The general theory of first-order spatio-temporal distortions of Gaussian pulses and beams
The general theory of first-order spatio-temporal distortions of Gaussian pulses and beams
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DOI：
10.1117/12.645107
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发表时间：
2006-02
期刊：
影响因子：
--
通讯作者：
S. Akturk;X. Gu;P. Gabolde;R. Trebino
中科院分区：
文献类型：
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作者：
S. Akturk;X. Gu;P. Gabolde;R. Trebino
超短激光脉冲通常用其电场的时间和光谱依赖性来表示。这种方法忽略了空间坐标与时间和/或频率之间的任何耦合。然而，这种假设往往是失败的，因为超短脉冲的产生和操作需要引入时空耦合。此外，忽略超短脉冲中的这些耦合也极大地限制了只有利用时空行为才能实现的潜在应用。由于这些原因，近年来时空耦合越来越受到研究者的关注。然而，迄今为止提出的大多数工作都集中在一些特定的耦合上，缺乏一般和严格的分析。我们提出了高斯脉冲和光束的一阶时空畸变的一个严格的和数学上优雅的理论。我们把脉冲写在四个可能的域中，xt, xω， kω和kt，包括耦合。我们确定了强度分布中的耦合：脉冲前倾斜、空间色散、角色散和时间与角度的关系。我们确定了四种新的同步耦合：“波前旋转”、“波前倾斜色散”、“角时间啁啾”和“角频率啁啾”。此外，我们还为它们提供了标准化的无量纲定义，其范围从-1到1。最后，我们表明，对于脉冲长度、带宽、光束光斑大小和发散角等参数，在存在耦合的情况下，需要两个单独的定义作为“局部”和“全局”量。我们的方法完全确定了高斯脉冲和光束中各种时空耦合之间的显式关系。通过计算分析，可以将其推广到任意剖面。
Ultrashort laser pulses are usually expressed in terms of the temporal and spectral dependences of their electric field. This approach disregards any couplings between the spatial coordinates and time and/or frequency. This assumption, however, often fails, as the generation and manipulation of ultrashort pulses require the introduction of spatio-temporal couplings. Furthermore, disregarding these couplings in ultrashort pulses also greatly limits the potential applications that could only be possible by exploiting the spatio-temporal behaviors. For these reasons, spatio-temporal couplings are receiving increased attention from researchers in recent years. Most of the work presented to date, however, focuses on a few particular couplings, lacking a general and rigorous analysis. We present a rigorous and mathematically elegant theory of first-order spatio-temporal distortions of Gaussian pulses and beams. We write pulses in four possible domains, xt, xω, kω, and kt, including the couplings. We identify couplings in intensity profiles as: pulse-front tilt, spatial dispersion, angular dispersion, and time vs. angle. We identify four new couplings that occur in phase: "wave-front rotation," "wave-front-tilt dispersion," "angular temporal chirp," and "angular frequency chirp." In addition, we provide normalized, dimensionless definitions for them, which range from -1 to 1. Finally, we show that for such parameters as pulse length, bandwidth, beam spot size and divergence angle, two separate definitions are required as "local" and "global" quantities, in presence of the couplings. Our approach completely determines the explicit relations between various spatio-temporal couplings in Gaussian pulses and beams. It can be generalized to arbitrary profiles by using computational analysis.