I was working in the lab last night, trying to boost a laser's intensity to a high enough level to achieve amplification in a crystal. Intensity, for those whose physics is a bit rusty, is the amount of energy delivered per unit are per unit time. Thus, when I was told that I would be unable to pick off more energy from the main laser for my experiment, my only option was to shrink the beam: a smaller area with the same energy and pulse duration (which is fixed at a constant 450 picoseconds until after amplification) gives a higher intensity. I therefore spent a good part of the night playing with two lenses, trying to reduce the beam's waist from o.5 cm to 0.2 cm.
In any case, at one point during the night, Steve and I noticed that the laser had a hole in its middle so that it looked like a ring on the sheet which we were using as a screen. We were puzzled by this, noticing that a bit of the beam was reflected from our first lens, but also quite certain that not all of the beam was being so reflected. After blocking the beam "upstream" from our lens, we noticed that a piece of the reflecting surface from one of our aluminum mirrors was missing: it had been ablated by the laser. We spent a moment in mourning the damage to this previously unblemished mirror--such are a rare find in a high-power optics lab.
After observing a moment of silence for our tarnished mirror, we chose a more beat-up gold mirror to do our alignment. After all, the beam quality doesn't need to be perfect, a a beat, scratchy mirror works fine for determining whether the spot size is constant. We continued with our alignment, and found that the spot size was approximately constant over the fifteen or so feet between the scratchy mirror and the wall.Blocking the beam upstream, we found no (new) damage from the laser on the mirror; thus satisfied, we replaced the gold mirror with the aluminum one (which was rotated so that the damaged spot would be out of the way) and unblocked the beam. About five minutes later, we noticed that the beam once again had a hole in it, and that the aluminum mirror had yet another hole in its surface.
Perplexed, we decided to forgo shrinking the beam for now--we did not have the right lenses to shrink the beam to a more suitable size (smaller than 0.5 cm, larger than 0.2 cm), and besides which, we decided that some calculations were necessary to determine just what the suitable size was. There were other things which needed to be accomplished in the lab.
After leaving the lab, I sat down an calculated what size the beam ought to be to avoid damaging the mirror. Our beam has up to 30 millijoules of energy (20 in practice), and the damage threshold is a fluence of 1 Joule per square centimeter or about 10^12 Joules per square centimeter per second. The result was a waist of about 0.1 cm: meaning that theoretically, the beam could be smaller still without damaging the lens. Steve was similarly confused: he saw no error in the calculation, and in fact had done his own, getting a similar result. The theory told us that the mirror should be fine; our observations told us that it wasn't.
Something was clearly wrong with the theory, but we could not determine exactly what it was. The damages thresholds are pretty standard numbers, and the calculation itself is very straight forward. The possible explanation that these damage threshold use more standard (read: more consistent) lasers than ours was unsatisfactory: ours it not so inconsistent as to have occasional power spikes of an order of magnitude difference. What, then, was at the source of this problem?
Neither the theory nor the observations were incorrect. Rather, it was an underlying assumption which was wrong. Aluminim reflects only about 70% of the light incident upon it--absorbing the other 30%. The damage threshold numbers which we were using assume a much smaller absorption: usually around 1%. The assumption that the theory was valid for our mirror as stated was therefor incorrect. Yet these assumptions are often the easiest thing to overlook. The theory is just a bunch of standard numbers, in this case time-tested numbers.
It appeared invalid, not because our calculations were wrong, but because our assumptions were wrong. This is the reason why the gold mirror was left unscathed by the laser: gold reflects nearly 99% of the incident light, absorbing only about 1%; thus, the theory was valid not for aluminum, but for gold. One is left to wonder, what other invalid assumptions lie hidden behind the theories and explanations of life, the universe, and everything? A bad assumption can easily unmake an otherwise good theory.