Bandwidth-limited pulse

A bandwidth-limited pulse (also known as Fourier-transform-limited pulse, or more commonly, transform-limited pulse) is a <a href="/facts/Pulse_(physics)/jetWIb8h">pulse</a> of a <a href="/facts/Wave/fU0HH6St">wave</a> that has the minimum possible duration for a given <a href="/facts/Power_spectrum/q3Rfs7b0">spectral</a> <a href="/facts/Bandwidth_(signal_processing)/7eMDzfJI">bandwidth</a>. Bandwidth-limited pulses have a constant <a href="/facts/Phase_(waves)/cpGtuVll">phase</a> across all frequencies making up the pulse. <a href="/facts/Optics/p0vq4S1T">Optical</a> pulses of this type can be generated by <a href="/facts/Modelocking/7p9MjBjT">mode-locked</a> <a href="/facts/Laser/jk6PTvvT">lasers</a>.
Any waveform can be disassembled into its <a href="/facts/Spectral_component/6sQKKI3k">spectral components</a> by <a href="/facts/Fourier_analysis/sUA8JP6q">Fourier analysis</a> or <a href="/facts/Fourier_transform/XXhKJtc8">Fourier transformation</a>. The length of a pulse thereby is determined by its <a href="/facts/Complex_value/2w7mqI7e">complex</a> spectral components, which include not just their relative intensities, but also the relative positions (<a href="/facts/Spectral_phase/q3Rfs7b0">spectral phase</a>) 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, 
 
 
 
 
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 {\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 <a href="/facts/Dispersion_(optics)/cUdHnYXz">dispersion</a> 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 <a href="/facts/Ultrashort_pulse/V8joGdvF">ultrashort pulse</a> passes through a block of glass, the glass medium broadens the pulse due to <a href="/facts/Group_velocity_dispersion/yYnGnjvF">group velocity dispersion</a>.
Keeping pulses bandwidth-limited is necessary to compress information in time or to achieve high field densities, as with <a href="/facts/Ultrashort_pulse/V8joGdvF">ultrashort pulses</a> in <a href="/facts/Kerr-lens_modelocking/exJ3mYXj">modelocked lasers</a>.

Bandwidth-limited pulse open-in-new

Bandwidth-limited pulse