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Sech2-shaped Pulses

Author: the photonics expert

Definition: pulses with a temporal intensity profile which has the shape of a sech2 function

More general term: light pulses

Category: article belongs to category light pulses light pulses

DOI: 10.61835/42v   Cite the article: BibTex plain textHTML

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:

$$P(t) = P_{\rm{p}} \: {{\mathop{\rm sech}\nolimits} ^2}(t/\tau ) = \frac{{{P_{\rm{p}}}}}{{{{\cosh }^2}(t/\tau )}}$$

Here, <$P_{\rm P}$> is the peak power. The full width at half-maximum pulse duration is approximately 1.7627 times the parameter <$\tau$>. (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.

comparison of sech-shaped and Gaussian pulses
Figure 1: Temporal shapes of sech2 and Gaussian pulses.

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, 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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Do sech2-shaped pulses have an intensity autocorrelation with the same analytical shape (i.e. sech2)?

The author's answer:

No, that shape is mathematically more complicated, but still can be computed analytically.

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