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A bandwidth-limited pulse (also known as Fourier-transform-limited pulse, or more commonly, transform-limited pulse) is a pulse of a wave that has the minimum possible duration for a given spectral bandwidth. Bandwidth-limited pulses have a constant phase across all frequencies making up the pulse. Optical pulses of this type can be generated by mode-locked lasers.

Any waveform can be disassembled into its spectral components by Fourier analysis or Fourier transformation. The length of a pulse thereby is determined by its complex spectral components, which include not just their relative intensities, but also the relative positions ( spectral phase) of these spectral components. For different pulse shapes, the minimum duration-bandwidth product is different. The duration-bandwidth product is minimal for zero phase-modulation. For example, ${\displaystyle \mathrm {sech^{2}} }$ pulses have a minimum duration-bandwidth product of 0.315 while gaussian pulses have a minimum value of 0.441.

A bandwidth-limited pulse can only be kept together if the dispersion of the medium the wave is travelling through is zero; otherwise dispersion management is needed to revert the effects of unwanted spectral phase changes. For example, when an ultrashort pulse passes through a block of glass, the glass medium broadens the pulse due to group velocity dispersion.

Keeping pulses bandwidth-limited is necessary to compress information in time or to achieve high field densities, as with ultrashort pulses in modelocked lasers.

Further reading

• J. C. Diels and W. Rudolph (2006). Ultrashort Laser Pulse phenomena. New York, Academic. ISBN  978-0-12-215493-5.