High-resolution Interferometric Diagnostics for Ultrashort Pulses

2.3 Introduction to ultrashort pulse metrologyθωyyT = 0 T = 0yωωTFigure 2.5: Fourier-transform spatio-spectral interferometry. The beams are dispersed and focusedin the horizontal plane. In the vertical plane they impinge on the detector at an angle.Typical fringe patterns with and without a time delay are shown.cos(φ 2 − φ 1 + α j ) where α j is the small phase shift applied at that shot. Judicious choice of α jenables unique determination of φ 2 − φ 1 — for example, if the phase shifts are 0 and π/2 radians,then the cosine and sine of the phase difference is obtained, enabling unambiguous and robustquadrature detection [88]. An alternative is to scan the phase shift continuously, acquiring a twodimensional data set [97]. A Fourier-domain filtering step similar to the carrier case yields thephase of the interferometric term.2.3.3.3 Summary — linear time-stationary operationsLinear-time stationary operations and slow photodetectors can recover the spectral intensity |E (ω)| 2of a single pulse, and pairwise interferometric products E i (ω)E ∗ j(ω) of multiple pulses. When asuitable reference is available, interferometry is one of the most powerful characterisation methodsavailable.2.3.4 Nonlinear correlationsNonlinear correlations represent the next step in complexity, and involve mixing the unknownpulse with a gate pulse, and recording the energy of the result as a function of the time delay ofthe gate pulse. If the gate is the unknown pulse itself, the method is an autocorrelation; otherwiseit is a crosscorrelation. In general, nonlinear correlations are not considered complete characterisationsunless additional information or assumptions are made. Nonetheless they are importanthistorically, and remain in use for their relative simplicity.31