what is your point in expanding pulsed laser output

@Hassan S.Ashour

For learning...

The primary concern is Laser Damage Threshold (LDT). As it generally requires high peak power to nucleate damage, pulsed is much worse than CW. Damage thresholds are usually quoted in terms maximum peak fluence for 10ns FWHM pulses of 1064 nm light (because q-switched Nd:YAG lasers are the most common high-pulse-energy lasers).

As a rule of thumb you can extrapolate a little for longer or shorter pulses. The LDT is inversely proportional to the square root of the pulse length. Note that that is in terms of peak power, so the same energy in a shorter pulse (higher peak power) is more damaging while the same peak power in a shorter pulse (lower energy) is less damaging. This is a rule of thumb, so I wouldn’t extrapolate more than, say, a factor of ten in either direction.

Standard e-beam coatings can achieve LDTs of ~100-500 MW/cm^2 depending on the complexity of the coating. IBS or plasma coatings can promise 1-2 GW/cm^2. The quality of the surface polishing is very important, so the best coaters will promise the highest thresholds only if they also manufacture the part.

In determining what LDT you need, you start with the nominal fluence, say the pulse energy over the 1/e^2 area. However, remember that parts of the beam are brighter than this average number according to the transverse mode. The center of a Gaussian beam is twice as bright as this nominal value suggests. Multi mode beams can be closer to the average depending on how many modes participate. However, even at best some part of the mode is brighter than this average. What’s worse, multi mode beams can have hot spots. When being aligned they might be driven to a particularly bad mode. Even if they are perfectly aligned they may evolve through a series of transverse modes as they warm up after being turned on. For these reasons designers typically insist on at least a factor of 4 margin to the LDT.

In designing your beam expander, of course, the beam will be brightest at the entrance surface where the beam is the smallest, so pay particular attention there. Also, watch out for ghost reflections. Each surface might reflect as much as 0.2% of the light even with a good AR coating. It doesn’t sound like much, but the curved surfaces can focus that to a small spot (= high fluence) on prior optical surfaces. It is fairly common to design two lens expanders backwards. Rather than convex-Plano followed by Plano-convex, you can flip each lens around and use Plano-convex followed by convex-Plano. This assures that neither of the curved surfaces produces a focused ghost reflection. Of course the optical performance is a little worse, but generally is completely acceptable if the telescope isn’t too fast. However, this is mostly laziness for quick and dirty designs. You are welcome to design a nice optical solution just so long as you check and make sure the fluence of the ghost reflections doesn’t exceed the LDT at any surface. Note that it is the surfaces that matter. LDTs inside a bulk material are generally at least an order of magnitude higher, so, while I wouldn’t focus the outgoing beam inside an optic, you don’t have to worry about ghosts being focused in the bulk. Just check the surfaces.