# Split-And-Delay Unit for FEL Interferometry in the XUV Spectral Range
## 1 Introduction  
The recent fast development of table-top high harmonic generation (HHG) [1; 2] and free-electron laser (FEL) light sources [3; 4; 5] made short and intense light pulses available in the extreme ultraviolet (XUV) and soft X-ray wavelength ranges. This opens new opportunities for ultrafast science, in particular new time-resolved studies. Currently, FELs have two major advantages over HHG sources: the wavelength tunability and the high intensity. Multidimensional spectroscopy [6], coherent control [7] and coherent nonlinear optics [8] require multiple intense pulses in the XUV or soft X-ray spectral range with a precisely defined relative phase. The simplest interferometric experiment requires two phase-locked light fields. A sequence of two phase-locked pulses can either be directly generated or produced from a single pulse by physical manipulation of the beam using a beam splitter and a delay stage. Direct generation andattosecond control of phase-locked pulse sequences were recently demonstrated at a seeded FEL [9; 10]. Nevertheless, mechanical split-and-delay units (SDUs) offer a number of advantages over the direct methods. The first advantage of SDUs lies in their versatility as they are not tied to a particular light source, making the experimental setup more flexible and mobile. The second advantage is a wide continuous range of the pulse replica delays SDUs can provide. Today, the direct methods are limited to either very short (<1 fs) [9] or relatively long (>300 fs) pulse delays [10]. This leaves uncovered a large 0.3-300 fs gap interesting for investigation of ultrafast dynamics of light-matter interaction. By contrast, the delay window of an SDU is limited solely by the travel magnitude of its driving mechanism and can continuously cover a larger range. For a long time the working horse for XUV pump-XUV probe experiments was a double-mirror split-and-delay unit [11; 12; 13] which impedes phase-resolved measurements due to the nature of its wavefront splitting (see [14; 15; 16] and Section 2). However, recent successful adaptations of ideas originally invented for far-infrared interferometry [17; 18; 19; 20] to UV [21] and XUV [22] frequencies open new opportunities for phase-resolved (interferometric) experiments at short wavelength FELs with a typical spectral bandwidth of 1%. One of the major challenges presented by interferometry at short wavelengths is the need for a precise control of the light phase. Any interferometric experiment requires the delay between the light fields to be controlled within a fraction of their optical cycle. For XUV frequencies, these times lie in the attosecond domain. When applied to an SDU, this requires the geometry of the device to be manipulated with nanometer precision, which imposes very high demands on the precision of mechanics and electronics. Yet sometimes the complexity of the task can be reduced. Precise control over some variable involves two steps: (1) measuring this variable and (2) steering the variable to the desired value, i.e., controlling it. Usually the second step--the actual control--requires much more effort than the measurement. However, in many parameter dependence studies the genuine control can be omitted if one can measure the independent variable and then appropriately sort the dependent observables. All interferometric studies investigate dependence of some observable (photon flux, ion or electron yield) on the phase delay between the light fields. With respect to an SDU, it is sufficient to measure the delay in real time and later sort the data accordingly, provided that some sort of \"coarse\" delay control is available for the desired time scale. In this way, the question how precisely one can control the delay is transformed into how precisely one can measure it. Typically, high-precision piezo actuators employed in SDUs possess measurement and control systems based on strain-gauge and capacitive sensors.