High-resolution Interferometric Diagnostics for Ultrashort Pulses

5. COMPACT SPACE-TIME SPIDER5.3.2 Role of ancilla spatial profileIn the ST-SPIDER design of Fig. 5.2, the ancilla are not focused into the crystal. The reason for thisdesign decision, which reduces signal intensity, is to do with the role played by the spatial profileof the ancilla. I shall now explain this. Sum-frequency generation, which occurs at the focus,is multiplicative in the spatial domain. The spatial profile of the upconverted beam is thereforethe product of the spatial profile of the unknown with that of the ancilla. In the collimated beam,which is detected, the two spatial profiles are therefore convolved. Such an operation will, in general,scramble the phase. It is therefore necessary to ensure that the ancilla is close to a plane wavepropagating along the z -axis at the two frequencies ω up and ω up −Ω. This can be achieved by spatiallyfiltering the ancilla [296], or as in Fig. 5.2, making the ancilla much larger than the unknownpulse focus.5.4 A common-path re-imaging ST-SPIDERI now present the new design, shown in Fig. 5.3, and explain how it addresses the issues of section5.3. A common path is used for the spatial and spectral shearing; only a single interferometeris needed, which performs both the spatial shear and the time delay that is necessary for the spectralshear. In the diagram, the spatial characterization is in the vertical plane i.e. out of the page inthe top view of Fig. 5.3. However, this only requires minor modification to change. In layout, thedesign is very similar to the SPIDER in Fig. 5.2. A crucial difference is that the lenses L 1 and L 2 arenot in a telescopic configuration; their separation is larger than the sum of their focal lengths. Thecrystal C is located slightly downstream of the focus of L 1 the first lens. It therefore has conjugateplane O some distance upstream. Lens L 2 re-images the crystal plane onto the entrance slit of theimaging spectrometer D.The re-imaging configuration prevents the ancilla spatial profile from scrambling the spatialphase of the upconverted beams, as discussed in section 5.3.2. The spatial profile acts multiplicatively,but is frequency-independent since only one frequency of the ancilla participates in the upconversion.The ancilla can therefore be focused with the beams, although it is useful to enlarge it110