FERMI | TIMEX Self-induced nonlinear optics in the XUV regime Elettra Highlights 2024–2025 92 Self-driven third order nonlinear effects represent a key element for the realization of several optical spectroscopies and photonic devices. By the simple interaction between one pulse and matter, they can induce spectral modifications, such as supercontinuum generation, wavelength converters, and chirped pulse amplification. The lack of stable and high brilliance light sources prevents such observation in this fundamental regime dominated by core electron interactions. The recent advent of Free Electron Lasers (FEL) and High-Harmonic Generation (HHG) systems enables the extension of these effects in the wavelength regime of x-ray and XUV and the realization of new spectroscopic schemes taking advantage of the shorter wavelength involved. Here we show the first experimental evidence for self-phase modulation of femtosecond seeded FEL pulses, allowing peak intensity > 200 TW/cm2. In the first part of our work, the nonlinear effects were investigated above and below the absorption edge of magnesium, taking advantage of the wavelength tunability in FERMI FEL facility. The system was based on a simultaneous single-shot detection of FEL spectrum before and after the interaction with a thin (140 nm) freestanding Mg foil. The average of the difference of normalized single-shot spectra before and after the interaction reveals a spectral modification from a non-linear blue-shift to a red-shifted broadening, above and below the absorption edge L2,3, respectively (see Fig. 1 a). These findings can be rationalized by considering three distinct contributions: above the edge, the observed blue-shift is attributed to ultrafast electron ionization; below the edge, the red-shift arises from the delayed thermal response of highly excited electrons, and the spectral broadening is driven by self-phase modulation. These nonlinear evidences were verified also in selenium, aluminum, while in silicon the effects are negligible. Although the tuning capability of the wavelength shift and spectral broadening represents a key advantage for the spectroscopic application, the weakness of the effect (6% of bandwidth and ~20 meV of shift) and the high peak intensity required (~500 TW/cm2) prevent the implementation in technological devices. In terms of nonlinear applications, epsilon-near-zero (ENZ) materials offer extraordinary possibilities, owing to the tremendous field enhancement that they can provide. Indeed, for low-absorbing media, exhibiting low dielectric permittivity modulus (vanishing for non-absorbing media), nonlinear effects become non-perturbative, thus opening novel avenues for strong-field physical applications. Currently, ENZ materials operate efficiently only in the near and mid infrared (IR) frequency part of the spectrum and, although potentially disruptive, their XUV functionality remains unexplored. In the second part of our work, we investigated the enhancement of self-induced nonlinear effects by means of plasmonic interaction in a submicrometric foil of aluminum. Specifically, a permittivity (ϵAl (λ)) lower than 1 in a large spectral range (30-85 nm) enables the near-zero effectiveindex (NZI) condition for transverse magnetic radiation, which leads to a dramatic field enhancement, amplifying nonlinear responses with remarkable efficiency. NZI condition, i.e. Re√(ϵAl (λ)-sin2 θ NZI (λ) = 0, can be reach by tuning opportunely the impinging angle θ of light at specific θNZI (λ) (see Fig. 1 c). In this regime, broadband Ferrell-Berreman (FB) modes in the Al thin foils occurs, leading to an enhancement of self-induced nonlinear effects. Our experiments, performed in the facility FERMI, demonstrates a strong enhancement of delayed thermal response at θNZI (λ)≈65° for a FEL wavelength of 44.25 nm, which is well below the plasma frequency ~85 nm. Moreover, this condition of large enhancement generates an appreciable self-phase modulation. The difference of normalized single-shot spectra before and after the interaction (see Fig. 1 d) reaches an enhancement of a factor 4 with respect to magnesium close to the absorption edge (Fig. 1 b), enabling a direct observation of the spectral shift in the experiment. Our angle-dependent measurements of spectral modulation enhancement, supported by theoretical analysis, reveal efficient spectral modification at peak intensities as low as 380 GW/ cm2, which we attribute to ultrafast heating and saturation effects. These findings mark a breakthrough in the enhancement of typically weak nonlinearities in the XUV regime through nonlinear plasmonics, potentially paving the way for unprecedented tools for the manipulation and control of XUV radiation. In conclusion, we have reported the experimental evidence of selfinduced nonlinear effects in the XUV spectral range. The nonlinear response of materials in this regime exhibits completely different behavior below and above the targeted absorption edges. With the purpose to enhance these weak nonlinear effects, we show the first evidence of NZI enhancement below the absorption edge of aluminum. The latter NZI enhancement can push the applicability of nonlinearity in XUV to sources with low brilliance.
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