Self-induced nonlinear effects in the extreme ultraviolet

The study of nonlinear effects arising from the interaction between visible light and matter is typically conducted using pulsed, high-brilliance femtosecond optical lasers. Among other effects, third-order nonlinearity is key to several optical spectroscopies and photonic devices. For example, when a single light pulse interacts with matter, the occurrence of a Kerr nonlinearity can induce self-phase modulation (SPM), which plays a crucial role in supercontinuum generation, wavelength conversion, and chirped pulse amplification. Extending these concepts to the extreme ultraviolet (XUV) spectral region would enable the investigation of core electron levels, providing access to element-specific responses and opening the way to novel nonlinear spectroscopies. 

Until recently, the lack of bright and stable XUV femtosecond sources had hindered for many years the direct observation of self-induced nonlinear effects in this spectral domain. The free-electron laser (FEL) FERMI overcomes these limitations by delivering high-fluence, laser-like spectrally pure pulses with remarkable temporal coherence and stability. These properties make FERMI uniquely suited for detecting self-induced spectral modifications in the XUV range that would be inaccessible with conventional table-top high-harmonic generation (HHG) sources. This capability is essential for isolating the intrinsic nonlinear optical responses of materials in a spectral region where such phenomena have never been observed before.

Figure 1: Sketch of the measurement at the EIS-TIMEX beamline of FERMI. The FEL beam interacts with a tilted free-standing aluminium foil. An enhanced red shift is observed, upon reaching the ENZ condition.

In this work we report the first observation of a third-order nonlinearity in the XUV. A sub-micrometric free-standing aluminum foil, which naturally exhibits an epsilon-near-zero (ENZ) condition for transverse-magnetic radiation in the 30–85 nm range, was used as the nonlinear medium. Measurements performed at the TIMEX beamline of FERMI (see Figure 1) using an FEL wavelength of 44.25 nm reveal pronounced self-phase modulation arising from the strong field enhancement characteristic of ENZ materials. Importantly, the observed nonlinear response persists at fluences up to three orders of magnitude lower than those typically required in XUV nonlinear experiments at FELs.

Figure 2: a) Sketch of the experimental geometry. b) The difference (ΔI) between normalized FEL spectra altered by the sample interaction and those measured without sample interaction is reported for selected tilt angles θ. The increase of ΔI with increasing angle demonstrates the ENZ enhancement, in accord with predictions. c) Real and imaginary diffraction index ε of aluminum; the real part of ε approaches zero for wavelenghts close to 85 nm.  

Our results demonstrate that ENZ-driven nonlinear enhancement (Fig. 2) can enable self-induced spectral reshaping in the XUV even when reducing the FERMI peak power, thereby significantly expanding the accessibility of XUV nonlinear optics and pointing toward future implementations with lower-brilliance table-top HHG sources. The observation of ENZ-enhanced SPM in the XUV constitutes a milestone for extreme nonlinear optics. Aluminium proves to be an exceptionally promising ENZ platform in this spectral window, and the unique capabilities of FERMI were essential to resolving an effect that would otherwise remain undetectable. These findings establish a foundation for new XUV nonlinear spectroscopies, which can provide an unprecedented tool for the fine tuning of wavelengths close to specific absorption thresholds of specific atomic elements.

Carino Ferrante¹, Emiliano Principi², Luca Assogna³, Ambaresh Sahoo³, Giovanni Batignani^4,5, Giuseppe Fumero^4,6,7, Laura Foglia², Riccardo Mincigrucci², Luca Giannessi^2,8, Tullio Scopigno^4,5, Claudio Masciovecchio², Andrea Marini^3,1
1 CNR-SPIN, c/o Dip.to di Scienze Fisiche e Chimiche - Via Vetoio, L’Aquila, Italy
² Elettra-Sincrotrone Trieste S.C.p.A., Trieste, Italy
³ Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell’Aquila, L’Aquila, Italy
⁴ Dipartimento di Fisica, Università di Roma “La Sapienza”, Roma, Italy
⁵ Graphene Labs, Istituto Italiano di Tecnologia, Genova, Italy
⁶ Associate, Nanoscale Device Characterization Division, National Institute of Standards and Technology, Gaithersburg, MD, USA
⁷ Department of Physics and Astronomy, West Virginia University, Morgantown, WV, USA
⁸ INFN Laboratori Nazionali di Frascati, Frascati, Roma, Italy

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