Editing Bandwidth-limited pulse

{{short description|Type of wave pulse}}
{{refimprove|date=December 2009}}
[[File:Duration-bandwidth product.gif|upright=2|thumb|right|The duration-bandwidth product depends on the shape of the power spectrum of the pulse.]]
A '''bandwidth-limited pulse''' (also known as '''Fourier-transform-limited pulse''', or more commonly, '''transform-limited pulse''') is a [[pulse_(physics)|pulse]] of a [[wave]] that has the minimum possible duration for a given [[power spectrum|spectral]] [[Bandwidth (signal processing)|bandwidth]].  Bandwidth-limited pulses have a constant [[phase (waves)|phase]] across all frequencies making up the pulse. [[Optics|Optical]] pulses of this type can be generated by [[modelocking|mode-locked]] [[laser]]s.

Any waveform can be disassembled into its [[spectral component]]s by [[Fourier analysis]] or [[Fourier transform]]ation. The length of a pulse thereby is determined by its {{em|[[Complex value|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, <math>\mathrm{sech^2}</math> 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 (optics)|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 pulse]]s in [[Kerr-lens modelocking|modelocked lasers]].

==Further reading==
* {{cite book |title=Ultrashort Laser Pulse phenomena |author=J. C. Diels and W. Rudolph |isbn=978-0-12-215493-5 |year=2006 |publisher=New York, Academic}}

{{DEFAULTSORT:Bandwidth-Limited Pulse}}
[[Category:Optics]]
[[Category:Nonlinear optics]]
[[Category:Laser science]]