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 was the most intense beam ever sent from Earth?

To avoid any ambiguities or confusion introduced by comments, well use radiant intensity with units like W/sr,

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), though if it turns out to be more helpful, *spectral intensity or W/sr/Hz.

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. $\endgroup$ Commented Feb 26, 2021 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
    Commented Feb 26, 2021 at 14:44
  • $\begingroup$ Note that I've suggested units of kW/sr specifically for this reason. $\endgroup$
    – uhoh
    Commented Feb 26, 2021 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. $\endgroup$ Commented Feb 26, 2021 at 15:13
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    $\begingroup$ The most intense (but brief) signal from Earth was definitely the detonation of the Tsar Bomba 50megaton bomb. The signal of an atmospheric detonation of a thermonuclear weapon is quite distinctive, and many, many magnitudes stronger than any directed radio signal. $\endgroup$ Commented Nov 15, 2021 at 13:26


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