Excitonic effects on third-harmonic generation in quantum wells via a fractional-dimentional space approach

Abstract

Abstract:

Exciton effects on the third-harmonic generation in GaAs/AlGaAs infinite and finite square quantum wells are calculated within the framework of the fractional-dimensional space approach. The wave functions and bound energies are obtained as functions of spatial dimensionality and the dimension is a function of the well width. For an infinite confining potential the dimension (D) has a transition from the 3D limit to the 2D limit when the well width decreases. However, in a finite well, when the well width decreases below a given value, the dimension increases. The analytical expression of the third-harmonic generation is described using the compact density method and the iterative procedure. The numerical results show that the third-harmonic generation coefficient with considering exciton effects is 40% greater than the one without considering exciton effects and it is very sensitively dependent on the exciton confinement. In addition, the smaller the relaxation constant is, the larger the third-harmonic generation will be.

Key words: nonlinear optics, third-harmonic generation, fractional-dimensional space, exciton effects, quantum wells

CLC Number:

O437

YU Fengmei, LI Wei，GUO Kangxian. Excitonic effects on third-harmonic generation in quantum wells via a fractional-dimentional space approach[J]. J4, 2011, 28(4): 473-482.

References

[1] Wang Guang-Hui, GUO Kang-Xian. Excitonic effects on the third-harmonic generation in parabolic quantum dots [J]. J. Phys: Condens. Matter, 2001, 13: 8197-8206.
[2] Chen R, Lin D L, Mendoza B. Enhancement of the 3rd-order nonlinear-optical susceptibility in si quantum wires [J]. Phys. Rev. B, 1993, 48 (16)11879-11882.
[3] Zhang Chao-Jin, Guo Kang-Xian and LU Zhi-En, Exciton effects on the optical absorptions in one-dimensional quantum dots [J]. Physica E, 2007, 36: 92-97.
[4] Mathieu H, Lefebvre P, and CHRISTOL P. Simple analytical method for calculating exciton binding energies in semiconductor quantum wells [J]. 1992, Phys. Rev. B, 46: 4092-4101.
[5] Christol P, Lefebvre P, and Mathieu H. Fractional‐dimensional calculation of exciton binding energies in semiconductor quantum wells and quantum‐well wires [J]. J. Appl. Phys. 1993, 74: 5626-5638.
[6] Yin Miao, Cheng Ze, Wu Zi-Xia, et al. Study of Squeezed Excitons in Polar Semiconductors [J]. Cnmmun. Theor. Phys, 2009, 51 (3): 545-549.
[7] Matos-Abiague A, OliveirA L E, and Dios-Leyva de M, Fractional-dimensional approach for excitons in GaAs-Ga1-x Alx As quantum wells [J]. Phys. Rev. B, 1998, 58: 4072-4076.
[8] Ekimov A I, Efros Al L, Onushchenko A A, Quantum size effect in semiconductor microcrystals [J]. Solid State Commun, 1985, 56:921-924.
[9] Brus L E. Zero-dimensional "excitons" in semiconductor clusters [J]. IEEE J. Quantum Electron, 1986, 22: 1909-1914.
[10] He X F. Anisotropy and isotropy: A model of fraction-dimensional space [J]. Solid State Commun, 1990, 75: 111-114.
[11] He X F. Excitons in anisotropic solids: The model of fractional-dimensional space [J]. Phys. Rev. B, 1991, 43: 2063-2069.
[12] Zhao Q X, Monemar B, Holtz P O, et al. Binding energies and diamagnetic shifts for free excitons in symmetric coupled double quantum wells [J]. Phys. Rev. B, 1994, 50: 4476-4481.
[13] Reyes-Go′mez e, Matos-Abiague A, Perdomo-leiva C A, et al. Excitons and shallow impurities in GaAs-Ga1-xAlxAs semiconductor heterostructures within a fractional-dimensional space approach:?Magnetic-field effects [J]. Phys. Rev. B, 2000, 61: 13104-13114 .
[14] Singh J, Birkedal D, Lyssenko V G, et al. Binding energy of two-dimensional biexcitons [J]. Phys. Rev. B, 1996, 53: 15909-15913.
[15] Thilagam A. Two-dimensional charged-exciton complexes [J]. Phys. Rev. B , 1997, 55: 7804-7808.
[16] Matos-abiague A, Oliveira l E, Dios-leyva de M. A fractional-dimensional space approach to the study of shallow-donor states in symmetric-coupled GaAs–Ga1?xAlxAs multiple quantum wells [J]. Physica B, 2001, 296: 342-350.
[17] Reyes-Go′mez e, Oliveira l E, Dios-Leyva de M. Shallow impurities in semiconductor superlattices: A fractional-dimensional space approach [J]. J. Appl. Phys, 1999, 85: 4045-4049.
[18] Tanguy C, Lefebvre P, Mathieu H, et al. Analytical model for the refractive index in quantum wells derived from the complex dielectric constant of Wannier excitons in noninteger dimensions [J]. J. Appl. Phys, 1997, 82: 798-802.
[19] Matos-Abiague A. Polaron effect in GaAs-Ga1-xAlxAs quantum wells: A fractional-dimensional space approach [J]. Phys. Rev. B, 2002, 65: 165321-165329.
[20] Lu Zhi-En, Guo Kang-Xian. Polaronic Electron-Phonon Interactions on the Third-Harmonic Generation in a Square Quantum Well [J]. Cnmmun. Theor. Phys, 2006, 45: 171-174.

Excitonic effects on third-harmonic generation in quantum wells via a fractional-dimentional space approach

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