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Journal of Applied Physics

Intensity-dependent refractive index of a Pöschl-Teller quantum well

Hasan Yıldırım, Mehmet Tomak

Published May 1, 2006• 53 citations
Publisher

Abstract

The linear and nonlinear changes in the refractive index of a Pöschl-Teller quantum well are studied. The Pöschl-Teller potential can easily become asymmetric by a correct choice of its parameter set. We use this feature to investigate the intensity-dependent refractive index of a GaAs quantum well within the density matrix formalism. Numerical results reveal large values of linear and nonlinear changes in the refractive index.

DOI
10.1063/1.2194124

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Yarıiletken heteroyapıların lineer olmayan optik özellikleri.

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•Jan 1, 2006•0 citations
The linear and nonlinear changes in the refractive index of a Pöschl-Teller quantum well are studied. The Pöschl-Teller potential can easily become asymmetric by a correct choice of its parameter set. We use this feature to investigate the intensity-dependent refractive index of a GaAs quantum well within the density matrix formalism. Numerical results reveal large values of linear and nonlinear changes in the refractive index.
Analytical expressions of linear and third-order nonlinear optical refractive index changes are obtained in Poschl-Teller well using the density matrix formalism taking into account the intrasubband relaxation. Since there are two adjustable parameters κ and λ in the Poschl-Teller well, the shape of the wells will change with the change of the parameters κ and λ, accordingly the linear and the third-order nonlinear refractive index will change with the parameters κ and λ. It is shown that the refractive index changes depends on the shape of the well, the tunnel bandwidth and the optical power. Numerical results are presented for a typical GaAs/AlGaAs Poschl-Teller well.
Linear, nonlinear, and total refractive index changes are investigated theoretically in asymmetric coupled quantum wells. The analytical expressions for the linear and third-order nonlinear refractive index changes are obtained based on the density matrix method and the iterative approach. Numerical calculations are performed for typical GaAs/Al(subscript x)Ga(subscript 1-x)As asymmetric coupled quantum wells. The calculated results reveal that a large variation of the refractive index near the transition energy can be obtained in asymmetric coupled quantum wells, and that the incident optical intensity and the structure parameters, such as the barrier width and the right-well width, have great effects on the total refractive index changes.
The linear,nonlinear and total refractive index changes are investigated theoretically in asymmetric double triangular quantum wells.The analytical expressions for the linear and third-order nonlinear refractive index changes are obtained based on the density matrix method and the iterative approach.Numerical calculations are performed for typical GaAs/AlxGa1-xAs asymmetric double triangular quantum wells.The calculated results reveal that a great change of the refractive index can be obtained in the asymmetric coupled quantum wells,and that the incident optical intensity,the structure parameters,and the applied electric field have a great influence on the total refractive index changes.
In the frame of quantum mechanics,the equation to describe the particle motion in Tan2x quantum well is reduced to the hypergeometric equation.The eigenvalue and the eigefunction are obtained by solving the Schrdinger equation.Analytical expressions of linear and the third-order nonlinear optical refractive index changes are obtained in Tan2x quantum well using the density matrix formalism taking into account the intrasubband relaxation.The linear and the third-order nonlinear refractive index changes are calculated.The results show that the refractive index changes depend on the shape of the well,the tunnel bandwith and the optical intensity.Numerical results are presented for a typical GaAs/AlGaAs Tan2x quantum well.
By using the compact density matrix approach and displacement harmonic variant and numerical calculation methods,the linear and nonlinear intersubband refractive index changes(RICs) in a semi-parabolic quantum well with applied electric field were investigated in detail.Numerical calculations on GaAs were performed for the dependence of RIC on the incident optical intensity,the frequency of confined potential of the semi-parabolic quantum well and the strength of applied electric field.Results reveal that the RICs in the semi-parabolic quantum well system sensitively depend on these factors.
The nonlinear optical properties of semiconductor heterostructures, such as GaAsAl/GaAs alloys, are studied with analytic and numerical methods on the basis of quantum mechanics. Particularly, second and third-order nonlinear optical properties of quantum wells described by the various types of confining potentials are considered within the density matrix formalism. We consider a Pöschl-Teller type potential which has been rarely considered in this area. It has a tunable asymmetry parameter, making it a good candidate to investigate the effect of the asymmetry on the nonlinear optical properties. The calculated nonlinear quantities include nonlinear absorption coefficient, second-harmonic generation, optical rectification, third-harmonic generation and the intensity-dependent refractive index. The effects of the DC electric field on the corresponding nonlinearities are also studied. The results are in good agreement with the results obtained in other types of quantum wells, such as square and parabolic quantum wells. The effects of the Coulomb interaction among the electrons on the nonlinear intersubband absorption are considered within the rotating wave approximation. The result is applied to a Si-delta-doped, square quantum well in which the Coulomb interaction among the electrons are relatively important, since there has been no work on the nonlinear absorption spectrum of the Si-\delta-doped quantum well. The results are found to be new and interesting, especially when a DC electric field is included in the calculations.