Spectral phase interferometry for direct electric-field reconstruction

In ultrafast optics, spectral phase interferometry for direct electric-field reconstruction (SPIDER) is an ultrashort pulse measurement technique originally developed by Chris Iaconis and Ian Walmsley. SPIDER is an interferometric ultrashort pulse measurement technique in the frequency domain based on spectral shearing interferometry. Spectral shearing interferometry is similar in concept to lateral shearing interferometry, except the shearing is performed in the frequency domain. The spectral shear is typically generated by sum-frequency mixing the test pulse with two different quasi-monochromatic frequencies (usually derived by chirping a copy of the pulse itself), although it can also be achieved by spectral filtering or even with linear electro-optic modulators for picosecond pulses. The interference between the two upconverted pulses allows the spectral phase at one frequency to be referenced to the spectral phase at a different frequency, separated by the spectral shear - the difference in frequency of the two monochromatic beams. In order to extract the phase information, a carrier fringe pattern is introduced, typically by delaying the two spectrally sheared copies with respect to one another. The intensity of the interference pattern from two time-delayed spectrally sheared pulses can be written as where is the analytic signal representing the unknown (upconverted) field being measured, is the spectral shear, is the time delay, is the spectral intensity and is the spectral phase. For a sufficiently large delay (from 10 to 1000 times the Fourier transform limited [FTL] pulse duration), the interference of the two time-delayed fields results in a cosine modulation with a nominal spacing of ; and any dispersion of the pulse results in minor deviations in the nominal fringe spacing. Effectively it is these deviations in the nominal phase spacing that yield the dispersion of the test pulse . The unknown spectral phase of the pulse can be extracted using a simple, direct algebraic algorithm first described by Takeda.