# Quantifying the Chirp of Ultrashort Pulses

Posted on 2008-02-03 as a part of the Photonics Spotlight (available as e-mail newsletter!)

Permanent link: https://www.rp-photonics.com/spotlight_2008_02_03.html

Author: Dr. Rüdiger Paschotta, RP Photonics Consulting GmbH

Abstract: When considering different ways of quantifying the chirp of an ultrashort pulse, one can arrive at definitions which in typical situations may not even agree on the question whether the magnitude of chirp increases or decreases. The article gives some examples.

Ref.: encyclopedia articles on chirp and ultrashort pulses

The chirp of an ultrashort pulse is a concept which is relatively easy to grasp. Nevertheless, rather surprising issues arise when one tries to quantify such chirp. It turns out that different definitions of chirp lead to quantities which can not simply be converted into each other. Furthermore, such quantities may not even agree on the question whether the magnitude of chirp increases or decreases in certain situations!

The article on chirp gives two examples, which are discussed in some more detail here:

## Effect of Chromatic Dispersion

Consider a situation where an initially unchirped (transform-limited) pulse experiences normal dispersion when propagating in a medium. Of course, one would expect this to lead to an increasing amount of chirp. It obviously does so, when the magnitude of chirp is considered to be the amount of anomalous dispersion required to recompress the pulse.

However, this is not the case for the rate of change of the instantaneous frequency, which is actually a rather natural definition for the magnitude of chirp. That kind of chirp first rises with increasing amount of dispersion, but then it decreases again. Why is that? Because the instantaneous frequency goes through an interval of finite width, and as the pulse becomes longer and longer, the rate of change (in Hz/s) decreases.

## Effect of Kerr Nonlinearity

Here we consider an initially unchirped pulse which is subject to self-phase modulation (SPM) via a Kerr nonlinearity of some medium. SPM creates a chirp, and the rate of change of the instantaneous frequency will increase with increasing propagation length. However, the amount of dispersion as required for maximum compression will initially increase, but then decrease. The reason for that is that the pulse bandwidth is increasing, and broadband pulses are more sensitive to dispersive effects.

## Conclusion

The conclusion of this insight is clear: be careful when considering the magnitude of chirp, as different definitions have very different meanings, and can not even be considered to quantify the same physical property.

This article is a posting of the Photonics Spotlight, authored by Dr. Rüdiger Paschotta. You may link to this page and cite it, because its location is permanent. See also the RP Photonics Encyclopedia.

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