Spectral phase is the argument of a complex spectral amplitude as a function of frequency. Writing a pulse spectrum as separates its spectral magnitude from the phase function .
Two pulses can have identical spectral intensities and different temporal shapes because their frequency components add with different relative phases. A phase linear in angular frequency shifts the pulse in time; quadratic phase adds group delay dispersion and commonly broadens an initially unchirped pulse. Measuring spectral intensity alone therefore cannot reconstruct the time-dependent electric field; phase-sensitive information is also required.
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