# Kuizenga–Siegman Theory

Definition: a theory predicting the durations of pulses from actively mode-locked lasers

German: Kuizenga-Siegman-Theorie

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Author: Dr. RĂ¼diger Paschotta

The Kuizenga–Siegman theory [1] is a theoretical treatment which can be used for calculating the pulse duration of an actively mode-locked laser. The basic underlying idea is that active mode locking involves two competing mechanisms acting on the duration of the circulating pulse:

- The modulator causes a slight attenuation of the wings of the pulse, effectively reducing the pulse duration.
- Due to its limited gain bandwidth, the gain medium tends to reduce the bandwidth of the pulse and thus to increase the pulse duration.

Note that for decreasing pulse duration the pulse-shortening effect of the modulator becomes less effective, whereas the pulse-broadening effect of the gain medium becomes more effective. For a certain pulse duration, both effects are in a balance, and this determines the steady-state pulse duration (see Figure 1).

The quantitative treatment based on this idea lead Kuizenga and Siegman to a relatively simple equation for calculating the steady-state pulse duration:

where *g* is the intensity gain, *M* is the modulation strength, *f*_{m} is the modulator frequency (which is assumed to match the round-trip frequency), and Δν_{g} is the FWHM gain bandwidth.
This equation is subject to a number of assumptions (which will not be discussed in detail here), but generalizations for other situations are possible.

This result shows that e.g. driving the modulator more strongly will hardly decrease the pulse duration. For shorter pulses, passive mode locking is much more effective. In that case, the blue curve in Figure 1 can be replaced with a steep straight line for the saturable absorber, which shifts the intersection point far to the left.

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### Bibliography

[1] | D. J. Kuizenga and A. E. Siegman, “FM and AM mode locking of the homogeneous laser – Part I: Theory”, IEEE J. Quantum Electron. 6 (11), 694 (1970), doi:10.1109/JQE.1970.1076343 |

[2] | D. J. Kuizenga and A. E. Siegman, “FM and AM mode locking of the homogeneous laser – Part II: experimental results in a Nd:YAG laser with internal FM modulation”, IEEE J. Quantum Electron. 6 (11), 709 (1970), doi:10.1109/JQE.1970.1076344 |

See also: active mode locking, mode locking, mode-locked lasers, pulse duration, pulse propagation modeling

and other articles in the category light pulses

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