Or better yet, use a passive element on the moon side. There are optical reflectors up there from moon missions that people can bounce (large) earth based laser

Or better yet, use a passive element on the moon side. There are optical reflectors up there from moon missions that people can bounce (large) earth based lasers off of. Imagine one of those with a single LCD film over it. You can then selectively polarize the reflected light at virtually zero power use. It won't be a fast bit rate, the LCD could to 100bps easily, but I wonder what the atmospheric scattering does to the wavefront.