The engineering is in fact a bit more involved. As the laser has to travel across kilometers, there is actually a very complex system of mirrors allowing to boost its power all along the way. But the key principle if very simple. We know the interference pattern of a gravitational wave and we "just" look for it.
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You nailed it, simple principles are the bedrock of most complex systems.
That is so true and holds for so many things... ;)
Thanks Bro'. Upvoted, Resteemed & Followed You.