光学倍频过程中感应衍射及色散的研究
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摘要
光波的倍频产生是一种典型的非线性光学过程，它源自介质对光场的二阶非线性响应或极化。以往，人们大都仅关注高效倍频的方式和技术，以获得高功率的短波长激光，满足应用的需求。在参量过程三波相互作用位相匹配的基础上，相应地发展了诸如腔内倍频、外腔共振及准位相匹配等多种技术。近年来，随着对级联非线性(位相失配条件下，二个二阶非线性的级联过程可等效为一个三阶非线性)的认识深入，倍频过程的研究获得了新的重视，新发现了多种重要的非线性光学现象如X型电磁波、宽带锥形光发射及高维光学孤子等，逐渐形成了一个新的研究方向。级联非线性同时也激发了多种新的技术应用，如高能量飞秒脉冲压缩及正常色散状态的克尔透镜锁模技术，对二阶非线性光学的应用和发展起到了推动作用。
在这些新的非线性现象和技术开发中，位相失配是共同的前提条件，它极大程度地丰富了非线性倍频过程。因此，有必要系统深入地研究位相失配的倍频过程。从光束传输的角度看，位相失配的倍频过程涉及到光波的非线性传输，也涉及到衍射和色散等线性传输行为。本论文着重关心和研究光波的线性传输行为和非线性传输行为之间的相互影响，试图回答非线性过程中光波的衍射和色散的变化规律。这些问题不仅是新的，也没有答案，而且对探索和理解新的二阶非线性光学现象是至关重要的。本文的主要研究工作包括以下几个方面：
1．位相失配倍频过程中感应色散的理论研究
飞秒脉冲在介质中色散展宽是典型的线性传输特征，其基本的物理过程是群速度色散。群速度色散来源于介质材料的本征色散，介质的结构或边界条件也可以导致群速度色散如光纤的模式色散和光栅等衍射引起的角色散，这些色散机制均是线性的，对超快激光的发展起到了不可替代的作用。非线性过程对色散的影响的研究工作较少，仅在畴反转的结构性光学晶体(PPLN)中研究了群速度色散的产生机制，它本质上也来源于材料的特殊结构。通过理论上的解析分析与数值模拟计算，我们研究了体材料介质中的感应色散新机制。在位相失配较大时，基波光的色散将被传递给倍频光波，因此倍频光波遭受到的等效色散来自于材料本身以及基波的群速度色散两部分，满足简单的代数相加的关系。论文同时也研究了这种新的感应色散的产生条件，并且讨论分析了其物理图像，可以用一阶极化率与二阶极化率的级联过程来解释[x~(2)(2w；w，w)：x~(1)(w)(?)x~(1)_(eff)(2w)]。
2．感应色散现象的实验验证及应用实例
为确信这种感应色散机制的存在，并且证实所起作用是不可忽略的，我们开展了实验验证的工作。选择波长为2.4um的飞秒激光在BBO晶体中的倍频作为研究对象，基波光的材料色散较倍频光的材料色散高一个量级以上，材料本身的倍频光色散可以被忽略。利用此设计思路开展的实验工作中，观察到了倍频光脉冲显著的啁啾展宽，其相应的色散量是基波色散一半，因此清楚地验证了感应色散机制。作为一个重要的应用实例，我们讨论分析了感应色散机制对时空光孤子产生的贡献。高维时空光孤子的产生要求基波和倍频光色散均为负值的实验环境，我们研究了所有的光学非线性晶体，在其透明波段内均不可能满足此基本要求。感应色散机制可以解决上述困境，倍频光频率处材料本身的色散可以为正值，只要远小于基波光反常色散的量值，我们就可以创造等效倍频色散为负值的实验环境。进一步的数值模拟计算，充分证明了该方案的可行性，它己被国外研究小组应用来实验产生了高维时空光孤子。
3．位相失配倍频过程中感应衍射的理论研究
光波的色散和衍射在数学形式上对易，在物理图像上可类比。因此，我们可以简单地猜测位相失配的倍频过程中也存在感应衍射的机制。通过解析讨论和数值计算，我们证实了感应衍射效应确实存在于位相失配的倍频过程中。尽管衍射和色散在性质上可类比，但在量值上是有所不同的。取决于介质材料，倍频和基波光的色散量值关系是相对任意的，而倍频光和基波光的衍射关系是确定的，倍频光的衍射程度基本上是基波光的一半。结合感应衍射的作用，倍频光的等效衍射将显著强于基波光，出现了一个新奇的现象，倍频光斑的大小将大于基波光斑。上述这些感应衍射的现象和规律均在数值计算中得到证明。
4．衍射和色散相关的非线性光学现象研究
时空不稳定性是非线性光学系统的基本特征，由此产生的多色锥形光发射(CCE)是其一个主要结果。我们在实验上观察和研究了由时空不稳定性导致的锥形光发射，它和传统的光参量产生(OPG)在外形上极为相似，在若干已有的研究工作中引发了混淆。利用二块非线性晶体，并设计了长短脉冲及窄带光束泵浦的实验环境，我们可以同时或分别在实验上产生锥形光发射和光参量产生，从而清楚地诊断和鉴别了这两种不同的非线性过程。据此，我们详细研究和讨论了衍射和色散的作用，帮助理解了新的锥形光发射形成的动力学过程。
Second-Harmonic Generation is a typical nonlinear optical process, which occurs as a result of the part of the atomic response that depends quadratically on the strength of the applied optical field. In order to get high power and short wavelength laser to meet application requirement, people mostly focused on the method and technique of highly efficient frequency doubling previously. Based on phase-matching parametric process, various techniques such as intra-cavity second-harmonic generation、extra-cavity resonance and quasi-phase matching. In recent years, with the progress in cascaded nonlinearities(under phase-mismatching condition, two cascaded quadratic nonlinearity processes can be treated as a third-order nonlinearity), research on second-harmonic process regained people's interest, many important nonlinear optical processes such as X-type electromagnetic wave、broad band conical emission and high dimensional optical soliton are discovered, and a new research field has been formed gradually. Cascaded nonlinearity also brings about many new technical applications, which promotes the development of quadratic nonlinear optics, for example, high-power femtosecond pulse compression and Kerr-lens mode locking technique under normal dispersion condition.
Among these new nonlinear phenomena and technique researches, phase-mismatching is their common preconditions, and this enriched nonlinear second-harmonic process greatly, therefore it is quite necessary to study second-harmonic process under phase-mismatching condition systematically. From the view of beam transmission, this process deals with nonlinear transmission of light wave、diffraction、dispersion etc. In this paper, we mainly focus on the interaction between linear and nonlinear transmission of light wave, and try to figure out rules that govern diffraction and dispersion in the nonlinear process. Our research work mainly deals with:
1. Theoretical research on induced dispersion in the phase-mismatching frequency doubling process.That femtosecond pulse will be broadened through dispersion in materials is the typical linear transmission characteristic, its basic physical process is group velocity dispersion (GVD), which resulted from the intrinsic dispersion of materials as well as the structure of material and boundary condition, for example, mode-dispersion in optical fiber, angle dispersion induced from grating diffraction. These dispersion mechanisms are all linear, and play an irreplaceable role in the development of ultra-fast laser system. Research work on nonlinear effect on dispersion only evolves the formation mechanism of GVD in periodically-poled lithium niobate (PPLN), which essentially roots in the special structure of materials. Through theoretical analysis and numerical computation, we studied the new mechanism of induced dispersion in material. When phase mismatching is relatively large, dispersion of fundamental wave will be transferred to the harmonic wave, hence the equivalent dispersion on the harmonic wave comes from material itself and GVD of fundamental wave. We also studied the conditions under which this new induced dispersion can form, as well as its physical mechanism.
2. Experimental validation and Applications of induced dispersion
In order to ascertain the existence of this induced dispersion and its important effect, we studied the second harmonic of femtosecond laser in BBO crystal. From this experiment we confirmed the mechanism of the induced dispersion. As an important example for application, the contribution of the induced dispersion to the form of spatiotemporal soliton is discussed. We found that when certain requirements are met, we could make the equivalent dispersion of second harmonic wave be negative. The feasibility of this scheme has been confirmed by numerical computation. High dimensional soliton is produced by the use of this technique.
3. Theoretical research on induced dispersion in the process of phase-mismatching second-harmonic generation
Though diffraction and dispersion are qualitatively comparable, they are quantitatively different. The equivalent diffraction is much larger than that of fundamental wave, which lead to a new phenomenon, that is, the spot size of harmonic wave is larger than that of fundamental wave. The above phenomena and conclusions are all confirmed by numerical computation.
4. Research on diffraction and dispersion correlated nonlinear optical phenomena
Space and time instability is the basic characteristic of nonlinear optical system, and Colorful Conical Emission (CCE) is one of its main results. We studied both experimentally and theoretically conical emission, and found that although it seems quite similar to traditional Optical Parametric Generation (OPG), they are two different nonlinear processes after experimental diagnosis. From this, we studied the effect of diffraction and dispersion in detail, which would be of help in understanding the kinetic process of this new conical emission.
在这些新的非线性现象和技术开发中，位相失配是共同的前提条件，它极大程度地丰富了非线性倍频过程。因此，有必要系统深入地研究位相失配的倍频过程。从光束传输的角度看，位相失配的倍频过程涉及到光波的非线性传输，也涉及到衍射和色散等线性传输行为。本论文着重关心和研究光波的线性传输行为和非线性传输行为之间的相互影响，试图回答非线性过程中光波的衍射和色散的变化规律。这些问题不仅是新的，也没有答案，而且对探索和理解新的二阶非线性光学现象是至关重要的。本文的主要研究工作包括以下几个方面：
1．位相失配倍频过程中感应色散的理论研究
飞秒脉冲在介质中色散展宽是典型的线性传输特征，其基本的物理过程是群速度色散。群速度色散来源于介质材料的本征色散，介质的结构或边界条件也可以导致群速度色散如光纤的模式色散和光栅等衍射引起的角色散，这些色散机制均是线性的，对超快激光的发展起到了不可替代的作用。非线性过程对色散的影响的研究工作较少，仅在畴反转的结构性光学晶体(PPLN)中研究了群速度色散的产生机制，它本质上也来源于材料的特殊结构。通过理论上的解析分析与数值模拟计算，我们研究了体材料介质中的感应色散新机制。在位相失配较大时，基波光的色散将被传递给倍频光波，因此倍频光波遭受到的等效色散来自于材料本身以及基波的群速度色散两部分，满足简单的代数相加的关系。论文同时也研究了这种新的感应色散的产生条件，并且讨论分析了其物理图像，可以用一阶极化率与二阶极化率的级联过程来解释[x~(2)(2w；w，w)：x~(1)(w)(?)x~(1)_(eff)(2w)]。
2．感应色散现象的实验验证及应用实例
为确信这种感应色散机制的存在，并且证实所起作用是不可忽略的，我们开展了实验验证的工作。选择波长为2.4um的飞秒激光在BBO晶体中的倍频作为研究对象，基波光的材料色散较倍频光的材料色散高一个量级以上，材料本身的倍频光色散可以被忽略。利用此设计思路开展的实验工作中，观察到了倍频光脉冲显著的啁啾展宽，其相应的色散量是基波色散一半，因此清楚地验证了感应色散机制。作为一个重要的应用实例，我们讨论分析了感应色散机制对时空光孤子产生的贡献。高维时空光孤子的产生要求基波和倍频光色散均为负值的实验环境，我们研究了所有的光学非线性晶体，在其透明波段内均不可能满足此基本要求。感应色散机制可以解决上述困境，倍频光频率处材料本身的色散可以为正值，只要远小于基波光反常色散的量值，我们就可以创造等效倍频色散为负值的实验环境。进一步的数值模拟计算，充分证明了该方案的可行性，它己被国外研究小组应用来实验产生了高维时空光孤子。
3．位相失配倍频过程中感应衍射的理论研究
光波的色散和衍射在数学形式上对易，在物理图像上可类比。因此，我们可以简单地猜测位相失配的倍频过程中也存在感应衍射的机制。通过解析讨论和数值计算，我们证实了感应衍射效应确实存在于位相失配的倍频过程中。尽管衍射和色散在性质上可类比，但在量值上是有所不同的。取决于介质材料，倍频和基波光的色散量值关系是相对任意的，而倍频光和基波光的衍射关系是确定的，倍频光的衍射程度基本上是基波光的一半。结合感应衍射的作用，倍频光的等效衍射将显著强于基波光，出现了一个新奇的现象，倍频光斑的大小将大于基波光斑。上述这些感应衍射的现象和规律均在数值计算中得到证明。
4．衍射和色散相关的非线性光学现象研究
时空不稳定性是非线性光学系统的基本特征，由此产生的多色锥形光发射(CCE)是其一个主要结果。我们在实验上观察和研究了由时空不稳定性导致的锥形光发射，它和传统的光参量产生(OPG)在外形上极为相似，在若干已有的研究工作中引发了混淆。利用二块非线性晶体，并设计了长短脉冲及窄带光束泵浦的实验环境，我们可以同时或分别在实验上产生锥形光发射和光参量产生，从而清楚地诊断和鉴别了这两种不同的非线性过程。据此，我们详细研究和讨论了衍射和色散的作用，帮助理解了新的锥形光发射形成的动力学过程。
Second-Harmonic Generation is a typical nonlinear optical process, which occurs as a result of the part of the atomic response that depends quadratically on the strength of the applied optical field. In order to get high power and short wavelength laser to meet application requirement, people mostly focused on the method and technique of highly efficient frequency doubling previously. Based on phase-matching parametric process, various techniques such as intra-cavity second-harmonic generation、extra-cavity resonance and quasi-phase matching. In recent years, with the progress in cascaded nonlinearities(under phase-mismatching condition, two cascaded quadratic nonlinearity processes can be treated as a third-order nonlinearity), research on second-harmonic process regained people's interest, many important nonlinear optical processes such as X-type electromagnetic wave、broad band conical emission and high dimensional optical soliton are discovered, and a new research field has been formed gradually. Cascaded nonlinearity also brings about many new technical applications, which promotes the development of quadratic nonlinear optics, for example, high-power femtosecond pulse compression and Kerr-lens mode locking technique under normal dispersion condition.
Among these new nonlinear phenomena and technique researches, phase-mismatching is their common preconditions, and this enriched nonlinear second-harmonic process greatly, therefore it is quite necessary to study second-harmonic process under phase-mismatching condition systematically. From the view of beam transmission, this process deals with nonlinear transmission of light wave、diffraction、dispersion etc. In this paper, we mainly focus on the interaction between linear and nonlinear transmission of light wave, and try to figure out rules that govern diffraction and dispersion in the nonlinear process. Our research work mainly deals with:
1. Theoretical research on induced dispersion in the phase-mismatching frequency doubling process.That femtosecond pulse will be broadened through dispersion in materials is the typical linear transmission characteristic, its basic physical process is group velocity dispersion (GVD), which resulted from the intrinsic dispersion of materials as well as the structure of material and boundary condition, for example, mode-dispersion in optical fiber, angle dispersion induced from grating diffraction. These dispersion mechanisms are all linear, and play an irreplaceable role in the development of ultra-fast laser system. Research work on nonlinear effect on dispersion only evolves the formation mechanism of GVD in periodically-poled lithium niobate (PPLN), which essentially roots in the special structure of materials. Through theoretical analysis and numerical computation, we studied the new mechanism of induced dispersion in material. When phase mismatching is relatively large, dispersion of fundamental wave will be transferred to the harmonic wave, hence the equivalent dispersion on the harmonic wave comes from material itself and GVD of fundamental wave. We also studied the conditions under which this new induced dispersion can form, as well as its physical mechanism.
2. Experimental validation and Applications of induced dispersion
In order to ascertain the existence of this induced dispersion and its important effect, we studied the second harmonic of femtosecond laser in BBO crystal. From this experiment we confirmed the mechanism of the induced dispersion. As an important example for application, the contribution of the induced dispersion to the form of spatiotemporal soliton is discussed. We found that when certain requirements are met, we could make the equivalent dispersion of second harmonic wave be negative. The feasibility of this scheme has been confirmed by numerical computation. High dimensional soliton is produced by the use of this technique.
3. Theoretical research on induced dispersion in the process of phase-mismatching second-harmonic generation
Though diffraction and dispersion are qualitatively comparable, they are quantitatively different. The equivalent diffraction is much larger than that of fundamental wave, which lead to a new phenomenon, that is, the spot size of harmonic wave is larger than that of fundamental wave. The above phenomena and conclusions are all confirmed by numerical computation.
4. Research on diffraction and dispersion correlated nonlinear optical phenomena
Space and time instability is the basic characteristic of nonlinear optical system, and Colorful Conical Emission (CCE) is one of its main results. We studied both experimentally and theoretically conical emission, and found that although it seems quite similar to traditional Optical Parametric Generation (OPG), they are two different nonlinear processes after experimental diagnosis. From this, we studied the effect of diffraction and dispersion in detail, which would be of help in understanding the kinetic process of this new conical emission.
引文
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