Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review B

Third-harmonic generation in cylindrical parabolic quantum wires with an applied electric field

Guanghui Wang

Published Oct 27, 2005• 129 citations
Publisher

Abstract

The third-harmonic generation (THG) in $\mathrm{GaAs}∕\mathrm{AlGaAs}$ cylindrical parabolic quantum wires with an applied static-electric field is studied in detail. An analytic formula for the THG susceptibility in the model is obtained by a compact density matrix approach and an iterative procedure. Finally, the calculated results show the parabolic confinement potential and the applied electric field have great influence on the THG susceptibilities in the system. Another important point is that the maximum THG susceptibility over ${10}^{\ensuremath{-}9}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{2}∕{\mathrm{V}}^{2}$ can be obtained by optimizing the parabolic confinement potential and the applied electric field, which is over ten orders of magnitude greater than in bulk GaAs. The contributors to the very giant three-order nonlinear include the very large dipole transition matrixes and the triple resonant condition.

DOI
10.1103/physrevb.72.155329

Related papers

Bound States and the Third Harmonic Generation in an Electric Field Biased Semi-parabolic Quantum Well

ZHANGLi, Li, Xie +1 more

Within the framework of the compact density matrix approach, the third-harmonic generation (THG) in an electric-field-biased semi-parabolic quantum well (QW) has been deduced and investigated. Via variant of displacement harmonic oscillation, the exact electronic states in the semi-parabolic QW with an applied electric field have also been obtained and discussed. Numerical results on typical GaAs material reveal that, electric fields and confined potential frequency of semi-parabolic QW have obvious influences on the energy levels of electronic states and the THG in the semi-parabolic QW systems.

理论物理通讯：英文版•Jan 1, 2003•0 citations

Bound States and the Third Harmonic Generation in an Electric Field Biased Semi-parabolic Quantum Well

Zhang Li, Hong‐Jing Xie

Within the framework of the compact density matrix approach, the third-harmonic generation (THG) in an electric-field-biased semi-parabolic quantum well (QW) has been deduced and investigated. Via variant of displacement harmonic oscillation, the exact electronic states in the semi-parabolic QW with an applied electric field have also been obtained and discussed. Numerical results on typical GaAs material reveal that, electric fields and confined potential frequency of semi-parabolic QW have obvious influences on the energy levels of electronic states and the THG in the semi-parabolic QW systems.

Communications in Theoretical Physics•Nov 15, 2003•6 citations

ELECTRON–PHONON INTERACTION EFFECTS ON THIRD-HARMONIC GENERATION IN CYLINDRICAL QUANTUM WIRES

Youbin Yu, Kangxian Guo

The influence of electron–phonon interaction on third-harmonic generation in cylindrical quantum wires are investigated. The third-harmonic generation coefficient is obtained using compact-density-matrix approach and iterative method, and the numerical results are presented for GaAs cylindrical quantum wires. The results show that the third-harmonic generation coefficient is greatly enhanced after taking into consideration the influence of electron–phonon interaction. It is about thirty times larger than that obtained by just considering electron states when electron–phonon resonance is met.

International Journal of Modern Physics B•Jan 10, 2004•4 citations

Effects of external fields and structural parameters on third harmonic generation of GaAs/AlGaAs Manning-like double quantum well structure

Ahmet Türker Tüzemen

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.

The European Physical Journal Plus•Jun 11, 2024•5 citations

The enhancement of optical third harmonic susceptibility in a parabolic quantum well by triple resonance

Yimin Huang, Chenhsin Lien

The third harmonic susceptibility for the finite parabolic quantum well (PQW) is studied theoretically. An important feature of the finite PQW is that the subband eigenenergies En form an equally spaced energy-level ladder. Since the eigenenergy spacing ℏω0 can be designed to resonate with the pumping source, the third harmonic susceptibility can be greatly enhanced through the triple resonance. A third harmonic susceptibility as high as 2000 (nm/V)2 could be achieved for the finite parabolic quantum well structure. This is a more than six orders of magnitude enhancement as compared to that of the bulk GaAs.

Journal of Applied Physics•Mar 15, 1994•29 citations

Second-Harmonic and Third-Harmonic Generation in Nanostructures with Asymmetric Confinement Potential: The Role of Two-level Atom Approximation

Dairo A. Causil, M. P. Urango Baquero, Alfonso A. Portacio

The second harmonic generation (SHG) and third harmonic generation (THG) into a cylindrical quantum dot (CQD) with asymmetric confinement potential is studied theoretically within the framework the two-level atom approximation, by using the matrix density formalism. The energy levels and waves functions of an electron into CQD they were obtained by solving the time-independent Schrodinger equation. The numerical calculations make for a CQD of GaAs/GaAlAs. It was found that the increase in the confinement of the charge carriers produced by the increase of the magnetic field and/or the dimensions of the nanostructure generates a shift to blue in the transition energies of the electrons. Also a multiple resonances in the two-level atom approximation was found. These were associated with transition between excited state and ground state and a second transition getting a change permanent dipole moment.For the English version of the abstract, please be careful with the language.

Revista cubana de física•Dec 15, 2018•0 citations
The third-harmonic generation (THG) in GaAs∕AlGaAs\mathrm{GaAs}∕\mathrm{AlGaAs}GaAs∕AlGaAs cylindrical parabolic quantum wires with an applied static-electric field is studied in detail. An analytic formula for the THG susceptibility in the model is obtained by a compact density matrix approach and an iterative procedure. Finally, the calculated results show the parabolic confinement potential and the applied electric field have great influence on the THG susceptibilities in the system. Another important point is that the maximum THG susceptibility over 10\ensuremath−9m2∕V2{10}^{\ensuremath{-}9}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{2}∕{\mathrm{V}}^{2}10\ensuremath−9m2∕V2 can be obtained by optimizing the parabolic confinement potential and the applied electric field, which is over ten orders of magnitude greater than in bulk GaAs. The contributors to the very giant three-order nonlinear include the very large dipole transition matrixes and the triple resonant condition.
Within the framework of the compact density matrix approach, the third-harmonic generation (THG) in an electric-field-biased semi-parabolic quantum well (QW) has been deduced and investigated. Via variant of displacement harmonic oscillation, the exact electronic states in the semi-parabolic QW with an applied electric field have also been obtained and discussed. Numerical results on typical GaAs material reveal that, electric fields and confined potential frequency of semi-parabolic QW have obvious influences on the energy levels of electronic states and the THG in the semi-parabolic QW systems.
Within the framework of the compact density matrix approach, the third-harmonic generation (THG) in an electric-field-biased semi-parabolic quantum well (QW) has been deduced and investigated. Via variant of displacement harmonic oscillation, the exact electronic states in the semi-parabolic QW with an applied electric field have also been obtained and discussed. Numerical results on typical GaAs material reveal that, electric fields and confined potential frequency of semi-parabolic QW have obvious influences on the energy levels of electronic states and the THG in the semi-parabolic QW systems.
The influence of electron–phonon interaction on third-harmonic generation in cylindrical quantum wires are investigated. The third-harmonic generation coefficient is obtained using compact-density-matrix approach and iterative method, and the numerical results are presented for GaAs cylindrical quantum wires. The results show that the third-harmonic generation coefficient is greatly enhanced after taking into consideration the influence of electron–phonon interaction. It is about thirty times larger than that obtained by just considering electron states when electron–phonon resonance is met.
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.
The third harmonic susceptibility for the finite parabolic quantum well (PQW) is studied theoretically. An important feature of the finite PQW is that the subband eigenenergies En form an equally spaced energy-level ladder. Since the eigenenergy spacing ℏω0 can be designed to resonate with the pumping source, the third harmonic susceptibility can be greatly enhanced through the triple resonance. A third harmonic susceptibility as high as 2000 (nm/V)2 could be achieved for the finite parabolic quantum well structure. This is a more than six orders of magnitude enhancement as compared to that of the bulk GaAs.
The second harmonic generation (SHG) and third harmonic generation (THG) into a cylindrical quantum dot (CQD) with asymmetric confinement potential is studied theoretically within the framework the two-level atom approximation, by using the matrix density formalism. The energy levels and waves functions of an electron into CQD they were obtained by solving the time-independent Schrodinger equation. The numerical calculations make for a CQD of GaAs/GaAlAs. It was found that the increase in the confinement of the charge carriers produced by the increase of the magnetic field and/or the dimensions of the nanostructure generates a shift to blue in the transition energies of the electrons. Also a multiple resonances in the two-level atom approximation was found. These were associated with transition between excited state and ground state and a second transition getting a change permanent dipole moment.For the English version of the abstract, please be careful with the language.