Allow me to be the first to exclaim, "Bullshit."
I'm sure the technology is real, and I'm sure that there are potential applications for the technology, perhaps in particular, maintaining precise alignment of a fleet of satellites.
However, as far as propelling a space craft to Mars using this? Not gonna happen. Why? Ohhh, just those pesky laws of physics. Let's go through it... First, we have conservation of momentum. The change in momentum of the space craft will be equal and opposite the change in momentum of the Earth. (See Newton, 3rd law.) This is no big deal though, because compared to the space craft, the earth is massive, leading to a very very small change in velocity. If a fly ran into me, I'd have a larger change in velocity as a result. This is good news though, for the space craft. Because the change in velocity of the earth is so small, so is the change in kinetic energy. Thus, most of the energy of the laser would be available for accelerating the space craft, not the earth. (Rather than the earth and satellite split the energy 50/50.)
Hey, speaking of energy, that's the important law: conservation of energy.
Let's see... earth is moving at 30km/s (slightly less, actually). So, to achieve a speed of 100km/s, a space craft would have to be accelerated "only" by 70km/s. And, this laser is going to do it in a week.
Let's see, we'll assume a 1000kg space craft... 1/2 mv^2 = 1/2 * 1000kg * (70,000m/s)^2 = 2.45x10^12 joules of kinetic energy. Let's pretend for a moment that this process is 100% efficient (yeah right, uh hum, sure.) That means, the laser needs to provide 2.45x10^12 joules of energy. It's got a week to do this? I'll also be nice to the laser, giving it the full week to get the satellite up to this speed. If you want to do it in half a week, it'll take twice as much power. Power = Energy/time. 604,800 seconds in a week.
2.45x10^12 joules divided by 604800 seconds = :shocked: Where the hell are you going to get a
4.05 MILLION WATT LASER??!
Okay. Skip the humans in the space craft. We'll just send up a probe. And, forget about it having a chance to slow down - we're going to spend the entire week just getting it up to 100km/s, a speed it will attain moments before it becomes smashed into the side of Mars. (Or missing Mars at the last second, only to be flung into space and lost forever, if Nasa and Lockheed Martin can't agree on which units to use). We can cut down the mass of this thing to, say, 100kg. Much betterer! Now we only need a 405,000 watt laser. (Assuming, of course, that the entire process is 100% efficient.)
Again, I'm certain there are applications that the technology is useful for. But, traveling to Mars in one week is not one of them. (I am actually hopeful that I made a calculation error - it would be neat to see this technology go forward for the purpose of space exploration.)
p.s. If any NASA people are reading this, and saying, "you know, he's right," kindly remit a few bucks my way as a consulting fee

Or, have a pizza sent to my house. Pepperoni and mushroom. Thanks.