Λ型三能级原子系统中光学性质相干控制及周期量级激光脉冲传播的研究
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摘要
本论文主要进行了两个方面的理论研究工作:一方面对非均匀展宽的Λ型三能级系统中无反转激光及量子相干控制进行理论研究;另一方面,采用时域有限差分法和预估校正运算法则数值求解麦克斯韦—布洛赫方程,模拟了周期量级激光脉冲在稠密的Lambda型三能级原子系统中的传播过程。全文内容共分八章,内容如下:
第一章为综述,对无粒子数反转激光,相干控制和无粒子数反转激光产生的基本原理以及超短激光脉冲的发展和应用作了简单的阐述,介绍了当前这一研究课题的研究现状和研究内容。
第二章讨论了封闭的Λ型三能级系统中Doppler展宽对LWI增益的影响,研究发现:不惯探测场和驱动场是同向传播还是反向传播,驱动场是失谐还是共振,系统获得的GWI都不随Doppler展宽值的增大而单调地减小或增大;除探测场和驱动场反向传播且驱动场失谐的情况外,在一定的条件下,选择适当的Doppler展宽值,可以得到比不存在Doppler效应时大得多的GWI;尤其是当探测场和驱动场同向传播且驱动场共振时,获得的GWI更大。另外,我们的研究还表明,在探测场和驱动场反向传播情况下,Doppler展宽值足够大时,增益出现振荡,振荡的区域和幅度随着Doppler展宽值的增大而增大。这些结论是与以前关于封闭Λ型系统中Doppler展宽对LWI增益影响的研究结果(即增益(或强度)随Doppler展宽值的增加而单调减小)大不相同的。
第三章在第二章研究的基础上首次讨论了自发辐射诱导相干对Doppler展宽的封闭∧型系统中探测场无反转增益的影响,结果表明:不管探测场和驱动场是同向传播还是反向传播,在Doppler展宽值较小时,存在SGC时系统可获得明显大于不存在SGC效应时的LWI增益;存在SGC效应时LWI增益所对应的探测场失谐的取值范围明显大于不存在SGC效应时的取值范围;Doppler展宽值一定时,LWI增益的极大值不随SGC强度的增大而单调地减小或增大,选择合适的SGC强度值,可获得最大的LWI增益。
第四章首次研究Doppler展宽的封闭系统中探测场和驱动场之间的相对位相对探测场的增益和粒子数布居的控制作用。结果发现:(1)不管探测场和驱动场是同向传播还是反向传播,驱动场是失谐还是共振,无反转增益总是随相对位相的改变而作周期性变化,周期为2π。(2)驱动场共振时,无反转增益极大值随Doppler展宽值的增大而单调减小,且反向传播时比同向传播时减小的速度更快;驱动场失谐时,无反转增益的极大值随Doppler展宽值的增大不再单调地减小或增大。在以上两种情况下,均可以通过调节相对相位的数值而得到最大的无反转增益。(3)自发辐射诱导相干性对无反转增益的贡献远大于动力学相干性的贡献。
第五章推导了不采用旋波近似和慢变包络近似下的全波麦克斯韦—布洛赫方程,并对时域有限差分法和预估校正运算法则作了细致的阐述。
第六章采用时域有限差分法和预估校正运算法则数值求解了不采用旋波近似和慢变包络近似下的全波麦克斯韦—布洛赫方程,模拟了周期量级脉冲在稠密Lambda型三能级原子介质中的传播特性,研究结果发现:超短脉冲在稀疏介质和稠密介质中的传播规律有明显的不同;在稀疏介质中,由于电场时间导数项的影响,脉冲的后沿出现振荡;在稠密介质中,脉冲的前沿和后沿均出现振荡;大面积脉冲在稀疏介质中传播时不发生分裂,而在稠密介质中传播时发生分裂;在稠密介质中脉冲的传播延迟于在稀疏介质中脉冲的传播,入射脉冲面积越大,差别越明显。脉冲在稀疏介质和稠密介质中传播过程中的粒子数布居演化情况明显不同。另外在稠密介质中,考虑和不考虑LFC两种情况下,脉冲的拉比频率的时间演化规律明显不同;由于NDD相互作用会增强和减弱光与物质的相互作用,导致考虑NDD相互作用时脉冲的振幅大于和小于不考虑NDD的情况;对大面积脉冲,脉冲发生分裂,脉冲发生分裂,子脉冲间的间距随着传播距离的增加而增大,而且考虑LFC时的子脉冲间的间距小于不考虑LFC时两脉冲的间距;原子密度大的介质内,考虑和不考虑LFC两种情况下,能级|1>, |2>和|3>上的粒子数布居的分布明显不同;入射脉冲的面积越大,LFC对脉冲和粒子数布居的影响越大。
第七章研究了单色周期量级激光脉冲在稀疏介质和稠密介质中传播时的脉冲频谱演化规律,结果发现:不管是在稀疏介质中还是在稠密介质中,由于自相位调制作用,频谱均被展宽,而在稠密介质中频谱的宽度要远大于稀疏介质中的情况,这主要是由于近偶极—偶极作用导致的。在稠密介质中,由于近偶极—偶极作用和自相位调制作用,频谱出现高频连续波,可以得到最高频率为10ωp的超连续谱。
第八章对双色周期量级激光脉冲在稠密的Λ型三能级原子介质中的传播特性进行了研究,结果发现两色脉冲的初始相位对脉冲的时间演化有很大的影响,脉冲的分裂现象与稀疏介质明显不同。
This paper represents mainly two aspects research: one is the study of lasing without inversion and coherent control in an inhomogeneous broadeningΛ-type three-level system; the other is to numerically solute the Maxwell-Bloch equations employing predictor-corrector finite-difference time-domain method, and simulate propagation of sub-cycle laser pulse in a denseΛ-type three-level system. This paper consists of eight chapters, and the main contents and results are illustrated as follows:
In chapter 1, we explain the significance of the studying coherent control, LWI showed the basic principle of producing LWI, give the development and applications of ultrashort laser pulses, and introduce simply the current research state of coherent control, LWI and the interaction of the ultrashort laser pulse with medium.
In chapter 2, we discuss the effect of the Doppler-broadening on the gain and the population difference. The result shows that regardless of the driving field being on resonance or not, for the counter- or co-propagating of the probe and driving fields (PDF), GWI does not monotonously decrease or increase with Doppler width increasing; except the case of the counter-propagating PDF with off-resonance driving field, at a suitable Doppler width one can get a gain maximum value much larger than that without Doppler broadening; especially in the situation of the resonant driving field, the co-propagating geometry leads to a more large GWI; in addition, for the counter-propagating geometry, when Doppler width is larger enough, GWI oscillation occurs, and the oscillation amplitude and region increase with Doppler width increasing. These conclusions are very different from that obtained in previous investigation (i.e. the gain monotonously decreases with Doppler width increasing).
In chapter 3, based on the work of chapter 2, we firstly investigate the effect of the spontaneously generated coherence (SGC) on gain of lasing without inversion (LWI) in a closed three-levelΛ-type atomic system with Doppler broadening. It is shown that, regardless of the driving and probe fields being co- or counter–propagating, at a suitable value of the Doppler width, we can obtain a much larger LWI gain with SGC than that without SGC; and the region of the LWI gain spectrum with SGC is obviously larger than that without SGC. When the Doppler width takes a constant value, the gain does not monotonously decrease or increase with increasing of strength of SGC, the largest LWI gain can be obtained by adjusting strength SGC. Generally speaking, the co-propagating probe and driving fields is favorable to obtain a larger LWI gain.
In chapter 4, for the first time, we studied the control role of the relative phase between the probe and driving fields on inversionless gain of the probe field in a closed and Doppler broadeningΛ-type three-level system with the spontaneously generated coherence (SGC). It is shown that:(1) Regardless of the driving field being on- or off- resonance, and regardless of the probe and driving fields being co- or counter- propagating, always the gain maximum value varies periodically with variation of the relative phase, the period is 2π. (2) When the driving field is on-resonance, the gain maximum value decreases monotonously with Doppler width increasing, moreover, the decreasing in the counter-propagation case is quicker than that in the co-propagation case; when the driving field is off-resonance, the gain maximum value does not monotonously decrease or increase with Doppler width increasing. For above both cases, the largest inversionless gain can be gotten by adjusting value of the relative phase. (3) The contribution of SGC to the inversionless gain is much larger than that of the dynamically induced coherence.
In chapter 5, we derive Maxwell-Bloch equations beyond slowly varying envelope approximation (SVEA) and rotation-wave approximation (RWA) are located in chapter five, and simply elucidate the predictor-corrector finite-difference time-domain method.
In chapter 6, by solving the full Maxwell-Bloch equations without SVEA and RWA, we numerically investigate the interaction of sub-cycle laser pulse and a denseΛ-type three-level atomic system. We find that the Rabi frequency and the populations in a dense medium are quite different from those in a dilute medium; the time derivative of the electric field has stronger effects on the time evolution of the pulse in the dense medium than that in a dilute medium, so the trailing and leading edge of the pulse occurs oscillations; for the larger pulse area, split of pulse occurs in a dense medium, and not occur in a dilute medium; the time of pulse appearing in a dense medium is later than that in the dilute medium; the larger is the area of the input pulse, the more evident is the difference. In addition, the time evolution rules of the carrier Rabi frequency in the two cases with and without LFC are much different in a dense medium; the amplitude of the main pulse is larger or smaller with LFC than that without LFC since the effect of the NDD interaction will enhanced or depresses the light-matter interaction; when the area of the input pulse is larger, split of pulse occurs, and the time interval between the two sub-pulses increase with propagation distance increasing and the time interval between the two sub-pulses in the case without LFC is longer than that with LFC; the time evolution rules of the populations of levels |1>, |2> and |3> in the two cases with and without LFC are much different in a dense medium; the larger is the area of the input pulse, the obviously evident are the effects of LFC on time evolutions of the pulse and populations.
In chapter 7, we analyze spectrum of a sub-cycle laser pulse propagating in a denseΛ-type three-level atomic medium. It is found that regardless of in a dilute medium and in a dense medium, the spectrum is broaden due to the self-phase modulation (SPM); however, the width is much larger in the dense medium than that in a dilute medium because of NDD interaction. In the dense medium, the supercontinuum spectrum occurs due to SPM and NDD interaction, and the maximum frequency is 10ωp.
In chapter 8, we investigate the propagating property of the two-color sub-cycle pulses in a denseΛ-type three-level atomic system, we find that the initial phase of the two-color pulse has the effect on the time evolution, and the pulse splitting in a dense medium is very different from those in a dilute medium.
第一章为综述,对无粒子数反转激光,相干控制和无粒子数反转激光产生的基本原理以及超短激光脉冲的发展和应用作了简单的阐述,介绍了当前这一研究课题的研究现状和研究内容。
第二章讨论了封闭的Λ型三能级系统中Doppler展宽对LWI增益的影响,研究发现:不惯探测场和驱动场是同向传播还是反向传播,驱动场是失谐还是共振,系统获得的GWI都不随Doppler展宽值的增大而单调地减小或增大;除探测场和驱动场反向传播且驱动场失谐的情况外,在一定的条件下,选择适当的Doppler展宽值,可以得到比不存在Doppler效应时大得多的GWI;尤其是当探测场和驱动场同向传播且驱动场共振时,获得的GWI更大。另外,我们的研究还表明,在探测场和驱动场反向传播情况下,Doppler展宽值足够大时,增益出现振荡,振荡的区域和幅度随着Doppler展宽值的增大而增大。这些结论是与以前关于封闭Λ型系统中Doppler展宽对LWI增益影响的研究结果(即增益(或强度)随Doppler展宽值的增加而单调减小)大不相同的。
第三章在第二章研究的基础上首次讨论了自发辐射诱导相干对Doppler展宽的封闭∧型系统中探测场无反转增益的影响,结果表明:不管探测场和驱动场是同向传播还是反向传播,在Doppler展宽值较小时,存在SGC时系统可获得明显大于不存在SGC效应时的LWI增益;存在SGC效应时LWI增益所对应的探测场失谐的取值范围明显大于不存在SGC效应时的取值范围;Doppler展宽值一定时,LWI增益的极大值不随SGC强度的增大而单调地减小或增大,选择合适的SGC强度值,可获得最大的LWI增益。
第四章首次研究Doppler展宽的封闭系统中探测场和驱动场之间的相对位相对探测场的增益和粒子数布居的控制作用。结果发现:(1)不管探测场和驱动场是同向传播还是反向传播,驱动场是失谐还是共振,无反转增益总是随相对位相的改变而作周期性变化,周期为2π。(2)驱动场共振时,无反转增益极大值随Doppler展宽值的增大而单调减小,且反向传播时比同向传播时减小的速度更快;驱动场失谐时,无反转增益的极大值随Doppler展宽值的增大不再单调地减小或增大。在以上两种情况下,均可以通过调节相对相位的数值而得到最大的无反转增益。(3)自发辐射诱导相干性对无反转增益的贡献远大于动力学相干性的贡献。
第五章推导了不采用旋波近似和慢变包络近似下的全波麦克斯韦—布洛赫方程,并对时域有限差分法和预估校正运算法则作了细致的阐述。
第六章采用时域有限差分法和预估校正运算法则数值求解了不采用旋波近似和慢变包络近似下的全波麦克斯韦—布洛赫方程,模拟了周期量级脉冲在稠密Lambda型三能级原子介质中的传播特性,研究结果发现:超短脉冲在稀疏介质和稠密介质中的传播规律有明显的不同;在稀疏介质中,由于电场时间导数项的影响,脉冲的后沿出现振荡;在稠密介质中,脉冲的前沿和后沿均出现振荡;大面积脉冲在稀疏介质中传播时不发生分裂,而在稠密介质中传播时发生分裂;在稠密介质中脉冲的传播延迟于在稀疏介质中脉冲的传播,入射脉冲面积越大,差别越明显。脉冲在稀疏介质和稠密介质中传播过程中的粒子数布居演化情况明显不同。另外在稠密介质中,考虑和不考虑LFC两种情况下,脉冲的拉比频率的时间演化规律明显不同;由于NDD相互作用会增强和减弱光与物质的相互作用,导致考虑NDD相互作用时脉冲的振幅大于和小于不考虑NDD的情况;对大面积脉冲,脉冲发生分裂,脉冲发生分裂,子脉冲间的间距随着传播距离的增加而增大,而且考虑LFC时的子脉冲间的间距小于不考虑LFC时两脉冲的间距;原子密度大的介质内,考虑和不考虑LFC两种情况下,能级|1>, |2>和|3>上的粒子数布居的分布明显不同;入射脉冲的面积越大,LFC对脉冲和粒子数布居的影响越大。
第七章研究了单色周期量级激光脉冲在稀疏介质和稠密介质中传播时的脉冲频谱演化规律,结果发现:不管是在稀疏介质中还是在稠密介质中,由于自相位调制作用,频谱均被展宽,而在稠密介质中频谱的宽度要远大于稀疏介质中的情况,这主要是由于近偶极—偶极作用导致的。在稠密介质中,由于近偶极—偶极作用和自相位调制作用,频谱出现高频连续波,可以得到最高频率为10ωp的超连续谱。
第八章对双色周期量级激光脉冲在稠密的Λ型三能级原子介质中的传播特性进行了研究,结果发现两色脉冲的初始相位对脉冲的时间演化有很大的影响,脉冲的分裂现象与稀疏介质明显不同。
This paper represents mainly two aspects research: one is the study of lasing without inversion and coherent control in an inhomogeneous broadeningΛ-type three-level system; the other is to numerically solute the Maxwell-Bloch equations employing predictor-corrector finite-difference time-domain method, and simulate propagation of sub-cycle laser pulse in a denseΛ-type three-level system. This paper consists of eight chapters, and the main contents and results are illustrated as follows:
In chapter 1, we explain the significance of the studying coherent control, LWI showed the basic principle of producing LWI, give the development and applications of ultrashort laser pulses, and introduce simply the current research state of coherent control, LWI and the interaction of the ultrashort laser pulse with medium.
In chapter 2, we discuss the effect of the Doppler-broadening on the gain and the population difference. The result shows that regardless of the driving field being on resonance or not, for the counter- or co-propagating of the probe and driving fields (PDF), GWI does not monotonously decrease or increase with Doppler width increasing; except the case of the counter-propagating PDF with off-resonance driving field, at a suitable Doppler width one can get a gain maximum value much larger than that without Doppler broadening; especially in the situation of the resonant driving field, the co-propagating geometry leads to a more large GWI; in addition, for the counter-propagating geometry, when Doppler width is larger enough, GWI oscillation occurs, and the oscillation amplitude and region increase with Doppler width increasing. These conclusions are very different from that obtained in previous investigation (i.e. the gain monotonously decreases with Doppler width increasing).
In chapter 3, based on the work of chapter 2, we firstly investigate the effect of the spontaneously generated coherence (SGC) on gain of lasing without inversion (LWI) in a closed three-levelΛ-type atomic system with Doppler broadening. It is shown that, regardless of the driving and probe fields being co- or counter–propagating, at a suitable value of the Doppler width, we can obtain a much larger LWI gain with SGC than that without SGC; and the region of the LWI gain spectrum with SGC is obviously larger than that without SGC. When the Doppler width takes a constant value, the gain does not monotonously decrease or increase with increasing of strength of SGC, the largest LWI gain can be obtained by adjusting strength SGC. Generally speaking, the co-propagating probe and driving fields is favorable to obtain a larger LWI gain.
In chapter 4, for the first time, we studied the control role of the relative phase between the probe and driving fields on inversionless gain of the probe field in a closed and Doppler broadeningΛ-type three-level system with the spontaneously generated coherence (SGC). It is shown that:(1) Regardless of the driving field being on- or off- resonance, and regardless of the probe and driving fields being co- or counter- propagating, always the gain maximum value varies periodically with variation of the relative phase, the period is 2π. (2) When the driving field is on-resonance, the gain maximum value decreases monotonously with Doppler width increasing, moreover, the decreasing in the counter-propagation case is quicker than that in the co-propagation case; when the driving field is off-resonance, the gain maximum value does not monotonously decrease or increase with Doppler width increasing. For above both cases, the largest inversionless gain can be gotten by adjusting value of the relative phase. (3) The contribution of SGC to the inversionless gain is much larger than that of the dynamically induced coherence.
In chapter 5, we derive Maxwell-Bloch equations beyond slowly varying envelope approximation (SVEA) and rotation-wave approximation (RWA) are located in chapter five, and simply elucidate the predictor-corrector finite-difference time-domain method.
In chapter 6, by solving the full Maxwell-Bloch equations without SVEA and RWA, we numerically investigate the interaction of sub-cycle laser pulse and a denseΛ-type three-level atomic system. We find that the Rabi frequency and the populations in a dense medium are quite different from those in a dilute medium; the time derivative of the electric field has stronger effects on the time evolution of the pulse in the dense medium than that in a dilute medium, so the trailing and leading edge of the pulse occurs oscillations; for the larger pulse area, split of pulse occurs in a dense medium, and not occur in a dilute medium; the time of pulse appearing in a dense medium is later than that in the dilute medium; the larger is the area of the input pulse, the more evident is the difference. In addition, the time evolution rules of the carrier Rabi frequency in the two cases with and without LFC are much different in a dense medium; the amplitude of the main pulse is larger or smaller with LFC than that without LFC since the effect of the NDD interaction will enhanced or depresses the light-matter interaction; when the area of the input pulse is larger, split of pulse occurs, and the time interval between the two sub-pulses increase with propagation distance increasing and the time interval between the two sub-pulses in the case without LFC is longer than that with LFC; the time evolution rules of the populations of levels |1>, |2> and |3> in the two cases with and without LFC are much different in a dense medium; the larger is the area of the input pulse, the obviously evident are the effects of LFC on time evolutions of the pulse and populations.
In chapter 7, we analyze spectrum of a sub-cycle laser pulse propagating in a denseΛ-type three-level atomic medium. It is found that regardless of in a dilute medium and in a dense medium, the spectrum is broaden due to the self-phase modulation (SPM); however, the width is much larger in the dense medium than that in a dilute medium because of NDD interaction. In the dense medium, the supercontinuum spectrum occurs due to SPM and NDD interaction, and the maximum frequency is 10ωp.
In chapter 8, we investigate the propagating property of the two-color sub-cycle pulses in a denseΛ-type three-level atomic system, we find that the initial phase of the two-color pulse has the effect on the time evolution, and the pulse splitting in a dense medium is very different from those in a dilute medium.
引文
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