High-resolution Interferometric Diagnostics for Ultrashort Pulses

5. COMPACT SPACE-TIME SPIDERThe arrangement is shown in Fig. 5.5. A plane mirror M 1 is placed in the unused output port.The mirror is perpendicular to the nominal beam direction. In fact, this mirror defines the planeof measurement. From the other output port, four double-passed beams emerge, labelled AA, AB,BA and BB by the order of the arms they traverse. For example, the path of beam AB is: reflectionoff beamsplitter BS A , reflection off corner-cube CC A , reflection off beamsplitter BS B , reflection offmirror M 1 , tranmission through BS B , reflection off CC B , and finally reflection off BS A . Two mirrorsM 2 and M 3 bring the double-passed beams back onto the main line for convenient measurement.For the calibration, one must relate the time delay, tilt, and shear of the double-passed beamsto those of the single pass. It is fairly intuitive that, with respect to the AA beam, AB and BA aredelayed by T since they take one pass through the B arm, and BB is delayed by 2T since it takestwo passes through the B arm. The shear and tilt are more challenging to visualize (for this authorat least) but can be understood using the diagrams of Fig. 5.6. The beams are “straightened-out”and viewed side-on i.e. up on the page is always up in the lab, whilst right on the page is always“forward” for the beam under consideration. The corner-cubes (retro-reflectors) flip the beam inthe vertical plane about their vertex, whilst the reflections apply a tilt. The effects of shear and tiltare additive and may be considered separately for simplicity. The incident beam is drawn straightand level with the vertex of corner-cube CC A . However, since transformations of the incident beamapply equally to all the outputs, the implications of the diagrams are general. Corner cube CC B israised by an amount Y /2, whilst beam splitter B is rotated in the vertical plane by θ /2.To introduce the notation used in the diagrams, Fig. 5.6(a) shows the effects of adjusting Y andθ on the single-pass output B.Figure 5.6(b) shows the effects of Y on the double-passed beams. The AB and BA outputs aresheared by Y in opposite directions, whilst adjustments to Y have no effect on the AA and BBoutputs.Figure 5.6(c) shows that adjusting θ does not affect BB, whilst AB and BA are deflected in oppositedirections by θ . AA is deflected downwards by 2θ , which causes a z -dependent shear. However,as the construction lines show, the shear is zero in the plane of the M 1 .This is the basis of the calibration method — interference of the AA and BB outputs produces114