Area of detectable optical transmission as a function of distance in the context of SETI The relevant page on SETI's official website states:

The SETI Institute, along with scientists from the University of California's Lick Observatory, UC Santa Cruz, and UC Berkeley has coupled the Lick Observatory's 40-inch Nickel Telescope with a new pulse-detection system capable of finding laser beacons from civilizations many light-years distant. Unlike other optical SETI searches, this experiment is largely immune to false alarms, due to a novel approach incorporating 3 light detectors.

The appeal of optical SETI is that it can detect a very high-gain beam rather than an omnidirectional or other less focused signal that will tend to peter out relatively quickly over long distances. However, my impression is that even a tightly focused laser beam will spread out over a substantial (or even cosmic) distance, so my question is, when such a beam has been projected out to some distance $d$, what is the area $a$ on the sphere of all possible destinations for that beam to end up, where it could possibly be detected, given a constant level of technological capability of the sender and another for the receiver? (The last part is necessarily speculative, which I'm willing to accept.)
 A: Personally I don't believe in feasibility of such SETI setup. Given typical Nd:YAG laser in optics lab(s) with a wavelength of $1.064 \,\mu m$ and a maximum laser output power of $2 \,kW$, focused to beam radius of $10 \,\mu m$- which gives Rayleigh range $Z_R \approx 300 \,\mu m$, one can calculate a maximum distance which such laser ray could penetrate and be detected until it will completely weakens, down to being undetectable due to beam divergence :
$$ z \approx Z_R \sqrt {~\frac {I_0}{I}~} $$,
(As for the lower bound of laser intensity detected at Earth- $I$, take 3 photons per 1 sec for example,- cause setup needs to detect at least 3 separate photons received in the same time-frame).
Given that detector stands in the line-of-sight (beam directed straightly towards Earth), which gives detector radial distance from the center axis of the beam $r=0$ (best case scenario, but mostly unlikely). One can calculate that such beam could be detected from distances $\approx 30 \times$ the distance to Proxima Centauri - closest star system located at about $4.2$ light years from us. Question - What's the probability that Proxima Centauri shines a laser beam straightly towards us ? Not big I think. If not, then due to radial distance from beam being $r>0$,- detectable distance $z$ drops even more than given formula above in an exponential way, which is described by Gaussian laser beam law :
$$ \frac {I(r,z)}{I_{0}} = \left({\frac {w_{0}}{w(z)}}\right)^{2}\exp \left({\frac {-2r^{2}}{w(z)^{2}}}\right) $$,
where $w_{0}$ is beam waist radius and $w(z)$ is the radius where field amplitudes fall to 1/e of their initial values.
So that for detection of laser beam from slightly deeper locations far inside of our own MilkyWay galaxy,- one needs a HUGE intensity laser beam being sent from exoplanet(s), intensities comparable to Trident laser,- $\approx 10^{20} ~W/cm^2$. Power requirements for feeding such laser beam are enormous, to the point that it is mostly ridiculous for "external-civilization"  to support such communication project, as we do not support such signal emitting too. Detector may be cheap, but laser setup - does not.
A: There are three key parameters for sending information via a laser beam over interstellar distances: beam power, aperture, and data rate.
Starting with aperture:  The larger the laser aperture, the smaller the focal spot of the laser beam. The inverse of this is equally true:  The larger a telescope mirror (aperture), the smaller the smallest feature that the telescope can resolve at long distances.  An aperture about the size of the Sun could focus a spot 4 light years away down to a few hundred meters across.
If the beam at the receiving end is 100 meters across, and detector optics at the other end are 100 meters across, effectively all of the laser's light could be focused down onto a small detector at the receiving end.  But if the beam is 1000 meters across and the detector optics are 100 meters across, only 1% of the light will be intercepted by the detector optics.
These values scale in a simple way: if the beam is being sent a fixed distance, then if the diameter of the laser aperture is doubled, the size of the focal spot is reduced to one-half.
Next, consider power and data rate.  Photons in the near infra-red have energy of about 1.24 eV or around 1.6 x 10^-19 joules.  A 1-milliwatt near IR laser, then, would emit about 10^16 photons per second. A few dozen photons would be needed to convey one byte. This suggests that, allowing for ~99.99% losses, a 1-mw laser with a Sun-sized ideal aperture could in principle communicate at 4 lightyears' distance at nearly a terabyte per second.
You can juggle the numbers: quadruple the power of the laser, and you can cut the size of the laser aperture by a half.  Bottom line is that you would need the aperture to be as big as it can possibly be; and it would probably need to be a phased array rather than a fixed mirror.  Perhaps a 10 km wide aperture could be engineered.  The Sun's diameter is about 1.4 million kilometers, so the aperture would be on the order of 1/140,000 of the Sun's diameter, which means to achieve the same near-terabyte per second data rate the laser power would need to be scaled up by a factor of (140,000)^2 or about 2 x 10^10, or to about 20 gigawatts.  The proposed Breakthrough Starshot laser would have an output power of about 100 GW and an aperture on the order of 10 km; and it's considered an engineering challenge that will not require new science.
Bottom line: interstellar communication by laser is possible.  Very expensive, but possible.
