High-resolution Interferometric Diagnostics for Ultrashort Pulses

2.3 Introduction to ultrashort pulse metrologyLong-crystal arrangement SPIDER (LX-SPIDER). Spectrally sheared replicas may be producedwithout chirping the ancillae using the phase matching properties of a long crystal [199]. Severalcrystals exhibit the property that when oriented for type II sum-frequency generation, the acceptancebandwidth is much greater in the ordinary polarisation than the extraordinary polarisation.The asymmetry is due to group-velocity matching between the incident o-wave and the generatede -wave at the sum frequency, but a group-velocity mismatch between the incident and generatede -waves. In the time domain, the generated e -wave pulse travels at the same group velocity asthe incident o-wave pulse but the incident e -wave pulse walks through them. (This descriptionapplied to a negative uniaxial crystal; for a positive crystal the o and e are reversed.)Figure 2.14 illustrates the use of a long crystal to produce spectrally sheared replicas. Theincident e -wave plays the role of the ancilla, with phase-matching selecting only a narrow portionof its spectrum for upconversion. The test pulse experiences the broad acceptance bandwidth ofthe o-ray, providing accurate upconversion. The ancilla pulse is sent into the crystal behind thetest pulse and walks through it during propagation. Crucially, the phase-matched frequency isangle-dependent, so sending two pairs of beams at different angles achieves the desired spectralshear.Chirped-Arrangement SPIDER (CAR-SPIDER) uses upconverted replicas with spatially varyingupconversion frequency. The long-crystal concept may be used to this end. Instead of sendingtwo noncollinear beams into the long crystal, as in an LX-SPIDER, a single tightly focused beamcan be used since it contains a range of wavevectors [200]. Figure 2.15 illustrates the principle.Each wavevector experiences a different upconversion frequency. After subsequent propagationand then collimation, the generated pulse has an upconverted frequency which varies spatially:E A (ω,x )=E (ω − ω up + αx). The spatially chirped replica is passed through a Mach-Zehnder interferometerwhich performs a spatial flip in one arm. This is accomplished by having an oddnumber of reflections (in the horizontal plane) in one arm and an even number in the other. Thepulse from the flipped arm is therefore E B (ω,x)=E (ω−ω up −αx). Interfering the two arms on animaging spectrometer yields spectral shearing interferometry traces with a spatially varying shearΩ = 2αx.47