定义：
可得到主动锁模激光器脉冲持续时间的理论。

Kuizenga-Siegman理论是可用于计算主动锁模激光器的脉冲持续时间的理论。 基本理论基础是主动锁模涉及到两个影响循环脉冲持续时间的竞争机制： — 调制器导致脉冲边翼的轻微衰减，有效地减少脉冲持续时间。 — 由于增益带宽有限，增益介质往往会降低脉冲的带宽，从而增加脉冲持续时间。
注意，为了缩短脉冲持续时间，调制器的脉冲缩短效应变得不那么有效，而增益介质的脉冲展宽效应变得更有效。对于一定的脉冲持续时间，两种效应处于平衡状态，这决定了稳态的脉冲持续时间（见图1）。

图1：蓝色曲线：调制器引起的每次往返脉冲持续时间的减少。红色曲线：增益介质引起的脉冲持续时间的增加。在黑点处，两种效应处于平衡状态。
基于这一定量处理方法， Kuizenga和Siegman得到计算稳态脉冲持续时间的一个较简单的方程：

其中g是强度增益，M是调制强度，fm是调制器频率（假设与往返频率相匹配），Δvg是半高全宽的增益带宽。 这个方程式受到一些假设的约束（这里不再详细讨论），但是大多数情况下是适用的。
该结果表明，例如调制器驱动增强几乎不会降低脉冲持续时间。 对于较短的脉冲，被动锁模更有效。 在这种情况下，图1中的蓝色曲线可以用可饱和吸收器的更陡的曲线代替，使得交点偏向左边。

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

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).

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 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.

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 of 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 4^th 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.

Bibliography