【作者】 胡美林；

【导师】 郭康贤；

【作者基本信息】 广州大学 ， 凝聚态物理， 2019， 硕士

【摘要】 这篇文章主要是探讨不同量子阱系统对于非线性光学性质的影响。文章用三个章节分别阐述了质量随位置变化的量子阱,半指数量子阱以及短程无底指数势阱对于不同非线性光学特性的影响。在非线性光学特性方面,本文主要阐述了光吸收系数,折射率变化,三次谐波在不同量子阱的影响下产生的不同变化,以及产生这样变化的原因。文章中,通过求解不同量子阱的薛定谔方程,并将其能级和波函数代入到非线性光学的对应特性下,利用量子阱参数、能级间隙、矩阵元和光强的具体变化来分析存在特殊的量子阱效应时,非线性光学特性的具体变化趋势。经过研究,本文主要得到以下的结论:一,在迭代法和紧致密度矩阵法的框架下,从理论上研究了与位置相关的质量（PDM）对非线性光学吸收系数和折射率变化的影响。通过求解薛定谔方程,得到了本征函数和本征值,从理论上导出了光学吸收系数和折射率变化的解析表达式。研究结果表明,随位移变化的质量对光吸收系数和折射率的改变都有着很强的影响:当考虑质量影响时,它们的峰值均增大。二,关于极化子效应的非线性光学折射率变化的研究。在本章中,首先求出有极化子效应的薛定谔方程的能级和波函数,并代入到折射率变化的非线性情形下。本章不仅分析了有无极化子效应的区别,也分析了有极化子影响时,折射率变化的具体呈现。通过转化,系数f可以用来表征不同状态下的极化子效应。我们发现有极化子影响时,随着极化子系数f的变大,能级间隙E₂₁在减小,使得呈现折射率变化的能量区间减小,发生红移。而f的改变,会使得矩阵元M₂₁形成振荡曲线,曲线的单调性决定了折射率变化峰值的变化。同时强度大的光强对有极化子效应的折射率变化有漂白作用。三,引入一个短程的完全可积的奇异势能,通过超几何函数得出其薛定谔方程的精确解,将结果代入到三次谐波系统后,可以展现出短程反平方势能下三次谐波的特殊现象,即三次谐波系数会呈现出一个镜面的反向状态。同时,我们根据能隙和矩阵元的变化的趋势,具体阐述了三次谐波系数的能级区域、峰值大小及个数的变化。更多还原

【Abstract】 The main purpose of this paper is to investigate the influence of quantum wells on nonlinear optical properties.The quantum well formed by position-dependent mass(PDM),semi-exponential quantum wells with polaron effect and short-range bottomless exponential potential well are discussed in three chapters to study on the influence of different nonlinear optical properties.In terms of nonlinear optical properties,the optical absorption coefficient,refractive index change and the third-harmonic generation under the influence of different quantum wells are mainly described in this paper,as well as the reasons for the changes.By solving the Schr?dinger equation of different quantum wells and taking the energy levels and wave functions into the corresponding properties of nonlinear optics,as well as using the parameters,energy intervals,matrix elements and light intensity,the trend of nonlinear optical properties with the effect of special quantum well are mainly analyzed in this paper.After research,this paper mainly draws the following conclusions.Firstly,the influence of position-dependent mass on refractive index changes(RICs)and nonlinear optical absorption(OA)coefficients are theoretically studied,within the framework of the iterative method and the compact-density-matrix approach.Through solving Schr?dinger equation,the eigenfunctions and energy eigenvalues are obtained.The analytic expressions of the OA coefficients and RICs 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.Secondly,nonlinear optical refractive index changes with polaron effects are studied in this Letter.The energy levels and wave functions of the polaron Schr?dinger equation are calculated and brought into the nonlinear RICs to analyze the difference between the effects of the presence and absence of polarons,as well as the specific representation of RICs with polarons.And then,we introduce a short-range bottomless potential which can be exactly integrabled.And the exact solutions of Schr?dinger equation of the potential have been derived through the hypergeometric function.After the results are brought into the system of third-harmonic generation(THG),the special phenomenons of third-harmonic generation under short-range exponential potential with inverse square root singularity will be exhibited,that is,the third-harmonic coefficient(THC)will present a mirror reverse state.At the same time,according to the varied tendency of energy intervals and matrix elements,the energy regions of the third-harmonic coefficient and the value of the THC peaks,as well as thenumbers,are specifically elaborated.更多还原