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Ultrashort pulses from mode-locked lasers often have a temporal shape (i.e., shape of the curve showing optical power versus time) which can be described with a squared hyperbolic secant (sech) function:
The full width at half-maximum pulse duration is approximately 1.76 times the parameter τ. (That parameter itself is sometimes called the pulse duration.)
In many practical cases (e.g. soliton mode locking), sech2 pulses have hardly any chirp, i.e., they are close to transform-limited. The time–bandwidth product is then ≈ 0.315.
Compared with a Gaussian function with the same half-width, the sech2 function has stronger wings, as shown in Figure 1.
The peak power of a sech2 pulse is ≈ 0.88 times the pulse energy divided by the FWHM pulse duration.
The sech2 shape is typical of fundamental soliton pulses (in the absence of higher-order dispersion and self-steepening). Therefore, this pulse shape also occurs in soliton mode-locked lasers. However, it is also found in other situations; for example, passive mode locking with a slow absorber usually leads to a pulse shape which is relatively close to the sech2 shape.
See also: pulses, Gaussian pulses, solitons, soliton mode locking, transform limit
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