 Solution

Use spectral pulse shaping of a broadband coherent laser pulse. A 4f pulse shaper disperses the frequency components with a diffraction grating, maps them to different transverse positions with a lens, applies a programmable complex mask at the Fourier plane, and recombines them with a second lens and grating. A spatial light modulator or suitable amplitude-and-phase modulation stages impose the mask.

Compute the desired complex spectral field by Fourier transform of the required temporal envelope, including its phase. In the available spectral band, chooseThe mask amplitude changes the spectral weights, and its phase changes temporal interference and chirp. Recombining the masked spectrum produces the shaped temporal pulse. A phase-only device needs additional optics to implement independent amplitude control. Calibrate the mask-to-frequency mapping and verify the output pulse experimentally, correcting it iteratively if needed.

The source bandwidth must contain the requested spectral components; a passive mask attenuates rather than supplies missing energy, so an overall rescaling may be needed. Finite spectral resolution determines the accessible time window, and finite bandwidth limits rapid temporal features.