分子介质中强场激光动力学及X射线光谱学研究
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摘要
在过去的几十年里,随着超强超短脉冲激光技术的发展及高功率同步辐射光源和自由电子X射线激光器的产生,非线性光学及X射线光谱学取得了突飞猛进的发展,其应用领域和范围也得到了进一步拓展。与此同时,许多处理光与物质相互作用的理论近似方法如旋波近似、慢变幅近似等已经失效,各种新奇非线性光学现象的产生需要人们采用更加严格的理论模型和方法来进行处理和解释。
本论文的主要目的在于发展处理激光脉冲和物质相互作用的理论方法,解释和预测各种新的物理现象,主要涉及从红外到X射线波段的有关非线性光学现象。本论文的研究内容主要包括四部分。第一部分涉及双光子吸收(TPA)过程的量子相干控制。我们对TPA过程的旋波近似(RWA)解进行了修正,得到了多能级分子体系中TPA过程的非旋波近似(NRWA)解。基于共振TPA的非旋波近似解,我们还得到了描述脉冲传播过程中其双光子面积演化的面积定理。在第二部分我们分别研究了超短脉冲激光和长脉冲激光在不同分子介质中传播时的一步和两步TPA及其光限幅行为。第三部分我们对超短激光脉冲传播过程中超连续谱形成、阿秒脉冲的产生和两色超荧光的形成进行了研究。在第四部分,我们提出了一种新的泵浦—探测X射线光谱学方法,即强场激光感应下的X射线吸收和共振非弹性X射线拉曼散射。本论文研究的主要内容与结果如下。
一、双光子吸收量子相干控制及双光子面积定理
过去人们对TPA过程进行理论研究时大都采用RWA,但是RWA解给出了错误的能级动态Stark移动表达式;而且很多时候由外场引起的体系能级的动态Stark移动还被忽略(RWAZS)。本论文对多能级体系中的近共振双光子相互作用进行了研究,得到了体系的NRWA解析解,其中包含了动态Stark效应及分子固有偶极矩的影响。通过数值计算,我们对TPA的RWA解、RWAZS解、NRWA解及不采用任何近似时几率幅方程的严格数值解结果进行了比较,发现即使是在Rabi频率远小于光场载波频率的弱场情况下,TPA过程的RWA和RWAZS解也可能完全失效,而我们的NRWA解与严格数值解则符合的很好。TPA的NRWA解还表明,体系动态Stark移动的存在使双光子激发下的完全粒子数反转变的难以实现。对于空间固定的分子,可以通过脉冲频率调制或相位裁制来实现粒子数的完全反转。分子的无序排布降低了介质的双光子激发率,使得动态Stark效应不能得到完全的补偿。由共振TPA体系的NRWA解,我们还得到了描述脉冲面积(能量流量)在传播过程中演化的双光子面积定理。虽然双光子面积定理是关于单色激光脉冲双光子面积的演化规律,但是严格的数值计算结果表明,即使在伴有新的电场频率成分产生的情况下,双光子面积定理也能定性的解释脉冲传播的动力学性质,如脉冲的双光子吸收光限幅效应。
二、双光子吸收光限幅效应
我们分别对飞秒超短脉冲和微秒长脉冲激光在不同分子介质中传播的双光子吸收光限幅效应进行了研究。采用预估校正的时域有限差分法(FDTD)求解全波矢Maxwell-Bloch方程组,我们对超短脉冲激光在有机分子介质4,4′-二甲氨基二苯乙烯中的共振TPA过程进行了模拟。数值计算结果表明体系主要发生一步TPA,在脉冲传播过程中其光限幅行为可以用NRWA近似下的双光子面积定理进行很好的描述。利用脉冲通过介质后光场强度透射率与入射光强的关系,我们对分子的动态TPA截面进行了初步计算,发现随着脉冲持续时间的增加,体系发生两步TPA的几率增大,测得的分子动态TPA截面也不断增大。
当微秒时域内的长脉冲激光在介质中传播且涉及到自旋三重态的两步TPA过程时,利用体系的内部迟豫时间结构,可以将体系分为快变和慢变两个子体系。快速迟豫的各激发态将跟随由基态及最低三重态组成的慢变子体系进行绝热演化,因此对快变子体系采用绝热近似,同时结合体系粒子数守恒律,可以将多能级体系的速率方程约化为只是关于基态粒子数演化的一个动力学方程。对入射脉冲,考虑光场横向分布的不均匀性,我们利用Cranck-Nicholson方法数值求解光场的傍轴波动方程。将上述理论应用于富勒烯C60,模拟结果表明,长脉冲在C60中的主要光限幅机制为单重态到单重态及三重态到三重态之间的两步TPA。体系粒子从基态向最低三重态的有效转移速率随入射脉冲强度的增加而加快。由于脉冲前沿及远离光轴处光强较弱,粒子数转移速率较慢,此时主要发生的是基态粒子的弱的线性吸收;相反,在脉冲主体和近光轴处由于较高的光场强度引起的快速粒子数转移,体系发生两步非线性TPA,光场被强烈吸收。因此由于介质吸收性质对光场强度的依赖性,透射脉冲会发生严重的形变。由于C60分子单重态及三重态单光子吸收截面的相对大小依赖于所用的激发波长,因此可以通过改变激发脉冲的波长来获得不同的光限幅效应。同时,由于脉冲传播过程中线性吸收和两步非线性TPA之间的相互转换,传播效应对两步TPA感应的光限幅过程有很大的影响,它依赖于脉冲的强度、吸收介质的长度以及介质的粒子数密度。
三、超短脉冲激发下的非线性光学过程
通过数值求解全波矢Maxwell-Bloch方程组,我们还对超短脉冲激光在分子介质中传播时超连续谱的形成、阿秒脉冲的产生以及超荧光的产生进行了研究。对超短脉冲在极性或非极性两能级分子介质中的单光子共振传播,电场频谱的高频成分主要是由脉冲分裂后最前面的子脉冲的自相位调制作用产生的。该子脉冲在传播过程中被压缩,从而可以形成比入射飞秒脉冲持续时间短的多的阿秒脉冲。当入射脉冲面积足够大时,电场形成超连续谱,但是随着脉冲面积的进一步增大,电场频谱的平台特性被破坏,频谱变得离散化。分子固有偶极矩的存在使分子与光场的非线性相互作用增强,固有偶极矩对超连续谱及阿秒脉冲的产生可以起到建设性或破坏性的作用,取决于它与跃迁偶极矩的相对大小。同时,超短脉冲的载波包络相位对脉冲的时空和频谱演化也有很大影响。当考虑分子的含时电离效应时,入射电场基频成分的强度及其振荡特性被减弱,如果电离强度较强,电场高频成分的强度及最前面子脉冲的强度也被减弱。
对级联三能级分子体系,利用超短脉冲的共振双光子激发使体系的粒子数占有率发生反转,在脉冲传播过程中,被反转的分子介质所产生的两色超荧光辐射强度随粒子数密度的增加而增强,而偶极相干失相减弱并延缓了超荧光的产生。超荧光相对于激发脉冲的延迟时间随激发脉冲的强度、粒子数密度及传播距离的增加而减小。当体系粒子数密度较大、相干失相速率较慢时通过介质的超荧光辐射会形成品质较好的频率上转换激光。
四、X射线吸收和非弹性X射线拉曼散射
在论文的最后一部分我们提出了一种新的X射线泵浦—探测实验方案并以氮气分子为例来说明该一般性理论。一束较弱的X射线激光脉冲将分子中的内层电子激发到某一未占据轨道,使分子处于具有特定对称性的核激发态;而另外一束足够强的可见或红外激光脉冲可以将所产生的内层电子空位转移到具有相反对称性的分子轨道上,从而开通了原先电偶极跃迁选择定则所禁戒的拉曼散射通道。对称性禁戒拉曼通道的强度依赖于内层电子空位跃迁的Rabi周期与拉曼散射有效持续时间及X射线脉冲持续时间的相对大小。我们分别给出了空间固定和自由取向分子的X射线吸收和拉曼散射截面表达式。X射线吸收谱和共振非弹性X射线拉曼散射谱的形状依赖于分子的取向以及X射线与红外激光场的极化方向关系。由强的红外激光场产生的核激发态的Rabi分裂使X射线吸收谱展宽、峰值强度减弱、共振吸收位置发生移动,同时也降低了拉曼散射的几率。缩短入射激光场的持续时间会使拉曼散射谱展宽,出现明显的Rabi分裂成分,同时谱线共振位置的改变也受到散射过程中拉曼和非拉曼成分的相互影响。如果所入射的强红外激光场为少周期脉冲,X射线拉曼散射谱的形状还依赖于该少周期脉冲的绝对载波—包络相位,但是它并不受入射高频X射线脉冲的载波—包络相位的影响。
In the past few decades, the availability of ultrashort and intense laser pulses as well as the development in high power synchrotron radiation sources and X-ray free electron lasers has promoted a rapid development in nonlinear optics and X-ray spectroscopy technologies, and extended their range of applications. Meanwhile, the appearance of varieties of novel nonlinear phenomena calls for much more accurate theoretical treatment in order to be explained.
The main aim of this thesis is to develop further the nonlinear optical theories and methods and to explain and predict new phenomena occurred during the interaction of molecules with electromagnetic radiation ranging from infrared to X-ray region. This thesis consists of mainly four parts. The first part concerns the coherent control of quantum states by specifically designed laser pulses in resonant two-photon absorption (TPA) processes. The non-rotating wave approximation (NRWA) solution for the resonant TPA process in a multi-level system is derived, and the effects of the dynamical Stark shifts and the permanent dipole moments are included. In the second part, we investigate respectively the one-step and two-step TPA and optical limiting behavior of the ultrashort and microsecond long laser pulses. The third part is about the study and explanation of the supercontiuum generation, the formation of the attosecod laser pulses and the two-color superfluorescence related to the propagation of the ultrashort laser pulses. In the last part, a new scheme of X-ray pump-probe spectroscopy is proposed, i.e., strong infrared or optical laser pulse induced X-ray absorption and resonant inelastic X-ray Raman scattering. The main contents and results are summarized as follows.
First, we study the quantum coherent control of two-photon absorption and two-photon absorption area theorem beyond the conventional RWA. In the past when people investigated theoretically the TPA processes, RWA was adopted. However, the RWA solution of TPA gives wrong expressions of the dynamical Stark shifts, and usually the dynamical Stark shifts of the energy levels induced by the external field were neglected (RWAZS) without any physical background. In this theis, we investigate in detail the near resonant TPA of multi-level systems, and obtain the NRWA solution for TPA in which the effects of the dynamical Stark shifts and the permanent dipole moments of the molecules are included. The RWA, RWAZS and NRWA analytical solutions are compared with the strict numerical solutions of the amplitude equations. It is found that even for the weak incident pulse where the Rabi frequency is much smaller than the carrier frequency of the field the RWA and RWAZS solutions break down completely. In contrast, our NRWA solution coincides very well with the strict numerical results. The NRWA solution also shows that the existence of the dynamical Stark shifts prevents the complete inversion of the population in resonant TPA processes. For fixed-in-space molecules, the compensation of the dynamical Stark effect can be achieved by proper phase tailoring or two-photon detunings. It is demonstrated that the orientational disorder diminishes significantly the efficiency of the two-photon induced population transfer and does not allow complete compensation of the dynamical Stark shifts. Based on the NRWA solution of the amplitude equations, the two-photon area theorem taking into account the dynamical Stark shifts and the permanent dipole moments are derived. Although the two-photon area theorem is strict only for single-color field, numerical simulations for ultrashort laser pulses show that the two-photon area theorem can explain qualitatively the dynamical properties of pulse propagation in a two-photon resonant medium, even if the propagation is accompanied by the generation of fields with new frequencies.
Second, we investigate respectively the TPA induced optical limiting effects of the femtosecond ultrashort and miscrosecond long pulses. By solving numerically the full-wave Maxwell-Bloch equation with the predictor-corrector FDTD method, we investigate the propagation of the ultrashort laser pulses in the organic 4, 4’-bis(dimethylamino) stilbene molecules under the condition of TPA. It is found that for ultrshort laser pulses mainly one-step coherent TPA occurs, and the two-photon area therorem can describe qualitatively the optical limiting behavior of the ultrashort pulses. From the relation between the transmittance of the pulse intensity and the incident intensity the dynamical TPA cross section of the 4, 4’-bis(dimethylamino) stilbene molecule is calculated. It shows that the dynamical TPA cross section of the molecule increases with the increase of pulse duration due to the enhancement of two-step TPA.
A dynamical theory of the sequential two-photon absorption involving strong triplet-triplet transitions and of the propagation of laser pulses with durations in the microsecond time domain is presented. Making use of the decay time hierarchy of the energy levels, the system can be devided into fast and slow subsystems. The subsystem with fast decay rates will follow adiabatically the slow dynamics of the population of the ground and the lowest triplet states. Combining the adiabatic approximation of the fast subsystem with the particle conservation law, the rate equations can be reduced to a single dymamical equation for the ground state population. Taking into account the transverse inhomogeneity of the laser pulse, the Cranck-Nicholson method is used to solve numerically the paraxial wave equation of the field intensity. The general theory is applied to fullerene C60 because of its good optical limiting properties. It is shown that the main mechanism of optical limiting for long pulses in C60 is the sequential (singlet-singlet)×(triplet-triplet) two-photon absorption. The effective rate of population transfer from the ground state to the lowest triplet state increases with the increase of the field intensity. Due to this circumstance, the front part of the pulse propagates with mainly linear absorption, while the main body of the pulse is significantly attenuated due to the strong nonlinear sequential two-photon absorption. An incident pulse with a gaussian transverse distribution is strongly absorbed near the axis due to the higher intensity there. Different optical limiting behavior can be obtained by tuning the excitation wavelength because of the wavelength sensitivity of the singlet-singlet and triplet-triplet photoabsorption cross sections. Simulations show that the propagation effect which depends on the field intensity, the length of the absorber and the molecular concentration plays an important role in the sequential TPA induced optical power limiting performance.
In the third part, the propagation of ultrashort laser pulses in both nondipolar and dipolar media is studied and special attention has been paid to supercontinuum generation, formation of attosecond laser pulses and superfluorescence. When an ultrashort pulse propagates in a two-level nondipolar or dipolar medium, supercontinuum of the spectrum is generated mainly due to the self-phase modulation of the foregoing subpulse which is strongly compressed during propagation. The supercontinuum generation of the spectrum and the formation of attosecond pulse can be constructed or destructed by the permanent dipole moment, depending on its value relative to the transition dipole moment. They are also very sensitive to the carrier-envelope phase of the incident few-cycle pulse. Multiphoton ionization of the medium weakens the oscillating feature and the intensity of the basic spectral component. Strong ionization also weakens the intensity of the high spectral components and of the forgoing attosecond subpulse.
When an ultrashort laser pulse propagates in a cascade three-level nondipolar molecular medium, it is found that the intensity of the two-color superfluorescence is enhanced for large number density of the molecule, while the fast dephasing of the dipole coherence reduces the intensity of the cooperative radiation and delays the emission times or even inhibits the formation of the emission. The delay time of the superfluorescence radiation deceases with the increase of the intensity of the excitation pulse, of the molecular number density and of the propagation distance. A well-shaped up-conversion laser pulse is generated when the concentration of the molecule is large and when the dephasing rate of the dipole coherence is small.
In the last part of this thesis, a new scheme of X-ray pump-probe experiment, namely X-ray absorption (XA) and resonant inelastic X-ray scattering (RIXS) accompanied by core-hole hopping induced by a strong laser field, is presented. The relevant theory is developed and is exemplified in detail with the nitrogen molecule. It is shown that a strong-laser-field induced promotion of core holes opens the scattering channels that are forbidden by the dipole selection rules and gives rise to new features in the X-ray absorption and scattering spectra. The strength of the symmetry forbidden channels strongly depends on the competition of the time of Rabi flopping between the core holes and the effective duration of the scattering process or the duration of the X-ray pulse. The XA and RIXS spectra depend on the orientation of the molecule and the relative polarization directions of the X-ray and IR-laser fields. Expressions of the XA and RIXS cross sections for both fixed-in-space and randomly oriented molecules are derived. The Rabi splitting of the core-excited states induced by the strong IR pulses results in broadening of the XA profile and decreases the XA and RIXS probabilities. Moreover, the resonant frequencies are shifted due to the Rabi splitting and the interplay of the Raman and non-Raman components of the scattering process. The RIXS profile is sensitive to the absolute carrier-envelope phase of the few-cycle strong IR field and is independent of the phase of the high-frequency X-ray pulse.
本论文的主要目的在于发展处理激光脉冲和物质相互作用的理论方法,解释和预测各种新的物理现象,主要涉及从红外到X射线波段的有关非线性光学现象。本论文的研究内容主要包括四部分。第一部分涉及双光子吸收(TPA)过程的量子相干控制。我们对TPA过程的旋波近似(RWA)解进行了修正,得到了多能级分子体系中TPA过程的非旋波近似(NRWA)解。基于共振TPA的非旋波近似解,我们还得到了描述脉冲传播过程中其双光子面积演化的面积定理。在第二部分我们分别研究了超短脉冲激光和长脉冲激光在不同分子介质中传播时的一步和两步TPA及其光限幅行为。第三部分我们对超短激光脉冲传播过程中超连续谱形成、阿秒脉冲的产生和两色超荧光的形成进行了研究。在第四部分,我们提出了一种新的泵浦—探测X射线光谱学方法,即强场激光感应下的X射线吸收和共振非弹性X射线拉曼散射。本论文研究的主要内容与结果如下。
一、双光子吸收量子相干控制及双光子面积定理
过去人们对TPA过程进行理论研究时大都采用RWA,但是RWA解给出了错误的能级动态Stark移动表达式;而且很多时候由外场引起的体系能级的动态Stark移动还被忽略(RWAZS)。本论文对多能级体系中的近共振双光子相互作用进行了研究,得到了体系的NRWA解析解,其中包含了动态Stark效应及分子固有偶极矩的影响。通过数值计算,我们对TPA的RWA解、RWAZS解、NRWA解及不采用任何近似时几率幅方程的严格数值解结果进行了比较,发现即使是在Rabi频率远小于光场载波频率的弱场情况下,TPA过程的RWA和RWAZS解也可能完全失效,而我们的NRWA解与严格数值解则符合的很好。TPA的NRWA解还表明,体系动态Stark移动的存在使双光子激发下的完全粒子数反转变的难以实现。对于空间固定的分子,可以通过脉冲频率调制或相位裁制来实现粒子数的完全反转。分子的无序排布降低了介质的双光子激发率,使得动态Stark效应不能得到完全的补偿。由共振TPA体系的NRWA解,我们还得到了描述脉冲面积(能量流量)在传播过程中演化的双光子面积定理。虽然双光子面积定理是关于单色激光脉冲双光子面积的演化规律,但是严格的数值计算结果表明,即使在伴有新的电场频率成分产生的情况下,双光子面积定理也能定性的解释脉冲传播的动力学性质,如脉冲的双光子吸收光限幅效应。
二、双光子吸收光限幅效应
我们分别对飞秒超短脉冲和微秒长脉冲激光在不同分子介质中传播的双光子吸收光限幅效应进行了研究。采用预估校正的时域有限差分法(FDTD)求解全波矢Maxwell-Bloch方程组,我们对超短脉冲激光在有机分子介质4,4′-二甲氨基二苯乙烯中的共振TPA过程进行了模拟。数值计算结果表明体系主要发生一步TPA,在脉冲传播过程中其光限幅行为可以用NRWA近似下的双光子面积定理进行很好的描述。利用脉冲通过介质后光场强度透射率与入射光强的关系,我们对分子的动态TPA截面进行了初步计算,发现随着脉冲持续时间的增加,体系发生两步TPA的几率增大,测得的分子动态TPA截面也不断增大。
当微秒时域内的长脉冲激光在介质中传播且涉及到自旋三重态的两步TPA过程时,利用体系的内部迟豫时间结构,可以将体系分为快变和慢变两个子体系。快速迟豫的各激发态将跟随由基态及最低三重态组成的慢变子体系进行绝热演化,因此对快变子体系采用绝热近似,同时结合体系粒子数守恒律,可以将多能级体系的速率方程约化为只是关于基态粒子数演化的一个动力学方程。对入射脉冲,考虑光场横向分布的不均匀性,我们利用Cranck-Nicholson方法数值求解光场的傍轴波动方程。将上述理论应用于富勒烯C60,模拟结果表明,长脉冲在C60中的主要光限幅机制为单重态到单重态及三重态到三重态之间的两步TPA。体系粒子从基态向最低三重态的有效转移速率随入射脉冲强度的增加而加快。由于脉冲前沿及远离光轴处光强较弱,粒子数转移速率较慢,此时主要发生的是基态粒子的弱的线性吸收;相反,在脉冲主体和近光轴处由于较高的光场强度引起的快速粒子数转移,体系发生两步非线性TPA,光场被强烈吸收。因此由于介质吸收性质对光场强度的依赖性,透射脉冲会发生严重的形变。由于C60分子单重态及三重态单光子吸收截面的相对大小依赖于所用的激发波长,因此可以通过改变激发脉冲的波长来获得不同的光限幅效应。同时,由于脉冲传播过程中线性吸收和两步非线性TPA之间的相互转换,传播效应对两步TPA感应的光限幅过程有很大的影响,它依赖于脉冲的强度、吸收介质的长度以及介质的粒子数密度。
三、超短脉冲激发下的非线性光学过程
通过数值求解全波矢Maxwell-Bloch方程组,我们还对超短脉冲激光在分子介质中传播时超连续谱的形成、阿秒脉冲的产生以及超荧光的产生进行了研究。对超短脉冲在极性或非极性两能级分子介质中的单光子共振传播,电场频谱的高频成分主要是由脉冲分裂后最前面的子脉冲的自相位调制作用产生的。该子脉冲在传播过程中被压缩,从而可以形成比入射飞秒脉冲持续时间短的多的阿秒脉冲。当入射脉冲面积足够大时,电场形成超连续谱,但是随着脉冲面积的进一步增大,电场频谱的平台特性被破坏,频谱变得离散化。分子固有偶极矩的存在使分子与光场的非线性相互作用增强,固有偶极矩对超连续谱及阿秒脉冲的产生可以起到建设性或破坏性的作用,取决于它与跃迁偶极矩的相对大小。同时,超短脉冲的载波包络相位对脉冲的时空和频谱演化也有很大影响。当考虑分子的含时电离效应时,入射电场基频成分的强度及其振荡特性被减弱,如果电离强度较强,电场高频成分的强度及最前面子脉冲的强度也被减弱。
对级联三能级分子体系,利用超短脉冲的共振双光子激发使体系的粒子数占有率发生反转,在脉冲传播过程中,被反转的分子介质所产生的两色超荧光辐射强度随粒子数密度的增加而增强,而偶极相干失相减弱并延缓了超荧光的产生。超荧光相对于激发脉冲的延迟时间随激发脉冲的强度、粒子数密度及传播距离的增加而减小。当体系粒子数密度较大、相干失相速率较慢时通过介质的超荧光辐射会形成品质较好的频率上转换激光。
四、X射线吸收和非弹性X射线拉曼散射
在论文的最后一部分我们提出了一种新的X射线泵浦—探测实验方案并以氮气分子为例来说明该一般性理论。一束较弱的X射线激光脉冲将分子中的内层电子激发到某一未占据轨道,使分子处于具有特定对称性的核激发态;而另外一束足够强的可见或红外激光脉冲可以将所产生的内层电子空位转移到具有相反对称性的分子轨道上,从而开通了原先电偶极跃迁选择定则所禁戒的拉曼散射通道。对称性禁戒拉曼通道的强度依赖于内层电子空位跃迁的Rabi周期与拉曼散射有效持续时间及X射线脉冲持续时间的相对大小。我们分别给出了空间固定和自由取向分子的X射线吸收和拉曼散射截面表达式。X射线吸收谱和共振非弹性X射线拉曼散射谱的形状依赖于分子的取向以及X射线与红外激光场的极化方向关系。由强的红外激光场产生的核激发态的Rabi分裂使X射线吸收谱展宽、峰值强度减弱、共振吸收位置发生移动,同时也降低了拉曼散射的几率。缩短入射激光场的持续时间会使拉曼散射谱展宽,出现明显的Rabi分裂成分,同时谱线共振位置的改变也受到散射过程中拉曼和非拉曼成分的相互影响。如果所入射的强红外激光场为少周期脉冲,X射线拉曼散射谱的形状还依赖于该少周期脉冲的绝对载波—包络相位,但是它并不受入射高频X射线脉冲的载波—包络相位的影响。
In the past few decades, the availability of ultrashort and intense laser pulses as well as the development in high power synchrotron radiation sources and X-ray free electron lasers has promoted a rapid development in nonlinear optics and X-ray spectroscopy technologies, and extended their range of applications. Meanwhile, the appearance of varieties of novel nonlinear phenomena calls for much more accurate theoretical treatment in order to be explained.
The main aim of this thesis is to develop further the nonlinear optical theories and methods and to explain and predict new phenomena occurred during the interaction of molecules with electromagnetic radiation ranging from infrared to X-ray region. This thesis consists of mainly four parts. The first part concerns the coherent control of quantum states by specifically designed laser pulses in resonant two-photon absorption (TPA) processes. The non-rotating wave approximation (NRWA) solution for the resonant TPA process in a multi-level system is derived, and the effects of the dynamical Stark shifts and the permanent dipole moments are included. In the second part, we investigate respectively the one-step and two-step TPA and optical limiting behavior of the ultrashort and microsecond long laser pulses. The third part is about the study and explanation of the supercontiuum generation, the formation of the attosecod laser pulses and the two-color superfluorescence related to the propagation of the ultrashort laser pulses. In the last part, a new scheme of X-ray pump-probe spectroscopy is proposed, i.e., strong infrared or optical laser pulse induced X-ray absorption and resonant inelastic X-ray Raman scattering. The main contents and results are summarized as follows.
First, we study the quantum coherent control of two-photon absorption and two-photon absorption area theorem beyond the conventional RWA. In the past when people investigated theoretically the TPA processes, RWA was adopted. However, the RWA solution of TPA gives wrong expressions of the dynamical Stark shifts, and usually the dynamical Stark shifts of the energy levels induced by the external field were neglected (RWAZS) without any physical background. In this theis, we investigate in detail the near resonant TPA of multi-level systems, and obtain the NRWA solution for TPA in which the effects of the dynamical Stark shifts and the permanent dipole moments of the molecules are included. The RWA, RWAZS and NRWA analytical solutions are compared with the strict numerical solutions of the amplitude equations. It is found that even for the weak incident pulse where the Rabi frequency is much smaller than the carrier frequency of the field the RWA and RWAZS solutions break down completely. In contrast, our NRWA solution coincides very well with the strict numerical results. The NRWA solution also shows that the existence of the dynamical Stark shifts prevents the complete inversion of the population in resonant TPA processes. For fixed-in-space molecules, the compensation of the dynamical Stark effect can be achieved by proper phase tailoring or two-photon detunings. It is demonstrated that the orientational disorder diminishes significantly the efficiency of the two-photon induced population transfer and does not allow complete compensation of the dynamical Stark shifts. Based on the NRWA solution of the amplitude equations, the two-photon area theorem taking into account the dynamical Stark shifts and the permanent dipole moments are derived. Although the two-photon area theorem is strict only for single-color field, numerical simulations for ultrashort laser pulses show that the two-photon area theorem can explain qualitatively the dynamical properties of pulse propagation in a two-photon resonant medium, even if the propagation is accompanied by the generation of fields with new frequencies.
Second, we investigate respectively the TPA induced optical limiting effects of the femtosecond ultrashort and miscrosecond long pulses. By solving numerically the full-wave Maxwell-Bloch equation with the predictor-corrector FDTD method, we investigate the propagation of the ultrashort laser pulses in the organic 4, 4’-bis(dimethylamino) stilbene molecules under the condition of TPA. It is found that for ultrshort laser pulses mainly one-step coherent TPA occurs, and the two-photon area therorem can describe qualitatively the optical limiting behavior of the ultrashort pulses. From the relation between the transmittance of the pulse intensity and the incident intensity the dynamical TPA cross section of the 4, 4’-bis(dimethylamino) stilbene molecule is calculated. It shows that the dynamical TPA cross section of the molecule increases with the increase of pulse duration due to the enhancement of two-step TPA.
A dynamical theory of the sequential two-photon absorption involving strong triplet-triplet transitions and of the propagation of laser pulses with durations in the microsecond time domain is presented. Making use of the decay time hierarchy of the energy levels, the system can be devided into fast and slow subsystems. The subsystem with fast decay rates will follow adiabatically the slow dynamics of the population of the ground and the lowest triplet states. Combining the adiabatic approximation of the fast subsystem with the particle conservation law, the rate equations can be reduced to a single dymamical equation for the ground state population. Taking into account the transverse inhomogeneity of the laser pulse, the Cranck-Nicholson method is used to solve numerically the paraxial wave equation of the field intensity. The general theory is applied to fullerene C60 because of its good optical limiting properties. It is shown that the main mechanism of optical limiting for long pulses in C60 is the sequential (singlet-singlet)×(triplet-triplet) two-photon absorption. The effective rate of population transfer from the ground state to the lowest triplet state increases with the increase of the field intensity. Due to this circumstance, the front part of the pulse propagates with mainly linear absorption, while the main body of the pulse is significantly attenuated due to the strong nonlinear sequential two-photon absorption. An incident pulse with a gaussian transverse distribution is strongly absorbed near the axis due to the higher intensity there. Different optical limiting behavior can be obtained by tuning the excitation wavelength because of the wavelength sensitivity of the singlet-singlet and triplet-triplet photoabsorption cross sections. Simulations show that the propagation effect which depends on the field intensity, the length of the absorber and the molecular concentration plays an important role in the sequential TPA induced optical power limiting performance.
In the third part, the propagation of ultrashort laser pulses in both nondipolar and dipolar media is studied and special attention has been paid to supercontinuum generation, formation of attosecond laser pulses and superfluorescence. When an ultrashort pulse propagates in a two-level nondipolar or dipolar medium, supercontinuum of the spectrum is generated mainly due to the self-phase modulation of the foregoing subpulse which is strongly compressed during propagation. The supercontinuum generation of the spectrum and the formation of attosecond pulse can be constructed or destructed by the permanent dipole moment, depending on its value relative to the transition dipole moment. They are also very sensitive to the carrier-envelope phase of the incident few-cycle pulse. Multiphoton ionization of the medium weakens the oscillating feature and the intensity of the basic spectral component. Strong ionization also weakens the intensity of the high spectral components and of the forgoing attosecond subpulse.
When an ultrashort laser pulse propagates in a cascade three-level nondipolar molecular medium, it is found that the intensity of the two-color superfluorescence is enhanced for large number density of the molecule, while the fast dephasing of the dipole coherence reduces the intensity of the cooperative radiation and delays the emission times or even inhibits the formation of the emission. The delay time of the superfluorescence radiation deceases with the increase of the intensity of the excitation pulse, of the molecular number density and of the propagation distance. A well-shaped up-conversion laser pulse is generated when the concentration of the molecule is large and when the dephasing rate of the dipole coherence is small.
In the last part of this thesis, a new scheme of X-ray pump-probe experiment, namely X-ray absorption (XA) and resonant inelastic X-ray scattering (RIXS) accompanied by core-hole hopping induced by a strong laser field, is presented. The relevant theory is developed and is exemplified in detail with the nitrogen molecule. It is shown that a strong-laser-field induced promotion of core holes opens the scattering channels that are forbidden by the dipole selection rules and gives rise to new features in the X-ray absorption and scattering spectra. The strength of the symmetry forbidden channels strongly depends on the competition of the time of Rabi flopping between the core holes and the effective duration of the scattering process or the duration of the X-ray pulse. The XA and RIXS spectra depend on the orientation of the molecule and the relative polarization directions of the X-ray and IR-laser fields. Expressions of the XA and RIXS cross sections for both fixed-in-space and randomly oriented molecules are derived. The Rabi splitting of the core-excited states induced by the strong IR pulses results in broadening of the XA profile and decreases the XA and RIXS probabilities. Moreover, the resonant frequencies are shifted due to the Rabi splitting and the interplay of the Raman and non-Raman components of the scattering process. The RIXS profile is sensitive to the absolute carrier-envelope phase of the few-cycle strong IR field and is independent of the phase of the high-frequency X-ray pulse.
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