Coherence conversion for optimized resolution in optical measurements – example of femtosecond time resolution using the transverse coherence of 100-picosecond X-rays

Abstract

A way is proposed to obtain a femtosecond time resolution over a picosecond range in laser-pump, X-ray probe spectroscopic measurements where the light source and the detector are much slower than that. It is based on a phase-space transformation from the time/bandwidth to the spatial/wavenumber domain to match the coherence properties of synchrotron radiation to the requirements of femtosecond experiments. In a first step, the geometry of the laser incidence maps time, t, of laser-induced femtosecond dynamics to a spatial coordinate, x. Then, a far-field X-ray diffraction pattern, i.e. the optical Fourier transform, is obtained from the laser-induced modifications of the sample properties, including shifts of X-ray absorption edges and changes in crystallographic unit-cell form factors. Whereas the first step is similar to previously used schemes for femtosecond time resolution, the second one is substantially different with specific advantages discussed in the text. Key to this technique is that the modulus of the Fourier transform is invariant with respect to translations ξ along x, which are due to the t − x correlation. It can, therefore, be acquired in a simple intensity measurement with a slow detector. The phase, which does vary strongly with ξ , is missing in the intensity data, but can be recovered through a heterodyning technique. Data from a demonstration experiment are presented. The same concept can be used to obtain attosecond time resolution with an X-ray free-electron laser.