Abstract Attoscience is the emerging field that accesses the fastest electronic processes occurring at the atomic and molecular length scales with attosecond (1 as = 1 0 − 18 s) time resolution having wide ranging physical, chemical, material science and biological applications. The quintessential and one of the most fundamental processes in this domain is the generation of phase locked XUV attosecond pulses. The theoretical approach to understand the process incorporates a fully quantum or semi classical or relativistic description of coherent charge dynamics in intense ultrashort electromagnetic fields driving a quantum system (an atom, a molecule, solid band gap materials or surface plasmas). Modelling of such physical and dynamical systems in science and also in many other branches often leads to equations represented in terms of complex multi-dimensional integrals. These integrals can often be solved using the stationary phase approximation, which leads to a series of equations identifying the points in the multi-dimensional space, having most significant contributions in their evaluation. These points are usually indicated as saddle points. The description of the dynamics of quantum mechanical or relativistic systems that results from such an approach enables near to classical physics intuitive perceptions of the processes under investigation. Thus, the saddle point methods are very powerful and valuable general theoretical tools to obtain asymptotic expressions of such solutions and help also to gain physical insights on the underlying phenomena. Such techniques developed in the past have been adapted to study the emission of as pulses by different physical systems and have been widely employed in calculating and estimating the response of matter to intense electromagnetic pulses on ultrafast time scales. Here we provide an extensive disposition of the saddle point approaches unifying their ubiquitous applications within the domain of attoscience valid for simple atomic to more complex condensed matter systems undergoing ultrafast dynamics and present current trends and advancements in the field. In this review we would delineate the methodology, present a synthesis of seminal works and describe the state of the art applications. Finally we also address ultrashort time dynamics of novel materials that have gained much attention recently, namely lower dimensional material systems and micro-plasma systems.

中文翻译：

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强场物理学中的鞍点方法和阿秒脉冲的产生

摘要 Attoscience 是一个新兴领域，它以阿秒 (1 as = 1 0 − 18 s) 时间分辨率访问在原子和分子长度尺度上发生的最快电子过程，具有广泛的物理、化学、材料科学和生物应用。该领域的典型和最基本的过程之一是锁相 XUV 阿秒脉冲的产生。理解该过程的理论方法结合了对驱动量子系统（原子、分子、固体带隙材料或表面等离子体）的强超短电磁场中相干电荷动力学的完全量子或半经典或相对论描述。在科学和许多其他分支中对此类物理和动力系统进行建模通常会导致用复杂的多维积分表示的方程。这些积分通常可以使用固定相近似来求解，这会产生一系列方程来识别多维空间中的点，对它们的评估有最重要的贡献。这些点通常表示为鞍点。由这种方法产生的对量子力学或相对论系统动力学的描述使得对所研究过程的直观感知接近经典物理学。因此，鞍点方法是非常强大且有价值的通用理论工具，可用于获得此类解决方案的渐近表达式，并有助于获得对潜在现象的物理见解。过去开发的此类技术已适用于研究不同物理系统发出的脉冲，并已广泛用于计算和估计物质对超快时间尺度上的强电磁脉冲的响应。在这里，我们提供了鞍点方法的广泛配置，统一了它们在 attoscience 领域中无处不在的应用，适用于经历超快动力学的简单原子到更复杂的凝聚态系统，并展示了该领域的当前趋势和进展。在这次审查中，我们将描述方法论，呈现开创性作品的综合并描述最先进的应用程序。最后，我们还讨论了最近备受关注的新型材料的超短时动力学，即低维材料系统和微等离子体系统。