超短激光脉冲在V型三能级原子介质中的动力学特性研究
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摘要
周期量级超短激光脉冲与物质相互作用是国际上近年来兴起的激光物理学前沿课题。开展周期量级超短激光脉冲在原子、分子等介质中引起的极端非线性光学特性研究,能够丰富非线性光学内容,并将促进光物理、量子信息科学及阿秒科学等新兴或交叉学科的发展。量子相干控制也是国际上近年来兴起的前沿研究领域,周期量级超短激光脉冲与物质相互作用中的量子相干控制研究作为交叉前沿,具有重要的科学意义和潜在的应用价值。
基于光与物质相互作用的半经典理论,用Maxwell方程描述电场,用密度矩阵方程描述介质。本学位论文利用时域有限差分法和预估校正法,求解不包含旋波近似和慢变幅近似的Maxwell-Bloch方程,对极端非线性光学条件下,周期量级超短激光脉冲在V型三能级原子系统中的传输特性和频谱特性进行了理论研究,并分析了各能级的粒子数布居,取得了一系列创新性的研究成果。主要内容和结果如下:
1.对稠密的Rb原子介质中,周期量级超短激光脉冲的传播特性和各能级粒子数布居进行研究,结果表明:超短脉冲在稀疏介质和稠密介质中的传播规律明显不同,稀疏介质中,由于载波电场时间导数的影响,脉冲的后沿出现微弱振荡。稠密介质中,由于宏观极化强度的增强,脉冲的前沿和后沿均出现快速振荡成分,且入射脉冲面积越大,振荡现象越明显。稠密介质中,由于介质折射率的增大,脉冲群速度变小,又由于载波效应增强,脉冲更容易发生分裂。在入射介质处,稀疏介质中粒子数布居可以实现长时间的反转,而在z≠0μm处,粒子数布居仅在光场不为零的地方产生拉比振荡,面积越大,拉比振荡的次数越多。
稠密介质中,考虑和不考虑LFC效应两种情况下,脉冲的传输特性和各能级粒子数布居也明显不同。考虑LFC效应时,脉冲的群速度较大,NDD相互作用促进了脉冲的传播和分裂,并且脉冲面积越小NDD相互作用的影响越显著。粒子布居拉比振荡发生的时间较早,NDD相互作用加快了粒子数的反转。考虑和不考虑LFC效应两种情况下,载波的相位差明显不同,绝对相位可以相差π。
2.在第四章研究的基础上,首次讨论了跃迁电偶极矩的比值对周期量级激光脉冲的传输特性和各能级粒子数布居的影响。结果表明,两跃迁偶极矩的比值γ对脉冲的传输特性具有显著的影响。γ不同,入射面积为某些阈值时,脉冲传输过程中分裂的脉冲数发生改变。γ≤1的情况下,考虑LFC效应时,脉冲群速度减小,NDD相互作用延缓了脉冲的传播和分裂。脉冲传播出现时间延迟现象,入射脉冲面积越小,延迟现象越显著。入射面积相同时,γ越小,由于脉冲的有效面积减小,脉冲延迟现象也更加显著。两跃迁偶极矩的比值对稠密介质中的粒子数布居反转出现的时间和振荡的次数也具有显著的影响,γ不同,入射面积为某些阈值时,粒子数布居发生拉比振荡的次数发生改变。γ≤1时,考虑LFC效应时粒子数反转出现的时间较晚,NDD相互作用延缓了粒子数的反转。
3.通过数值模拟具有不同初始相位的周期量级激光脉冲的传播特性,结果表明,对于大面积的脉冲,由于强的自相位调制作用,周期量级激光脉冲的载波和相应的光谱对初始相位具有很强的敏感性。分裂子脉冲的相位差要大于主脉冲的相位差,子脉冲的传播距离显著不同,与φ= 0π时相比,φ= 0.5π时脉冲的传播发生了延迟现象,随着传播距离的增大,延迟现象更加明显。
脉冲的频谱出现振荡特性,随着传播距离的增加,这种振荡特性表现的更加明显。对于大面积脉冲,由于自相位调制作用频谱被展宽,频谱中出现高频成分,高频成分的振幅随着传播距离的增大而增大,出现较为显著的连续波。脉冲面积一定,脉宽较大时,脉冲较容易发生分裂,且共振频率附近的振荡较为强烈。脉宽较小时,脉冲频谱中的高频成分比较显著。其它条件一定,初始相位不同时,由于相干效应的不同,脉冲频谱受到初始相位的影响,但不足以引起高频成分的显著变化。φ= 0.5π时频谱中高频成分的连续性比φ= 0π时好,高频成分比较均匀,呈现良好的平坦性。
4.通过数值分析和模拟,研究了共振条件下,双色超短脉冲在稀疏介质中的传输特性和频谱特性,并分析了各能级的粒子数布居。结果表明:初始相对载波包络相位对脉冲的传播和分裂都有很大的影响。随着相对相位的增加,双色场的相干作用增强,脉冲的振幅变小,脉宽变大,分裂子脉冲的数目也会减少。相对相位较小时,色散作用对脉冲传输特性的影响较为显著。相对相位也直接影响各能级粒子数布居的演化,随着相对相位的增加,粒子数布居产生拉比振荡的次数减少。在入射界面处,通过调整相对相位可以实现粒子布居长时间的反转。初始相对载波包络相位不同时,由于相干效应的不同,双色场的拉比频率和载波拉比振荡受到相对相位的影响,引起高频成分的显著变化。传播距离一定时,随着初始相对相位的增大,频谱的振幅减小,高频成分逐渐减弱甚至消失。在共振频率附近,透射光谱的振荡特性强烈依赖于初始相对相位和两脉冲的时间间隔。
5.研究了稠密的Rb原子介质中,双色超短脉冲的传输特性和频谱特性,并分析了各能级粒子数布居特性。结果表明:在稠密介质中,随着初始相对相位的增大,脉冲前沿的振荡相对增强而后沿的振荡减弱。与考虑LFC效应时相比,不考虑LFC效应时,脉冲的传播出现延迟现象,随着初始相对相位的增大,延迟现象更加显著,NDD相互作用促进了脉冲的传播和分裂。随着粒子数密度的增加,由于四波混频和自相位调制的影响,光谱特性受到很大的影响,光谱发生分裂,光谱成分发生移动。原中心频谱逐渐消失,光谱的蓝移(高频成分)和红移(低频成分)发生。蓝移频带的振幅大于红移频带的振幅。初始相对相位越小,光谱红移和蓝移的现象越明显。频谱的振幅主要取决于粒子数密度,粒子数密度越大,频谱的振幅越小。初始相对相位对频谱的振幅也具有一定的影响,频谱的振幅随着相对相位的增大而减小,相应的高频成分逐渐减弱。
全文内容共分为九章,前三章主要介绍当前这一研究课题的研究现状、主要内容和研究方法。第一章为绪论,概述了超短脉冲激光技术的发展与应用,周期量级超短激光脉冲与物质的相互作用以及量子相干控制的研究概况。第二章介绍了周期量级脉冲传播的基础理论。首先给出了脉冲电场的复函数表示形式,简单分析了脉冲载波相位的物理意义,然后简述了周期量级脉冲放大中的主要效应,并简单介绍了传统的面积定理。第三章给出研究超短脉冲激光与物质相互作用的半经典数值计算方法,先推导出描述三能级原子体系的Maxwell-Bloch方程,然后介绍数值计算Maxwell-Bloch方程所采用的时域有限差分法和预估校正法及相应的编程过程。从第四章到第八章是应用上述方法和理论所做的具体的研究工作,主要结果上文中已经提及。最后总结本论文得到的主要结论及创新点,并对下一步要深入开展的工作做一简单介绍。
The interaction of few-cycle ultrashort laser pulses with mater is currently being a hot subject in the high intensity laser physics. Research on the extremely nonlinear optical phenomena induced by few-cycle laser pulses in media, such as atoms etc., will reveal unknown domain in nonlinear optics. It is sure that this work give great contributions to the advance of rising or cross disciplines such as optical physics, quantum information and attosecond physics etc.. Quantum coherent control is also a frontier area arisen in recent years. As an intersection frontier, coherent controls with few-cycle laser pulses have great academic significance and application potential.
Based on the semi-classical theory, the Maxwell and Bloch equations are used to describe the laser fields and media. In this paper, the full Maxwell–Bloch equations without the rotating wave and slowly varying envelope approximations are solved by using a predictor-corrector finite-difference time-domain method. Under extreme nonlinear optics condition, the propagation properties and spectral effects of a few-cycle laser pulse in a V-type three-level atomic medium are investigated theoretically. And the populations are also analyzed and series new results are achieved. The main innovative results are as follows:
1.We investigated the propagation of a few-cycle laser pulse and the population of each energy level in a dense Rb atomic medium. It is found that the Rabi frequency and the populations in a dense medium are quite different from those in a dilute medium. In a dilute medium, oscillations arise at the trailing edge of the pulse due to the time derivative of the electric field. While in the dense medium, oscillations appear at both the leading and trailing edges of the pulse due to strength increasing of macroscopic polarization, moreover, the larger the area of the input pulse is, the more obvious the oscillation amplitude is. In the dense medium, pulse group velocity is slower due to the increasing of medium refractive. And pulse splits easily due to the increasing carrier effects. At the input surface, the population transfer completely appears with the time evolution in a dilute medium. While in the distance of z≠0μm, the Rabi flopping of the populations only occur at the zero points of the optical field. The larger the area of the input pulse is, the more the times of the Rabi flopping are.
In a dense medium, the propagation and populations in the two cases with and without LFC are much different. The pulse group velocity is larger with LFC than that without LFC. NDD interaction accelerates the pulse propagation and split. Moreover, this phenomenon is more obvious for a small pulse area. The appearing time of the Rabi flopping with LFC is earlier than that without LFC and NDD interaction accelerates the population transfer. The carrier-envelope phases between the cases with and without LFC are much different. The difference can go up toπ.
2.Based on the work of chapter 4, we firstly investigate the influence of the ratio,γ, of the transition dipole moments on the propagation and the populations of the pulse. It is found that the ratio of the transition dipole moments has strong influence on the pulse propagation. When the initial area is some threshold value, the times of population Rabi flopping can be changed with differentγ. Whenγ≤1, the pulse group velocity is less with LFC and NDD interaction delays the pulse propagation and split. The phenomenon of time delay is more obvious with the decreasing of pulse area. Moreover, that phenomenon is more obvious with the decreasing value ofγdue to the decreasing effective pulse area. The ratio,γ, of the transition dipole moments also has strong influence on the appearing time and the Rabi flopping times of the population transfer. When the initial area is some threshold value, the times of populations Rabi flopping can be changed with differentγ. Whenγ≤1, NDD interaction delays the population transfer.
3.The phase-dependent feature of few-cycle ultrashort pulse laser propagating is demonstrated. The carrier propagation and spectrum evolution of the pulse are sensitive to its initial phase and the phase sensitivity is more obvious for larger area pulse. For sub-pulses, the phase difference between two carrier envelope phasesφ=0πandφ=0.5πis bigger than that of main pulses at a same propagation distance. And the propagation distances of sub-pulses are much different. Comparing to the case ofφ=0π, the pulse propagation occurs delay phenomenon whenφ=0.5π. The phenomenon is more obvious with the increasing distance.
Oscillatory features in spectra can be found, which are more obvious with the propagation distance increasing. For larger area pulse, the pulse spectra are broadened due to the influence of self-phase modulation. Significantly higher spectral components can occur and the oscillatory feature becomes more and more intense with the increasing of distance. Moreover, higher spectral components also exhibit a continuous feature. When the pulse area is a certain value and the pulse width is larger, the pulse is split easily and the oscillatory feature around the resonance frequency is more obvious. When the pulse width is smaller, the higher spectral components in the spectra are more obvious. Under the same condition, the pulse spectra are affected by the initial carrier-envelope phases due to the different coherence effect, which don’t induce obvious changes of higher spectral components. Comparing to the case ofφ=0π, the consistent property of higher spectral components is better whenφ=0.5π. The higher spectral components are uniform and show better flat.
4.By the numerical analyzing and simulation, we investigate the temporal evolution and spectral properties of the two-color ultrashort laser pulses propagating in a V-type three-level atomic medium and analyze the population of each energy level. It is found that the initial relative carrier envelope phase has strong influence on the time evolution and split of the pulse. With the relative phase increasing, the pulse amplitude is smaller and the pulse width becomes larger due to the strengthened coherent interaction. The number of sub-pulses can be reduced. When the relative phase is relatively smaller, dispersion plays a major role on the properties of pulse propagation. Moreover, the relative phase affects directly the population of each energy level. The Rabi flopping times of the population transfer can be decreased with the increasing of relative phase. At the input surface, the population transfer completely appears with the time evolution by adjusting the relative phase. Under different initial carrier envelope phase, the changes of higher spectral components in spectra are more obvious because the Rabi frequency and carrier Rabi flopping are influenced greatly by the different coherent effects. With a certain propagation distance, the spectra amplitude is induced and the higher spectral components are gradually weakened even disappeared with the increasing of the initial carrier envelope phase. The oscillatory feature around the resonance frequency depends crucially on both the initial relative phase and the delay time between the sub-pulses.
5. We investigated the propagation and spectra of two-color ultrshort laser pulses in a dense Rb atomic medium. And the populations are also analyzed. It is found that in a dense medium, oscillations at the leading edges of the pulse are relatively strengthened with the relative phase increasing and it is gradually weakened at the trailing edges. Comparing with LFC, the pulse propagation appears delay phenomenon without LFC. And the phenomenon is more obvious with the increasing of initial relative phase. NDD interaction accelerates the pulse propagation and split. With medium density increasing, because of four-wave mixing and self-phase modulation, spectral properties get great influence that new features such as spectra splitting and components shift arise. The spectral component of central frequency gradually disappears and spectral blueshift (higher spectral components) and redshift (lower spectral components) of the corresponding spectra arise. The smaller the initial relative phase is, the more obvious the phenomenon of spectral blueshift and redshift is. Spectral amplitude depends mainly on the medium density. It is gradually decreased with the medium density increasing. The initial relative phase has a definite effect on spectral amplitude. With the increasing of initial relative phase, spectral amplitude is decreased and the higher spectral components are gradually weakened.
This paper consists of night chapters, and in the first three chapters, we introduce simply the current research state, the main contents and the calculation method of this research subject. The first chapter gives a brief introduction of the development and applications of few-cycle ultrashort laser pulses, the interaction of few-cycle ultrashort laser pulses with matter and coherent control. In chapter 2, we introduce the basic theories on the propagation of the few-cycle laser pulses. The complex function form of the pulse eclectic field is presented first. Then we introduce simply the physical meaning of the pulse carrier phase, the main effects on the few- cycle pulse amplification and the traditional area theorem. In chapter 3, we derive Maxwell-Bloch equations beyond slowly varying envelope approximation (SVEA) and rotation-wave approximation (RWA), and detailed elucidate the predictor-corrector finite-difference time-domain method. From the fourth chapter to eighth chapter, my own study works are showed and the main results are alluded above. At last, the conclusions and prospect are given in the ninth chapter.
基于光与物质相互作用的半经典理论,用Maxwell方程描述电场,用密度矩阵方程描述介质。本学位论文利用时域有限差分法和预估校正法,求解不包含旋波近似和慢变幅近似的Maxwell-Bloch方程,对极端非线性光学条件下,周期量级超短激光脉冲在V型三能级原子系统中的传输特性和频谱特性进行了理论研究,并分析了各能级的粒子数布居,取得了一系列创新性的研究成果。主要内容和结果如下:
1.对稠密的Rb原子介质中,周期量级超短激光脉冲的传播特性和各能级粒子数布居进行研究,结果表明:超短脉冲在稀疏介质和稠密介质中的传播规律明显不同,稀疏介质中,由于载波电场时间导数的影响,脉冲的后沿出现微弱振荡。稠密介质中,由于宏观极化强度的增强,脉冲的前沿和后沿均出现快速振荡成分,且入射脉冲面积越大,振荡现象越明显。稠密介质中,由于介质折射率的增大,脉冲群速度变小,又由于载波效应增强,脉冲更容易发生分裂。在入射介质处,稀疏介质中粒子数布居可以实现长时间的反转,而在z≠0μm处,粒子数布居仅在光场不为零的地方产生拉比振荡,面积越大,拉比振荡的次数越多。
稠密介质中,考虑和不考虑LFC效应两种情况下,脉冲的传输特性和各能级粒子数布居也明显不同。考虑LFC效应时,脉冲的群速度较大,NDD相互作用促进了脉冲的传播和分裂,并且脉冲面积越小NDD相互作用的影响越显著。粒子布居拉比振荡发生的时间较早,NDD相互作用加快了粒子数的反转。考虑和不考虑LFC效应两种情况下,载波的相位差明显不同,绝对相位可以相差π。
2.在第四章研究的基础上,首次讨论了跃迁电偶极矩的比值对周期量级激光脉冲的传输特性和各能级粒子数布居的影响。结果表明,两跃迁偶极矩的比值γ对脉冲的传输特性具有显著的影响。γ不同,入射面积为某些阈值时,脉冲传输过程中分裂的脉冲数发生改变。γ≤1的情况下,考虑LFC效应时,脉冲群速度减小,NDD相互作用延缓了脉冲的传播和分裂。脉冲传播出现时间延迟现象,入射脉冲面积越小,延迟现象越显著。入射面积相同时,γ越小,由于脉冲的有效面积减小,脉冲延迟现象也更加显著。两跃迁偶极矩的比值对稠密介质中的粒子数布居反转出现的时间和振荡的次数也具有显著的影响,γ不同,入射面积为某些阈值时,粒子数布居发生拉比振荡的次数发生改变。γ≤1时,考虑LFC效应时粒子数反转出现的时间较晚,NDD相互作用延缓了粒子数的反转。
3.通过数值模拟具有不同初始相位的周期量级激光脉冲的传播特性,结果表明,对于大面积的脉冲,由于强的自相位调制作用,周期量级激光脉冲的载波和相应的光谱对初始相位具有很强的敏感性。分裂子脉冲的相位差要大于主脉冲的相位差,子脉冲的传播距离显著不同,与φ= 0π时相比,φ= 0.5π时脉冲的传播发生了延迟现象,随着传播距离的增大,延迟现象更加明显。
脉冲的频谱出现振荡特性,随着传播距离的增加,这种振荡特性表现的更加明显。对于大面积脉冲,由于自相位调制作用频谱被展宽,频谱中出现高频成分,高频成分的振幅随着传播距离的增大而增大,出现较为显著的连续波。脉冲面积一定,脉宽较大时,脉冲较容易发生分裂,且共振频率附近的振荡较为强烈。脉宽较小时,脉冲频谱中的高频成分比较显著。其它条件一定,初始相位不同时,由于相干效应的不同,脉冲频谱受到初始相位的影响,但不足以引起高频成分的显著变化。φ= 0.5π时频谱中高频成分的连续性比φ= 0π时好,高频成分比较均匀,呈现良好的平坦性。
4.通过数值分析和模拟,研究了共振条件下,双色超短脉冲在稀疏介质中的传输特性和频谱特性,并分析了各能级的粒子数布居。结果表明:初始相对载波包络相位对脉冲的传播和分裂都有很大的影响。随着相对相位的增加,双色场的相干作用增强,脉冲的振幅变小,脉宽变大,分裂子脉冲的数目也会减少。相对相位较小时,色散作用对脉冲传输特性的影响较为显著。相对相位也直接影响各能级粒子数布居的演化,随着相对相位的增加,粒子数布居产生拉比振荡的次数减少。在入射界面处,通过调整相对相位可以实现粒子布居长时间的反转。初始相对载波包络相位不同时,由于相干效应的不同,双色场的拉比频率和载波拉比振荡受到相对相位的影响,引起高频成分的显著变化。传播距离一定时,随着初始相对相位的增大,频谱的振幅减小,高频成分逐渐减弱甚至消失。在共振频率附近,透射光谱的振荡特性强烈依赖于初始相对相位和两脉冲的时间间隔。
5.研究了稠密的Rb原子介质中,双色超短脉冲的传输特性和频谱特性,并分析了各能级粒子数布居特性。结果表明:在稠密介质中,随着初始相对相位的增大,脉冲前沿的振荡相对增强而后沿的振荡减弱。与考虑LFC效应时相比,不考虑LFC效应时,脉冲的传播出现延迟现象,随着初始相对相位的增大,延迟现象更加显著,NDD相互作用促进了脉冲的传播和分裂。随着粒子数密度的增加,由于四波混频和自相位调制的影响,光谱特性受到很大的影响,光谱发生分裂,光谱成分发生移动。原中心频谱逐渐消失,光谱的蓝移(高频成分)和红移(低频成分)发生。蓝移频带的振幅大于红移频带的振幅。初始相对相位越小,光谱红移和蓝移的现象越明显。频谱的振幅主要取决于粒子数密度,粒子数密度越大,频谱的振幅越小。初始相对相位对频谱的振幅也具有一定的影响,频谱的振幅随着相对相位的增大而减小,相应的高频成分逐渐减弱。
全文内容共分为九章,前三章主要介绍当前这一研究课题的研究现状、主要内容和研究方法。第一章为绪论,概述了超短脉冲激光技术的发展与应用,周期量级超短激光脉冲与物质的相互作用以及量子相干控制的研究概况。第二章介绍了周期量级脉冲传播的基础理论。首先给出了脉冲电场的复函数表示形式,简单分析了脉冲载波相位的物理意义,然后简述了周期量级脉冲放大中的主要效应,并简单介绍了传统的面积定理。第三章给出研究超短脉冲激光与物质相互作用的半经典数值计算方法,先推导出描述三能级原子体系的Maxwell-Bloch方程,然后介绍数值计算Maxwell-Bloch方程所采用的时域有限差分法和预估校正法及相应的编程过程。从第四章到第八章是应用上述方法和理论所做的具体的研究工作,主要结果上文中已经提及。最后总结本论文得到的主要结论及创新点,并对下一步要深入开展的工作做一简单介绍。
The interaction of few-cycle ultrashort laser pulses with mater is currently being a hot subject in the high intensity laser physics. Research on the extremely nonlinear optical phenomena induced by few-cycle laser pulses in media, such as atoms etc., will reveal unknown domain in nonlinear optics. It is sure that this work give great contributions to the advance of rising or cross disciplines such as optical physics, quantum information and attosecond physics etc.. Quantum coherent control is also a frontier area arisen in recent years. As an intersection frontier, coherent controls with few-cycle laser pulses have great academic significance and application potential.
Based on the semi-classical theory, the Maxwell and Bloch equations are used to describe the laser fields and media. In this paper, the full Maxwell–Bloch equations without the rotating wave and slowly varying envelope approximations are solved by using a predictor-corrector finite-difference time-domain method. Under extreme nonlinear optics condition, the propagation properties and spectral effects of a few-cycle laser pulse in a V-type three-level atomic medium are investigated theoretically. And the populations are also analyzed and series new results are achieved. The main innovative results are as follows:
1.We investigated the propagation of a few-cycle laser pulse and the population of each energy level in a dense Rb atomic medium. It is found that the Rabi frequency and the populations in a dense medium are quite different from those in a dilute medium. In a dilute medium, oscillations arise at the trailing edge of the pulse due to the time derivative of the electric field. While in the dense medium, oscillations appear at both the leading and trailing edges of the pulse due to strength increasing of macroscopic polarization, moreover, the larger the area of the input pulse is, the more obvious the oscillation amplitude is. In the dense medium, pulse group velocity is slower due to the increasing of medium refractive. And pulse splits easily due to the increasing carrier effects. At the input surface, the population transfer completely appears with the time evolution in a dilute medium. While in the distance of z≠0μm, the Rabi flopping of the populations only occur at the zero points of the optical field. The larger the area of the input pulse is, the more the times of the Rabi flopping are.
In a dense medium, the propagation and populations in the two cases with and without LFC are much different. The pulse group velocity is larger with LFC than that without LFC. NDD interaction accelerates the pulse propagation and split. Moreover, this phenomenon is more obvious for a small pulse area. The appearing time of the Rabi flopping with LFC is earlier than that without LFC and NDD interaction accelerates the population transfer. The carrier-envelope phases between the cases with and without LFC are much different. The difference can go up toπ.
2.Based on the work of chapter 4, we firstly investigate the influence of the ratio,γ, of the transition dipole moments on the propagation and the populations of the pulse. It is found that the ratio of the transition dipole moments has strong influence on the pulse propagation. When the initial area is some threshold value, the times of population Rabi flopping can be changed with differentγ. Whenγ≤1, the pulse group velocity is less with LFC and NDD interaction delays the pulse propagation and split. The phenomenon of time delay is more obvious with the decreasing of pulse area. Moreover, that phenomenon is more obvious with the decreasing value ofγdue to the decreasing effective pulse area. The ratio,γ, of the transition dipole moments also has strong influence on the appearing time and the Rabi flopping times of the population transfer. When the initial area is some threshold value, the times of populations Rabi flopping can be changed with differentγ. Whenγ≤1, NDD interaction delays the population transfer.
3.The phase-dependent feature of few-cycle ultrashort pulse laser propagating is demonstrated. The carrier propagation and spectrum evolution of the pulse are sensitive to its initial phase and the phase sensitivity is more obvious for larger area pulse. For sub-pulses, the phase difference between two carrier envelope phasesφ=0πandφ=0.5πis bigger than that of main pulses at a same propagation distance. And the propagation distances of sub-pulses are much different. Comparing to the case ofφ=0π, the pulse propagation occurs delay phenomenon whenφ=0.5π. The phenomenon is more obvious with the increasing distance.
Oscillatory features in spectra can be found, which are more obvious with the propagation distance increasing. For larger area pulse, the pulse spectra are broadened due to the influence of self-phase modulation. Significantly higher spectral components can occur and the oscillatory feature becomes more and more intense with the increasing of distance. Moreover, higher spectral components also exhibit a continuous feature. When the pulse area is a certain value and the pulse width is larger, the pulse is split easily and the oscillatory feature around the resonance frequency is more obvious. When the pulse width is smaller, the higher spectral components in the spectra are more obvious. Under the same condition, the pulse spectra are affected by the initial carrier-envelope phases due to the different coherence effect, which don’t induce obvious changes of higher spectral components. Comparing to the case ofφ=0π, the consistent property of higher spectral components is better whenφ=0.5π. The higher spectral components are uniform and show better flat.
4.By the numerical analyzing and simulation, we investigate the temporal evolution and spectral properties of the two-color ultrashort laser pulses propagating in a V-type three-level atomic medium and analyze the population of each energy level. It is found that the initial relative carrier envelope phase has strong influence on the time evolution and split of the pulse. With the relative phase increasing, the pulse amplitude is smaller and the pulse width becomes larger due to the strengthened coherent interaction. The number of sub-pulses can be reduced. When the relative phase is relatively smaller, dispersion plays a major role on the properties of pulse propagation. Moreover, the relative phase affects directly the population of each energy level. The Rabi flopping times of the population transfer can be decreased with the increasing of relative phase. At the input surface, the population transfer completely appears with the time evolution by adjusting the relative phase. Under different initial carrier envelope phase, the changes of higher spectral components in spectra are more obvious because the Rabi frequency and carrier Rabi flopping are influenced greatly by the different coherent effects. With a certain propagation distance, the spectra amplitude is induced and the higher spectral components are gradually weakened even disappeared with the increasing of the initial carrier envelope phase. The oscillatory feature around the resonance frequency depends crucially on both the initial relative phase and the delay time between the sub-pulses.
5. We investigated the propagation and spectra of two-color ultrshort laser pulses in a dense Rb atomic medium. And the populations are also analyzed. It is found that in a dense medium, oscillations at the leading edges of the pulse are relatively strengthened with the relative phase increasing and it is gradually weakened at the trailing edges. Comparing with LFC, the pulse propagation appears delay phenomenon without LFC. And the phenomenon is more obvious with the increasing of initial relative phase. NDD interaction accelerates the pulse propagation and split. With medium density increasing, because of four-wave mixing and self-phase modulation, spectral properties get great influence that new features such as spectra splitting and components shift arise. The spectral component of central frequency gradually disappears and spectral blueshift (higher spectral components) and redshift (lower spectral components) of the corresponding spectra arise. The smaller the initial relative phase is, the more obvious the phenomenon of spectral blueshift and redshift is. Spectral amplitude depends mainly on the medium density. It is gradually decreased with the medium density increasing. The initial relative phase has a definite effect on spectral amplitude. With the increasing of initial relative phase, spectral amplitude is decreased and the higher spectral components are gradually weakened.
This paper consists of night chapters, and in the first three chapters, we introduce simply the current research state, the main contents and the calculation method of this research subject. The first chapter gives a brief introduction of the development and applications of few-cycle ultrashort laser pulses, the interaction of few-cycle ultrashort laser pulses with matter and coherent control. In chapter 2, we introduce the basic theories on the propagation of the few-cycle laser pulses. The complex function form of the pulse eclectic field is presented first. Then we introduce simply the physical meaning of the pulse carrier phase, the main effects on the few- cycle pulse amplification and the traditional area theorem. In chapter 3, we derive Maxwell-Bloch equations beyond slowly varying envelope approximation (SVEA) and rotation-wave approximation (RWA), and detailed elucidate the predictor-corrector finite-difference time-domain method. From the fourth chapter to eighth chapter, my own study works are showed and the main results are alluded above. At last, the conclusions and prospect are given in the ninth chapter.
引文
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