In mode-locked laser studies and other applications, it is desirable to derive relationships giving the time-domain length and the properties of the waveform under the envelope for pulses presenting narrow spectral widths, without performing inverse-Fourier-transform calculations. The method presented is based on an approximate expression for the transform of a sinusoid with variable frequency, and leads to simple rules for pulse-length evaluation from the frequency-domain phase function. If the phase function has no inflection points, the length is approximately equal to the range covered by the slope of the phase function, and the actual waveform sweeps monotonically in frequency. When inflection points occur, the pulse comprises several superimposed envelopes, each modulating a monotonically swept sinusoid. The effect of dispersive filters is also analyzed. Illustrative examples are discussed numerically.
J. R. FONTANA, "Time-Domain Configuration of Certain Narrow Frequency-Bandwidth Pulses," J. Opt. Soc. Am. 62, 898-901 (1972)