High-resolution Interferometric Diagnostics for Ultrashort Pulses

2. BACKGROUNDgrating. Spectrally resolving the intensity of one of the diffracted beams gives the SD-FROG signalB(τ,ω)= ∞−∞2E 2 (t )E ∗ (t − τ)e i ωt dt. (2.37)In polarisation-gating FROG (PG-FROG), the delayed replica induces a time-dependent birefringencein a third order medium [45]. The test pulse, polarised at 45°to the replica, experiences apolarisation rotation which depends on the temporal intensity of the delayed replica I (t − τ). Ananalysing polariser, placed after the nonlinear medium, selects the component of the test pulsewhich has been rotated by 90°. For a small birefringence, this is proportional to E (t )I (t −τ), so themeasured signal isB(τ,ω)= ∞−∞2E (t )I (t − τ)e i ωt dt. (2.38)Because the gate is real-valued, PG-FROG has a particularly intuitive trace and, for simple referencepulses without significant satellite structure, conforms to the technical mathematical notionof a spectrogram.Other forms of the third-order nonlinearity used for FROG include third-harmonic generation[168–170], transient grating [171], and four-wave mixing [172, 173].Crosscorrelation frequency-resolved optical gating. (XFROG) is the nonself-referenced versionof FROG, in which the temporal gating is performed using a well-characterised reference pulse[174–178]. It is potentially more sensitive than self-referenced versions, because a strong referencepulse may be used to characterise a weak unknown. Because the reference may be at a differentfrequency to the unknown, a wider range of phase-matched nonlinear processes are available. Ifthe reference pulse is simple, then the acquired signal is similar to the gated Fourier transform,eq. (2.11), which has an intuitive interpretation. It also lacks the arrival time ambiguity. Notableuses for XFROG include spectrograms of supercontinuum [64, 179] and soliton dynamics [180] inphotonic crystal fibres.Single-shot geometries of FROG employ the same principle as single-shot autocorrelators, withthe beams crossing at an angle in the nonlinear medium. The gated pulse is then spectrally dis-40