Focal shift induced by source displacements and optical figure errors

In this work the longitudinal shifts of the focal plane of an ellipsoidal mirror induced by longitudinal shifts of the source and by the optical figure error of the mirror itself are investigated. The case of an ideal mirror illuminated by a Gaussian beam is considered first, deriving an analytical formula predicting the source-to-focus shift. Then the realistic case of a mirror affected by surface shape defects is examined, by taking into account metrological data and numerically solving the Huygens–Fresnel integral. The analytical and numerical solutions in the ideal and real cases are compared. Finally, it is shown that an additional dependence of the focal shift is introduced on the wavelength and the pointing angle of the source. Both effects are investigated by numerical computations. We limit the treatment in the XUV spectral range, choosing as a test bench the Kirkpatrick–Baez mirror system of the DiProI and LDM end-stations and at the FERMI seeded free-electron laser (FEL). The work is primarily aimed at disentangling the different causes of focal shift at FEL light sources, where source position, wavelength and pointing angle are either tunable or rapidly fluctuating. The method can be easily extended to parabolic reflectors and refractors (lenses) with other kinds of illuminating sources and wavelengths.

Intense sub-micrometre focusing of soft X-ray free-electron laser beyond 1016 W cm−2 with an ellipsoidal mirror

Intense sub-micrometre focusing of a soft X-ray free-electron laser (FEL) was achieved by using an ellipsoidal mirror with a high numerical aperture. A hybrid focusing system in combination with a Kirkpatrick–Baez mirror was applied for compensation of a small spatial acceptance of the ellipsoidal mirror. With this system, the soft X-ray FEL pulses were focused down to 480 nm × 680 nm with an extremely high intensity of 8.8×1016 W cm−2 at a photon energy of 120 eV, which yielded saturable absorption at the L-edge of Si (99.8 eV) with a drastic increase of transmittance from 8% to 48%.