Cat's_Cradle is a great, easy to read, endlessly discussable sci-fi book by a master.
A diode laser, like we are using is also about 50% efficient in turning electrons into photons, so under ideal conditions you get around 25% of the electricity out the other end that you put in. I will point out that you still have to heat the Stirling engine with something like a laser so it has exactly the same lose on that end as beaming to a PV does.
Turns out that divergence is set by the wavelength, larger the wavelength the bigger the minimal divergence. Check out http://en.wikipedia.org/wiki/Diffraction-limited_system . Our lasers wavelength is 808 nanometers. Compare that to say 1 centimeter for microwave and you can see that microwaves will always require a much bigger "lens/mirror" to focus them.
Beam divergence is the biggest reason I'm aware of. Another sizable reason is kilowatt for kilowatt an infrared laser is a lot cheaper. Diode lasers (especially infrared ones) have collapsed in price in the last few years.
While the efficiency of a heat engine is great, the power to weight ratio is awful. So much in fact that it is really hard to build one that can lift itself.
A laser that is matched to the bad gap of a pv cell can be over 50% efficient. So it is not too bad on that front and a lot less weight then a heat engine.
By the way, a Sterling Engine is an engine made of silver, a Stirling Engine is a heat engine.
August 5-7th. All the action will be out on the lakebed in the "compass rose". Besides the web site you can also follow it on NASA tv.
One of the founders of LaserMotive, Jordin Kare is the originator of an idea for laser launch . Its a very cool idea that seems very workable for putting small payloads into orbit by heating H gas in a heat exchanger on a rocket with a ground based laser.
As far as why a laser and not solar? The laser is a lot brighter then the sun over the array of the PV array, and the PV array is allot more efficient at the lasers wavelength (color), so you can have a much more compact system. Besides this way you can send power where the sun don't shine.
I tend to think of the pilot as pretty brave too, but the contest organizers and NASA have gone to great lengths to make it as safe as possible. For example the helicopter actually hovers at about 1.3km and the lasers all aim in a direction where the helicopter should not be "illuminated". Furthermore while the lasers transmit many kilowatts of power, they are actually fairly spread out, over a square meter or so. They are an eye hazard, but there is no danger of cutting a hole in anything Goldfinger style.
The lasers are actually infrared and invisible. Ours is 808nm and is very slightly visible to some as a violet glow. For this use lasers are easier to work with then microwaves as they have a much smaller divergence so the transmitter can be much much smaller. For beaming microwaves over these distance you end up with a transmitter that does a fair imitation of a radio telescope.
Always draw your curves, then plot your reading.