We provide a rigorous, closed-form mathematical model of pulsed diffraction in both time and frequency domains and interpret its anomalies. The customary continuous-wave (cw) approximation is corrected for the regime below 3 fs in pulse width, the present state of the art. The time-differentiated aspect of diffraction is linked with old theory and the conservation of energy. Convolution of the pulse with differentiated aperture edges produces traveling waves in the focal plane. Their collision near the focal point corresponds to the cw case. (This is generalized for a Gaussian beam.) Spectral sampling depicts a mode-locked laser of extremely broad spectrum, validating the nonintuitive phenomena. The square-modulus tool is validated for these pulses. Ultrashort pulses are related to data transmission rates above 100 THz. Diffraction anomalies cause confusion and loss of information in the sidelobes. Anomalous diffraction may provide new diagnostics. Diffracted energy (salient sidelobes versus continuum) can measure transform-limited pulse width.
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