Pulse Peak Power, Average Power and Duty Cycle

There are two power numbers on every pulsed-laser datasheet and they can differ by four orders of magnitude. Average power is what a thermal power meter reads, what the chiller has to remove, and what goes on the nameplate. Peak power is what exists while the pulse is actually on. The bridge between them is the duty cycle $\tau f_{rep}$ — the fraction of the time the laser is emitting — and nothing else.

Put ordinary numbers in and the size of the gap becomes obvious. A 20 W marking laser firing 100 ns pulses at 20 kHz has a duty cycle of $10^{-7} \times 2\times10^4 = 0.002$, two tenths of one percent. Its pulse energy is 1 mJ and its peak power is 10 kW. A nameplate that says 20 W delivers ten kilowatts while the pulse is on, and that is the whole reason pulsed lasers exist: a modest average power the cooling loop can handle becomes, for a hundred nanoseconds at a time, enough intensity to vapourise metal before the heat has had time to conduct anywhere. Short pulses cut cleanly not because they are more energetic but because they beat thermal diffusion.

It is also why a "20 W" laser destroys an optic rated for 500 W of continuous light. Every damage threshold, every nonlinear effect, and every laser-safety calculation on a pulsed system runs on the peak figure. The average figure on the nameplate tells you almost nothing about any of them.

Two honesty notes on the arithmetic. The pulse is treated here as a rectangle of height $P_{pk}$ and width $\tau$, which is a convenient fiction. A real Q-switched pulse has a fast rise and a long tail, and its true peak is higher than $E_p/\tau$ by a shape factor of roughly 1.2 to 1.5 depending on how $\tau$ was defined — usually as an FWHM. If your margin on an optic is that tight, the rectangle is not good enough and you need the actual waveform.

And this page is bookkeeping; it does not know your gain medium. On a real Q-switched or MOPA laser, raising the repetition rate does not hold the pulse energy constant. The medium stores energy at a fixed rate, so emptying it more often gives weaker pulses; above a few times the inverse upper-state lifetime the pulse energy falls roughly as $1/f_{rep}$ and the average power flattens out. That is why a marking laser has a rated repetition rate for full pulse energy and simply gives less above it — the equation will happily compute a number the laser cannot produce.

One unit note, since the site's time picker stops at milliseconds: enter pulse durations in SECONDS. A 100 ns pulse is $10^{-7}$ s, a 10 ps pulse is $10^{-11}$ s. If the duty cycle comes out above 1, that is almost always what went wrong.