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I understand the difference between the two in terms of how they function; one will release all of it's energy in small pulses with the other creates a constant stream of radiation.

My question is for materials processing such as marking or cutting. Why would I use one over the other?

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Pulsed lasers release their energy in very short pulses which can have incredibly high peak powers. A run-of-the-mill nanosecond laser will have a peak power in the multi-kilowatt range while a femtosecond laser can easily reach into the megawatt range. In contrast, CW lasers generally do not reach power levels in excess of a few hundred Watts.

When these pulsed lasers are focused to a small spot size, the intensity is generally high enough to significantly alter the molecular state of the material through non-thermal processes such as ablation. These non-thermal processes are useful for creating very small features because they have a smaller 'heat affected zone'. The very high peak powers can also make use of nonlinear absorption in materials which would otherwise be transparent (and therefore not able to be processed by that wavelength).

In contrast, the energy from a tightly focused CW laser is deposited over long enough timescales that the material simply heats up and melts. This can be more useful for processes such as welding.

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