High-resolution Interferometric Diagnostics for Ultrashort Pulses

4.2 Simultaneous acquisition of shearsxATPBω Aχ (2)ω BzTP + BTP + AωωxImagingspectrometerFigure 4.6: SEA-CAR-SPIDER concept: test pulse (TP), spatially chirped ancillae A and B with localfrequencies ω A and ω B increasing along the arrows, and sum-frequency beams TP+A and TP+B.The coordinate system used in the text is shown. The entrance slit of the imaging spectrometer isparallel to the x-axis; the x -axis is reversed here by the reimaging of the crystal plane.tial fringes caused by the beam crossing angle. The resulting signal isS(ω,x)=|E (ω − ω A )| 2 + |E (ω − ω B )| 2 +2|E (ω − ω A )||E (ω − ω B )|·cos φ(ω − ω B ) − φ(ω − ω A )+ θω upx. (4.1)cFor each x, the measured data is an SSI trace with shear Ω(x)=ω A − ω B = 2αx.The experimental implementation of SEA-CAR-SPIDER is depicted in Fig. 4.7. The test pulseTP is split with beamsplitter BS1 and focussed into the nonlinear crystal χ (2) with a cylindricallens CL of focal length f cl = 500mm. The delay-line DL1 is only for coarse adjustment of the delaybetween ancillae and test pulse and only requires initial adjustment. The ancillae are prepared asfollows: the reflected beam from BS1 is dispersed by a grating G of pitch Λ = 300mm −1 and angleof incidence γ = 10 ◦ . The spherical lens L1 is positioned one focal length f 1 = 500mm away fromthe grating and the crystal is mounted f 1 further downstream. Between the lens and the crystalthe ancilla beam is split at 50/50 beamsplitter BS2 and one arm is spatially inverted by applying anodd number of reflections. The coarse delay line DL2 is used to achieve temporal overlap betweenthe ancillae and needs no subsequent adjustment. The χ (2) crystal (250 µm BBO) is placed in theback Fourier plane of L1, where the spatial chirp of the ancillae is α = cos[β(ω up )]ω 2 up /(2πcf 1Λ)where β(ω up ) is the diffracted angle of the beam from the grating as depicted. A half-wave retarderλ/2 is introduced into the ancilla arm to ensure type-II upconversion with the ancilla polarizationaligned to the e -axis and the TP polarization to the o-axis of the crystal, respectively. After spatial99