Pulse Duration

The duration of light pulses (also called pulse width or pulse length) can vary in a huge range:

• By modulating a continuous-wave light source, e.g., with an electro-optic modulator, pulses with durations from some tens of picoseconds to arbitrarily high values can be generated.
• Gain switching, e.g. of laser diodes, leads to pulses with durations down to a few nanoseconds or even to some hundred picoseconds.
• Pulse durations from Q-switched lasers typically vary between 100 ps and hundreds of nanoseconds.
• Mode-locked lasers can generate pulses with durations between ≈ 5 fs and hundreds of picoseconds.
• high harmonic generation allows the formation of single attosecond pulses or attosecond pulse trains, with pulse durations of a few hundred attoseconds or even below 100 as.

Here is an overview of the common prefixes:

• 1 ms (millisecond) = 10⁻³ s
• 1 μs (microsecond) = 10⁻⁶ s
• 1 ns (nanosecond) = 10⁻⁹ s
• 1 ps (picosecond) = 10⁻¹² s
• 1 fs (femtosecond) = 10⁻¹⁵ s
• 1 as (attosecond) = 10⁻¹⁸ s

There are actually different definitions of a pulse duration:

• The most frequently used definition is based on the full width at half-maximum (FWHM) of the optical power versus time. This is not sensitive to the weak pedestals that are often observed with light pulses.
• For calculations concerning soliton pulses, it is common to use a duration parameter ($\tau$) which is approximately the FWHM duration divided by 1.7627 because the temporal intensity profile can then be described as a constant times ($\textrm{sech}^2(t / \tau )$).
• For complicated pulse profiles, a definition based on the second moment of the temporal intensity profile is more appropriate. Here, possible pedestals substantially increase the obtained pulse duration.
• Particularly in the context of laser-induced damage, one sometimes uses an effective pulse duration, which is defined as the pulse energy divided by the peak power.

Particularly in cases with significant pulse pedestals, different methods can lead to substantially different pulse duration values.

The product of pulse duration and spectral bandwidth is called the time–bandwidth product. Typically, it is calculated using FWHM values of duration and bandwidth (see above). It cannot be significantly smaller than ≈ 0.3, depending on the pulse shape and the exact definition of pulse duration and bandwidth. This means that e.g. a 10-fs pulse must at least have a bandwidth of the order of 30 THz, and attosecond pulses have such a large bandwidth that their center frequency must be well above that of any visible light.

As optical pulses can have an extremely large bandwidth, they can also become extremely short. The shortest pulses directly generated with mode-locked lasers (titanium–sapphire lasers) are ≈ 5 fs short. Substantially shorter pulses, even down to attosecond durations, can be obtained with high harmonic generation, but these are no longer light pulses in a normal sense; their center frequencies are far higher, e.g. in the extreme ultraviolet.

See also the article on the transform limit.

Pulse durations down to roughly 10 ps can be measured with the fastest available photodiodes in combination with fast sampling oscilloscopes. For the measurement of shorter pulse durations, streak cameras can be used.

Another approach is optical sampling (or cross-correlation), using another source generating even shorter reference pulses. In most cases, however, one uses optical autocorrelators, not requiring any reference pulses.

Note that there are also techniques such as FROG or SPIDER (→ spectral phase interferometry), which can be used to obtain much more information on pulses than e.g. just the pulse duration and energy; see the article on pulse characterization.

In many cases, for example when using an autocorrelator, a large number of subsequent pulses is used to measure a pulse duration — assuming that all pulses are essentially identical. That assumption is often valid, but can be wrong in some cases, e.g. when a mode-locked laser is not operated in a stable regime, where substantial pulse-to-pulse fluctuations can occur. The results of pulse duration measurements can then be misleading.

There are also single-shot measurement techniques which can measure the duration of a single pulse. Typically, they require substantially higher pulse energy. They can be useful, for example, for characterizing pulses from amplifier systems where significant pulse-to-pulse fluctuations are expected.

Different pulse measurement techniques offer different trade-offs between complexity, cost, and information content:

• Autocorrelators (intensity or interferometric) are robust and relatively economical. They provide an estimate of the pulse duration assuming a specific pulse shape (e.g. sech²) but generally cannot retrieve the full temporal intensity and phase profile or the asymmetry of the pulse.
• FROG and SPIDER systems are more complex but allow for the complete reconstruction of the pulse's intensity and phase in the time and frequency domains. This is essential for detailed studies of pulse chirping and distortion.
• Streak cameras offer direct time-domain measurement with high resolution (down to the picosecond range) and can simultaneously resolve spatial or spectral information, but they are typically expensive and complex to operate.

The spatial width of a pulse in the propagation direction is given by the group velocity times the temporal pulse width. Despite the high velocity of light, ultrashort pulses can also be very short in the spatial domain. Whereas e.g. a 1-ns pulse still has a length of ≈ 30 cm in air, the shortest pulses which can be generated directly with a laser – with a duration of roughly 5 fs – have a spatial length of just 1.5 μm in air or vacuum. This corresponds to only a few wavelengths, or temporally a few optical cycles (few-cycle pulses).

As the transverse dimensions, characterized e.g. with a beam radius, are usually much larger than that, few-cycle pulses can be imagined to be like pancake-shaped bullets of light. This aspect is important; it explains e.g. why the apparent pulse duration as measured with an intensity autocorrelator can be increased when this measurement apparatus involves pulses crossing each other at some significant angle.

While pulses with durations of nanoseconds or longer hardly experience any changes in pulse duration during propagation even over long distances, ultrashort pulses are sensitive to various effects:

• Chromatic dispersion can lead to substantial pulse broadening, which can however be reversed by subsequently applying the opposite kind of dispersion (→ dispersion compensation).
• Optical nonlinearities often do not directly affect the pulse duration, but can e.g. broaden the optical spectrum, which makes the pulses more sensitive to chromatic dispersion during subsequent propagation.
• Any type of optical filter, including a gain medium with limited gain bandwidth, can affect the spectral width or shape of an ultrashort pulse. When the spectral width is reduced, this may lead to temporal broadening; however, there are cases where strongly chirped pulses become shorter when their spectral width is reduced.

In the steady-state operation of a mode-locked laser, the circulating pulses experience various effects which affect the pulse duration, but these effects are in a balance, so that the pulse duration is restored after every round trip. In some femtosecond lasers, the pulse duration undergoes substantial changes during each resonator round trip.

The definition and measurement of the pulse duration becomes considerably more complicated in cases where spatial and temporal pulse properties are coupled with each other. An example is the phenomenon of pulse front tilt, where a locally measured pulse duration may be smaller than the duration based on the whole beam profile.