Sech²-shaped Pulses

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

Ultrashort pulses from mode-locked lasers often have a temporal shape 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 . (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

Category: pulses