments are in favor of the existence of the SAS splitting in the DQWs at room temperature. Here we have shown that the SAS gap increases proportionally to the subband quantum number and the optical electron transitions between symmetric and antisymmetric states belonging to different subbands are allowed. These results were used for interpretation of the beating effect in the Shubnikov-de Haas ͑SdH͒ oscillations at low temperatures ͑0.6 and 4.2 K͒. The approach to the calculation of the Landau-levels energies for DQW structures developed earlier ͓D. Ploch et al., Phys. Rev. B 79, 195434 ͑2009͔͒ is used for the analysis and interpretation of the experimental data related to the beating effect. We also argue that in order to explain the beating effect in the SdH oscillations, one should introduce two different quasi-Fermi levels characterizing the two electron subsystems regarding symmetry properties of their wave functions, symmetric and antisymmetric ones. These states are not mixed neither by electronelectron interaction nor probably by electron-phonon interaction.
In this work, the diffraction of a Gaussian beam on a volume phase grating was researched theoretically and numerically. The proposed method is based on rigorous coupled-wave analysis (RCWA) and Fourier transform. The Gaussian beam is decomposed into plane waves using the Fourier transform. The number of plane waves is determined using the sampling theorem. The complex reflected and transmitted amplitudes are calculated for each RCWA plane wave. The distribution of the fields along the grating for the reflected and transmitted waves is determined using inverse Fourier transform. The powers of the reflected and transmitted waves are determined based on these distributions. Our method shows that the energy conservation law is satisfied for the phase grating. That is, the power of the incident Gaussian beam is equal to the sum of the powers of the reflected and transmitted beams. It is demonstration of our approach correctness. The numerous studies have shown that the spatial shapes of the reflected and transmitted beams differ from the Gaussian beam under resonance. In additional, the waveguide mode appears also in the grating. The spatial forms of the reflected and transmitted beams are Gaussian in the absence of resonance. It was found that the width of the resonance curves is wider for the Gaussian beam than for the plane wave. However, the spectral and angular sensitivities are the same as for the plane wave. The resonant wavelengths are slightly different for the plane wave and the Gaussian beam. Numerical calculations for four refractive index modulation coefficients of the grating medium were carried out by the proposed method. The widths of the resonance curves decrease with the increasing in the refractive index modulation. Moreover, the reflection coefficient also increases.
Abstract. The experimental results obtained for the magneto-transport in the InGaAs/InAlAs double quantum wells (DQW) structures of two different shapes of wells are reported. The beating-effect occurred in the Shubnikov-de Haas (SdH) oscillations was observed for both types of the structures at low temperatures in the parallel transport when magnetic field was perpendicular to the layers. An approach to the calculation of the Landau levels energies for DQW structures was developed and then applied to the analysis and interpretation of the experimental data related to the beating-effect. We also argue that in order to account for the observed magnetotransport phenomena (SdH and Integer Quantum Hall effect), one should introduce two different quasi-Fermi levels characterizing two electron sub-systems regarding symmetry properties of their states, symmetric and anti-symmetric ones which are not mixed by electron-electron interaction. Magnetospectroscopy of symmetric and anti-symmetric states in double quantum wells2
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