Abstract
X-ray techniques have evolved over decades to become highly refined tools for a broad range of investigations. Importantly, these approaches rely on X-ray measurements that depend linearly on the number of incident X-ray photons. The advent of X-ray free electron lasers (XFELs) is opening the ability to reach extremely high photon numbers within ultrashort X-ray pulse durations and is leading to a paradigm shift in our ability to explore nonlinear X-ray signals. However, the enormous increase in X-ray peak power is a double-edged sword with new and exciting methods being developed but at the same time well-established techniques proving unreliable. Consequently, accurate knowledge about the threshold for nonlinear X-ray signals is essential. Herein we report an X-ray spectroscopic study that reveals important details on the thresholds for nonlinear X-ray interactions. By varying both the incident X-ray intensity and photon energy, we establish the regimes at which the simplest nonlinear process, two-photon X-ray absorption (TPA), can be observed. From these measurements we can extract the probability of this process as a function of photon energy and confirm both the nature and sub-femtosecond lifetime of the virtual intermediate electronic state.
Highlights
We used high energy resolution off-resonant X-ray emission spectroscopy[26,27,28,29] (HEROS), which measures the X-ray emission from a sample while using an incidence X-ray energy set below a core level ionization threshold, to detect the ratio between one-photon absorption (OPA) and two-photon X-ray absorption (TPA) signals generated by ultra-short hard X-ray pulses in metallic copper as a function of X-ray fluence
In contrast to the OPA process in the off-resonant regime, for which the position of the high energy resolution off-resonant X-ray emission spectroscopy26–29 (HEROS) spectrum is strictly defined by the incoming photon energy, the TPA mechanism leads to ionization and the subsequent decay transition from final to initial core-states is independent of the incident X-ray photon energy
In addition the measured widths of the elastically scattered X-rays during the self-seeding operation were found to be about 0.75 eV so that the incidence X-ray energy (8967 eV) of the self-seeded beam was 16 sigma below the 1s ionization threshold. These elastically scattered signals were employed to sort the data shot-to-shot to ensure that the HEROS/TPA data used in the analysis corresponded to only well self-seeded pulses characterized by narrow spectral widths
Summary
X-ray pulses received: 16 May 2016 accepted: 19 August 2016 Published: 13 September 2016. The introduction of XFEL facilities that can produce high per-pulse photon flux (~1012) with short pulse durations (ranging from 2–50 femtoseconds) has provided the ability to reach very large peak powers in the keV regime[5,6,7] This has permitted the first observations of processes with very low probabilities, including double-core hole formation[8,9], two-photon absorption[10,11], amplified spontaneous X-ray emission[12,13], plasma creation[14], X-ray-optical wave mixing[15], X-ray second harmonic generation[16] and anomalous X-ray Compton scattering[17]. The TPA process, besides its possible application to quadrupole-allowed X-ray absorption spectroscopy, allows the verification of the quantum description of the interaction of X-ray radiation with bound electrons in the nonlinear regime[25]
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