Sech2-shaped Pulses
Author: the photonics expert Dr. Rüdiger Paschotta (RP)
Definition: pulses with a temporal intensity profile which has the shape of a sech2 function
- light pulses
- Gaussian pulses
- sech2-shaped pulses
- parabolic pulses
- solitons
- (more topics)
Related: light pulsesGaussian pulsessolitonssoliton mode lockingtransform limit
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DOI: 10.61835/42v Cite the article: BibTex BibLaTex plain textHTML Link to this page! LinkedIn
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What are sech2-shaped Pulses?
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:
$$P(t) = P_{\textrm{p}} \: \textrm{sech}^2(t/\tau ) = \frac{{P_\textrm{p}}}{\cosh^2(t/\tau )}$$Here, ($P_\textrm{P}$) 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.
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 pulse 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.
Frequently Asked Questions
This FAQ section was generated with AI based on the article content and has been reviewed by the article’s author (RP).
What is a sech2-shaped pulse?
A sech2-shaped pulse is an ultrashort pulse where the optical power over time can be described by a squared hyperbolic secant (sech2) function. This pulse shape is typical for fundamental soliton pulses.
What is the time-bandwidth product of a sech2 pulse?
For a transform-limited (i.e., unchirped) sech2 pulse, the time–bandwidth product is approximately 0.315.
Where do sech2-shaped pulses occur?
This pulse shape is characteristic of soliton mode-locked lasers. It can also be found in lasers with passive mode locking using a slow absorber, particularly when generating relatively long pulses.
How is the peak power of a sech2 pulse related to its energy?
The peak power of a sech2 pulse is approximately 0.88 times the pulse energy divided by the FWHM pulse duration.
2023-04-28
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.