Exciting solids with intense femtosecond laser pulses prompts electrons of the interrogated material to respond in highly non-linear manner, as is evident in the emission of high-order harmonic radiation and photoelectrons with kinetic energies well above that of the driving photons. Such high-field interactions can be resolved, for example, in above-threshold multiphoton photoemission (ATP) spectroscopy. In this work, we interrogate the nonlinear photoelectric responses of the pristine copper, silver, and gold noble metal surfaces in (111) and (100) crystal orientations in the perturbative regime. Using multi-photon photoemission spectroscopy (mPP) excited by finely tuned optical fields, we characterize enhancement of the mPP and ATP yields from (111) surfaces in selected $k_{||}$-momentum ranges when the occupied Shockley surface (SS) states are (near-)resonantly coupled by multi-photon transitions to image potential (IP) intermediate states in the excitation process. The ATP signal from the IP states of (111) surfaces is largely defined by their formation through polarization of SS electrons; this observation is contrasted with ATP experiments from the Ag(100) surface, for which the SS becomes an unoccupied resonance and the IP states can only be excited from bands with significantly more bulk character. In addition, based on the optical power and non-linear order dependent mPP spectra, we provide new evidence for ATP being a one-step, rather than a sequential process, as previously postulated.

中文翻译：

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贵金属表面的阈值以上多光子光发射

飞秒激光脉冲激发的固体激发被询问材料的电子以高度非线性的方式响应，这在高阶谐波辐射和动能远高于驱动光子的动能的光电子的发射中很明显。这样的高场相互作用可以例如在阈值以上的多光子光发射（ATP）光谱法中解决。在这项工作中，我们研究了在扰动状态下（111）和（100）晶体取向的原始铜，银和金贵金属表面的非线性光电响应。使用由微调光学场激发的多光子光发射光谱（mPP），我们表征了在选定的（111）表面中mPP和ATP产量的提高${ķ}_{||}$当在激发过程中，所占据的肖克利表面（SS）状态通过多光子跃迁（近）共振耦合到图像电势（IP）中间状态时，-动量范围。来自（111）表面IP状态的ATP信号在很大程度上取决于它们通过SS电子的极化而形成；将该观察结果与来自Ag（100）表面的ATP实验形成对比，在该实验中，SS变为未占据的共振，并且IP状态只能从具有明显更大体积特征的谱带中激发。此外，基于光功率和非线性阶跃相关的mPP光谱，我们提供了新的证据证明ATP是一步一步的过程，而不是先前假设的顺序过程。