Abbas Adeel, Wang Li-Gang
Opt Express. 2020 Oct 12;28(21):32077-32086. doi: 10.1364/OE.405726.
Hanbury Brown and Twiss (HBT) effect has broad applications in optics and other branches of physics, and traditionally this effect is considered in pure spatial or temporal domain. Here we investigate the spatiotemporal HBT effect, extending this phenomenon from spatial or temporal to spatiotemporal domain. By assuming the Gaussian statistics of partially coherent spatiotemporal pulsed sources, we find the generalized analytical results for spatiotemporal HBT effect in the compact form, with the help of the matrix-optics method, which can consider the HBT effect in spatial and temporal domain simultaneously. Furthermore, for Gaussian Schell-model pulsed beams (GSMPBs) used as a spatiotemporal correlated source, we have obtained the generalized expression to calculate spatiotemporal HBT effect, which is useful for up to three-dimensional cases in any second-order linear dispersive medium. By taking a simple two-dimensional case and using air as an example of a linear dispersive medium, we numerically illustrate the properties of the spatiotemporal HBT effect by adjusting the spatial and temporal parameters of the GSMPB source, and reveal the influence of both the spatial and temporal parameters on the spatiotemporal HBT effect. This work paves the path towards the detailed study of HBT effect for a source containing spatiotemporal information with Gaussian statistics.
汉伯里·布朗和蒂斯（HBT）效应在光学和物理学的其他分支中有广泛应用，传统上这种效应是在纯空间或时间域中考虑的。在此，我们研究时空HBT效应，将这一现象从空间或时间扩展到时空域。通过假设部分相干时空脉冲源的高斯统计特性，借助矩阵光学方法，我们以紧凑形式得到了时空HBT效应的广义解析结果，该方法可同时考虑空间和时间域中的HBT效应。此外，对于用作时空相关源的高斯谢尔模型脉冲光束（GSMPB），我们得到了计算时空HBT效应的广义表达式，这对于任何二阶线性色散介质中的三维情况都很有用。通过以简单的二维情况为例，将空气作为线性色散介质，我们通过调整GSMPB源的空间和时间参数，数值说明了时空HBT效应的特性，并揭示了空间和时间参数对时空HBT效应的影响。这项工作为详细研究具有高斯统计特性的包含时空信息的源的HBT效应铺平了道路。
