Leaving the serious engineering difficulties involved in a solar gravitational lensing system aside, such a system doesn't necessarily help in picking up just random omnidirectional broadcasts from an ETI.
Say we had an SGL telescope positioned such to image an Earth-sized planet we know is in orbit of Alpha Centauri A. For ease of math we'll say this Earth sized planet is at a distance such the solar constant is the same as Earth. So that's a total power received from the Sun of 1.74x10^17 watts and with the Earth's mean albedo of 0.3 about 5.22x10^16 watts being reflected off into space.
We can use our SGL to image the planet around Alpha Centauri because it's reflecting 52.2 petawatts of sunlight out into space. So it takes the power of a star reflecting off a disc with a cross sectional area of 1.26x10^8 square kilometers for a proposed SGL system to detect and image a planet.
The amount of power an omnidirectional antenna can possibly emit is somewhat less than 52 petawatts. Broadcast antennas output at most a few megawatts EIRP because there's no utility in blasting out hundreds of megawatts for terrestrial transmission. Such broadcasts just aren't going to be detectable even with gravitational lensing from our Centauran neighbors.
Nor are gravitational lenses terribly useful for beacons since you need the right geometry between the sender, star, and receiver to use the lens. You could use lensing to increase the EIRP of your transmission but only at a specific target. Nobody outside the focal plane of the lensing system is going to benefit from the lens.
SGLs are a neat idea and an interesting topic but I don't think they solve many SETI problems.
Say we had an SGL telescope positioned such to image an Earth-sized planet we know is in orbit of Alpha Centauri A. For ease of math we'll say this Earth sized planet is at a distance such the solar constant is the same as Earth. So that's a total power received from the Sun of 1.74x10^17 watts and with the Earth's mean albedo of 0.3 about 5.22x10^16 watts being reflected off into space.
We can use our SGL to image the planet around Alpha Centauri because it's reflecting 52.2 petawatts of sunlight out into space. So it takes the power of a star reflecting off a disc with a cross sectional area of 1.26x10^8 square kilometers for a proposed SGL system to detect and image a planet.
The amount of power an omnidirectional antenna can possibly emit is somewhat less than 52 petawatts. Broadcast antennas output at most a few megawatts EIRP because there's no utility in blasting out hundreds of megawatts for terrestrial transmission. Such broadcasts just aren't going to be detectable even with gravitational lensing from our Centauran neighbors.
Nor are gravitational lenses terribly useful for beacons since you need the right geometry between the sender, star, and receiver to use the lens. You could use lensing to increase the EIRP of your transmission but only at a specific target. Nobody outside the focal plane of the lensing system is going to benefit from the lens.
SGLs are a neat idea and an interesting topic but I don't think they solve many SETI problems.