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.)
Compared with a Gaussian function with the same half-width, the sech2 function has stronger wings, as shown in Figure 1.
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, including quasi-soliton-mode-locked bulk lasers. However, it is also found in other situations; for example, passive mode locking with a slow absorber in a regime with relatively long pulses durations (e.g. due to a narrow gain bandwidth and with low chromatic dispersion and weak nonlinear effects) usually leads to a pulse shape which is relatively close to the sech2 shape.
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