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Journal of Applied Physics

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

Yimin Huang, Chenhsin Lien

Published Mar 15, 1994• 29 citations
Publisher

Abstract

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.

DOI
10.1063/1.356129

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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.
A semi parabolic quantum well model to study the third order optical nonlinearities was proposed. A concise formulation of the third harmonic generation was presented. Using a compact density matrix approach, the extremely large third order nonlinearities were obtained. The reason is the possibility of tuning independently the frequency of the semi parabolic potential and the triply resonance effect. The value of | χ (3) max (3 ω )| is as high as 2.7×10 -12 (m/V) 2 at 10.7 μm.
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 ${10}^{\ensuremath{-}9}\phantom{\rule{0.3em}{0ex}}{\mathrm{m}}^{2}∕{\mathrm{V}}^{2}$ 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.
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.
Third-order optical nonlinearities in semi-parabolic quantum wells are studied. The third-harmonic generation coefficient is obtained by using compact-density-matrix approach and iterative method, and the numerical results are presented for spical semi-parabolic quantum wells. The very large third-harmonic-generation coefficient is obtained in this semi-parabolic quantum wells and it is over 10 times bigger than that obtained in parabolic quantum wells. In addition, the relations among the third-harmonic-generation coefficient, the photons energy, the parabolic confinement frequency, and the relaxation constant are also investigated, respectively.
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.