GTOM
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Multiple reflective layers wouldn't be a good idea, the massive concentrated heat once the mirror breaks down the expanding hot gas will surely affect underlying layers, also like I said it is difficult if not impossible to build a mirror that could reflect enough of a laser with, say, two different frequencies.
http://news.stanford.edu/news/2014/november/radiative-cooling-mirror-112614.html
I have found this one, i thought about more advanced broadband metallic mirrors.
But this coolant pumping stuff also a good idea.
Otherwise even if we harvest antimatter from the Sun, the systems will need regular maintenance, if it is done by robots, they have to be maintained, so it will be far from free.