You are putting out 100 gigawatts for 2 minutes. One does not need 100 one gigawatt powerplants, just some way to store and release a lot of energy really fast.
Second, we have mirrors that can reflect up to 99.999% of a single wavelength of light(such as that emitted by a laser)[0]. There is a detailed analysis of the concept in [0] and the Breakthrough Foundation has a detailed list of challenges associated with this project at [1].
Getting the laser out of the atmosphere is probably one of the biggest challenges with this.
[0] http://www.deepspace.ucsb.edu/wp-content/uploads/2015/04/A-R...
[1] http://breakthroughinitiatives.org/Challenges/3