Modulation of probe signals in pump-probe measurements of coherent phonons in dielectrics, with and without spectral resolution, are investigated theoretically taking diamond as an example. Analytical investigation as well as first-principles calculations based on time-dependent density-functional theory is utilized to clarify the mechanism of the modulation of the probe signals. Boundary and bulk effects are investigated systematically, putting emphasis on the phase relation between the modulation and the atomic motion of the coherent phonon. They are summarized as follows: Modulation by the boundary effect is in phase with the coherent phonon amplitude, while that by the bulk effect shows $\pi /2$ phase difference. Strong frequency dependence appears in the modulation by the bulk effect, while no frequency dependence by the boundary effect. First-principles calculations support the reliability of the analytical result.

中文翻译：

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再次探讨相干声子检测中探针信号的调制：分析和第一性原理计算分析

从理论上以菱形为例，研究了在有和无光谱分辨率的情况下，电介质中相干声子的泵浦探针测量中探针信号的调制。利用基于时间的密度泛函理论的分析研究以及第一性原理计算来阐明探测信号调制的机理。系统地研究了边界效应和体积效应，重点研究了相干声子的调制与原子运动之间的相位关系。它们总结如下：边界效应的调制与相干声子振幅同相，而体效应的调制表明$\pi /2$相位差。主体效应在调制中表现出很强的频率依赖性，而边界效应则没有频率依赖性。第一性原理计算支持分析结果的可靠性。