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By a freak coincidence sensors on a passing alien ship a hundred light years away had picked up a faint artificial blip from Earth, thereby discovering our inhabited planet. But which blip was it?

Question: What's the most intense beam ever sent from Earth?

Since we're talking far-field where everything drops as $1/r^2$ I'll define intensity as power per unit solid angle (e.g. kW/sr).

So we're looking for a lot of power and a large diameter to wavelength ratio.

Answers don't have to, but can consider issues like instantaneous vs average power and even the dispersion of pulsed signals (slightly different speeds) due to interstellar plasma, the same way they measure the distance to pulsars and FRB's (Just how fast is a Fast Radio Burst thought to be?)

1 RIP Arecibo

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    $\begingroup$ Far-field for a collimated beam isn't 1/r^2, though. MIght want to calculate peak power at center of the Airy disk instead. $\endgroup$ – Carl Witthoft Feb 26 at 13:58
  • $\begingroup$ @CarlWitthoft Disagree x 2. In the far field the intensity pattern for these maintains a constant shape when plotted against angle, and it's height varies as $1/r^2$ where $r$ is the distance from source to observer. It's not going to be Airy because the sources (either spatially filtered lasers or microwave feed horns) do not illuminate the aperture uniformly. Airy disk is the Fourier transform of a 2D circular "top hat" but that's not what happens in these transmission systems; the primary apertures are somewhat under-filled by design in order to reduce power spillage over the edges. $\endgroup$ – uhoh Feb 26 at 14:44
  • $\begingroup$ Note that I've suggested units of kW/sr specifically for this reason. $\endgroup$ – uhoh Feb 26 at 14:47
  • $\begingroup$ OK, fair enough - I was looking at the optical regime where it's 'easier' to generate a uniform intensity source. Agreed about radio-wavelength transmitters. $\endgroup$ – Carl Witthoft Feb 26 at 15:13
  • $\begingroup$ @CarlWitthoft with lasers there is often plenty of power so we just way over-expand the beam and use the center flat-ish part. Top-hat beam formers do exist but they are difficult and finicky devices to use. But the laser that's bounced off the moon has no extra power to spare, so they have probably use a gaussian beam illuminating the aperture and no other special beam shaper. I'm almost certain of this but it's worth looking it up now. $\endgroup$ – uhoh Feb 26 at 15:20

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