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Journal of the Optical Society of America B

Research on third-harmonic generation with position-dependent mass in a quantum well

Qiucheng Yu, Kangxian Guo, Meilin Hu, Zhongmin Zhang, Zhihai Zhang, Dongfeng Liu

Published May 25, 2018• 11 citations
Publisher

Abstract

In this paper, the energy levels and the wave functions of the Schrödinger equation with position-dependent mass are theoretically deduced, and they are brought into nonlinear optical third-harmonic generation. We find that the peak of the third-harmonic coefficient becomes larger and a blueshift occurs under the condition of variable mass. Moreover, with the increment of mass variable k, the energy interval Eij decreases, which makes the coefficients suffer a redshift, and the absolute value of the matrix elements product |M12M23M34M41| presents different monotonicity, which makes the peak value of the coefficient change regularly.

DOI
10.1364/josab.35.001408

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Research on third-harmonic generation with position-dependent mass in a quantum well: comment

Emmanuel Paspalakis, Dionisis Stefanatos

We have discovered errors in the recent paper J. Opt. Soc. Am. B35, 1408 (2018)JOBPDE0740-322410.1364/JOSAB.35.001408. Specifically, we demonstrate that both the electric dipole matrix elements and the third-harmonic generation coefficient presented in the paper have mistakes. We also present the correct results for the electric dipole matrix elements and the third-harmonic generation coefficient.

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In this paper, the energy levels and the wave functions of the Schrödinger equation with position-dependent mass are theoretically deduced, and they are brought into nonlinear optical third-harmonic generation. We find that the peak of the third-harmonic coefficient becomes larger and a blueshift occurs under the condition of variable mass. Moreover, with the increment of mass variable k, the energy interval Eij decreases, which makes the coefficients suffer a redshift, and the absolute value of the matrix elements product |M12M23M34M41| presents different monotonicity, which makes the peak value of the coefficient change regularly.
The influence of position-dependent mass (PDM) on nonlinear optical absorption (OA) coefficients and refractive index changes (RICs) is theoretically studied, within the framework of the iterative method and the compact-density-matrix approach. Through solving Schrödinger equation, the eigenfunctions and energy eigenvalues are obtained. The analytic expressions of the optical absorption coefficients and the refraction index changes are derived theoretically. The results reveal that the OA coefficients and the RICs are strongly affected by PDM, and both the peaks of them increase when considering PDM.
The third harmonic generation coefficients( THG) in quantum wells with a new potential are studied theoretically. We obtain eigenfunctions and energy eigenvalues by means of solving Schrodinger equation within the framework of effective mass approximation method. The analytic expressions of the third-harmonic generation coefficients can be got using the compact-density-matrix approach and iterative method. It is found that the THG coefficients are affected by the width of the quantum well d and the parameter U0.
Abstract In this theoretical work, we investigate how external fields like as electric, magnetic, and intense laser fields, as well as structural factors, affect the third harmonic generation (THG) coefficient of an AlGaAs/GaAs Manning-like double quantum well heterostructure. To achieve our goals, we numerically solve the time-independent Schrödinger equation using the diagonalization approach with the effective mass approximation and then derive the subband energy levels and corresponding wave functions of the structure. After that, we derive the mathematical expression of the THG coefficient by using the compact density matrix method. According to our results, the resonance peaks of the THG coefficient show shifting to the high-energy region with an increase in the field’s magnitude in cases where external fields (electric, magnetic, and intense laser) are applied separately. At the same time, increasing the depth (width) of the quantum well structure causes the THG peaks to shift to the high (low) energy region. We believe that the findings from this search will have a substantial impact on existing experimental device designs and applications.
Optical properties of quantum well nanostructure for typical GaAs/AlxGa1-xAs are investigated in a new approach. By using the point canonical transformation method and numerical solution of the Schrödinger equation, the energy levels and wave functions of electrons in the quantum well confinement potential are calculated. Then, the effect of position-dependent effective mass on the intersubband optical absorption coefficient and the refractive index changes of the quantum well calculated by compact density matrix method, are studied. Results are compared with the case of constant mass. Our results show that with considering spatially varying electron effective mass linear and nonlinear optical properties increases and shifts toward the lower energies. Researches on this matter open a new field in fundamental and applied physics, and also offer a wide range of potential applications for photonic devices.
Abstract In the current work, we have studied the second and third harmonic generation in asymmetrical Gaussian potential quantum dot subjected to the applied electric field. To do this, confined wave function together with energies of electron in an effective mass approximation framework were obtained. Apply these, the analytic expression for the second- and third harmonic generation are determined using a compact density matrix approach and an iterative procedure. According to the results, it is found that applying an electric field, enhances the peak values of the second- and third harmonic generation and redshifts the peak position of their spectrum. Our calculations indicate that increases the radius of quantum dot causes enhances the values of -harmonic generation and redshifts the peak positions of photon energy. It means by optimizing the confinement potential, the maximum –harmonic generation can be obtained. It should be noted that the structural parameters have a significant effect on the –harmonic generation in the considered system.