High-resolution Interferometric Diagnostics for Ultrashort Pulses

7. LATERAL SHEARING INTERFEROMETRY FOR HIGH-HARMONIC GENERATIONAFocusingopticGas jetSlit2D detectorxBfzLGratingTop viewSide viewx ryωFigure 7.1: Setup for lateral shearing interferometry of high-harmonic generation; the focusingoptic is drawn as a lens for clarity but a concave mirror may also be used.7.2 Theory of the methodThe technique is a type of LSI, and is depicted in Fig. 7.1. A Mach-Zehnder interferometer (MZI)produces two laser pulses with slightly different propagation directions in the horizontal (xz)plane. These are focused into the target, where they produce separate harmonic sources A andB. The harmonics propagate along the z -axis to a spatially resolving XUV spectrometer, whichdisperses the harmonics along the vertical (y ) axis. In the xz plane, the beams undergo free propagation— no re-imaging occurs. Therefore, a two-source interference pattern is produced withspatial carrier k x = sk/L where s is the source separation in the focus and L the distance fromthe sources to the detector. The spatial carrier permits recovery of the phase difference betweenthe fields using the standard Fourier-domain filtering algorithm [92], although a refinement that Idescribe below gives improved noise rejection.We used multiple-shot LSI; this has practical advantages over a single-shot version. These areexplained below. The retro-reflector of arm B is laterally displaced by an amount x r to two or morepositions, causing a corresponding displacement x d = 2x r L/f on the detector. The mechanismis shown in Fig. 7.2. Interferograms patterns are recorded at each position. Arm A remains sta-158