Ultrashort Laser Pulse Phenomena, 2nd Edition

352 Ultrashort Sources II: Examples

smallest initial amplitude may be completely depleted because the SHG process

diminishes each component by the same amount. If the nonlinear propagation

continues beyond that point the SHG is replaced by difference frequency genera-

tion between the generated harmonic and the remaining fundamental component.

The new fundamental field appears on the polarization axis where the fundamen-

tal had disappeared but the phase of the created field is now shifted by π with

respect to the initial field. Difference frequency generation then goes on with

propagation distance until the power of the second harmonic goes to zero. If we

assume that the crystal behaves in the linear regime like a full-wave or half-wave

plate then the output polarization state remains linear in the nonlinear regime,

but the orientation of the output is intensity dependent. Two properly oriented

polarizers placed on either side of the nonlinear crystal permit us to build a device

with an intensity dependent transmission.

Details on the use of nonlinear polarization in a type II SHG for mode-locking

of a cw lamp pumped Nd:YAG laser are given in Kubecek et al. [52].

6.5. NEGATIVE FEEDBACK

In this section we will describe a technique that limits the peak power of

pulses circulating in the cavity. This can be accomplished by a combination of an

element producing nonlinear defocusing and an aperture. Negative feedback has

gained importance in Q-switched and mode-locked solid-state lasers because it

tends to lengthen the pulse train by limiting the peak power and thereby reducing

the gain depletion. Moreover, a longer time for pulse formation usually leads to

shorter output pulses and more stable operation.

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We have seen that the pulse formation—in passively mode-locked lasers—is

associated with a positive feedback element (Kerr lensing, saturable absorber)

which enhances positive intensity fluctuations (generally through a decrease of

losses with increasing intensity). Although a positive feedback leads to pulse

formation, it is inherently an unstable process, because intensity fluctuations

are amplified. Therefore, it is desirable, in particular in high-power lasers, to

have a negative feedback element that sets in at higher intensities than the positive

feedback element.

Pulses of 10, 5, and less than 1 ps have been generated with this technique

with Nd:YAG, Nd:YAP, and Nd:glass lasers, respectively. More importantly for

the fs field, the pulse-to-pulse reproducibility (better than 0.2% [53]) makes these

lasers ideal pump sources for synchronous or hybrid mode-locking. The flashlamp

pumped solid-state laser with negative feedback provides a much higher energy

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Note that in high-power solid-state lasers the typical Q-switched pulse is not much longer than

a few cavity round-trips.