Kuizenga–Siegman theory (original) (raw)

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

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What is Kuizenga–Siegman Theory?

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).

balance of broadening and shortening effects in an actively mode-locked laser

Figure 1: Blue curve: decrease in pulse duration per round-trip caused by the modulator. Red curve: increase in pulse duration caused by the gain medium. At the black point, both effects are in balance.

The quantitative treatment based on this idea led Kuizenga and Siegman to a relatively simple equation for calculating the steady-state pulse duration: {\tau _{\textrm{p}}} \approx 0.45 \cdot {\left( {\frac{g}{M}} \right)^{1/4}}{\left( {{f_{\textrm{m}}} \cdot \Delta {\nu _{\textrm{g}}}} \right)^{ - 1/2}}$$

where ($g$) is the intensity gain, ($M$) is the modulation strength, ($f_\textrm{m}$) is the modulator frequency (which is assumed to match the round-trip frequency), and ($\Delta \nu_\textrm{g}$) 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 by a steep straight line for the saturable absorber, which shifts the intersection point far to the left.

Modified Theories

For other kinds of mode-locked lasers, modified theories can be developed. For example, one can construct a model of a passively mode-locked laser, where a saturable absorber instead of a modulator has a pulse shortening effect. In that case, the change in pulse duration by the mode-locking element is proportional to the pulse duration, rather than to its square, and that leads to a substantially different equation for the pulse duration, where the square root rather than the 4th root of the modulation depth of the absorber occurs.

Substantially more complicated models (often to be treated with numerical simulations) need to be employed for lasers where chromatic dispersion and optical nonlinearities play substantial roles; one can then not simply work with a balance of pulse-shortening and pulse-broadening effects as in Kuizenga–Siegman theory. This usually applies to fiber lasers, for example.

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 the Kuizenga–Siegman theory used for?

The Kuizenga–Siegman theory is a model for calculating the steady-state pulse duration in an actively mode-locked laser. It is based on the balance between pulse shortening by the modulator and pulse broadening from the limited gain bandwidth.

Why is passive mode locking often better for achieving shorter pulses?

In passive mode locking, the pulse-shortening mechanism from a saturable absorber is typically much more effective than that of a modulator in active mode locking. This results in a balance point at a much shorter pulse duration.

When does the Kuizenga–Siegman theory not apply?

The theory is not applicable for lasers where effects like chromatic dispersion and optical nonlinearities are significant, as is often the case for fiber lasers. In such cases, the simple balance of pulse-shortening and broadening effects is invalid.

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

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