
Detectability Of Pulsed Laser Beacons9501001
9501001aPeak Power The relationship between peak power P_{pk} and average power for a pulsed laser is given by:
P_{av} P_{pk} =  W Tau.r
where:
Substituting the values in parentheses for a pulsed ETI laser beacon system with a 1 Hz repetition rate, we find that:
P_{pk} = 10^{18} W.
9501001bDiffractionLimited Telescope Gain The gain of a diffractionlimited dish or telescope is given by:
(pi.D)^{2} G =  Wl^{2}
where:
Substituting the values in parentheses for an ETI uplink transmitting at the center of the human photopic response, we find that:
G = 155.1 dB.
9501001cEffective Isotropic Radiated Power The Effective Isotropic Radiated Power is the power that the transmitter appears to have if it radiated isotropically. It is given by:
EIRP = P.G W
Substituting the values for P and G given above, we find that:
EIRP_{laser} = 3.2 x 10^{33} W.
For a star like the sun:
EIRP_{star} = 3.9 x 10^{26} W.
Note that EIRP_{laser} is the peak EIRP of the laser, while EIRP_{star} is the mean EIRP of the star.
9501001dReceived Intensity The intensity of the received signal and stellar background noise is given by:
EIRP I =  W/m2 4.pi.R^{2}
where R = range (9.461 x 10^{16} m).
Substituting the values in parenthesis for a range of 10 light years, we find that just outside the atmosphere:
I_{laser} = 2.8 x 10^{2} W/m^{2}.
I_{star} = 3.5 x 10^{9} W/m^{2}.
9501001eDetected Power The optical power appearing at the photodetector is given by:
(pi.d^{2}) S = T_{atm}.A_{eff}.F_{eff}..I W 4
where:
For the ETI laser: S_{laser} = 8.9 x 10^{5} W.
For a solartype star: S_{star} = 1.1 x 10^{11} W.
9501001fMagnitude For a solartype star and a laser centered on the human visual response, the apparent magnitude may be expressed in terms of its intensity I:
m = [19 + 2.5log(I)]
where:
Substituting the above values for a range of 10 light years, we find that:
m_{laser} = 15.
m_{star} ~ 2.
During each brief pulse, the laser is brighter than the ETIs' star by a factor of nearly 10 million!
9501001gPhoton Detection Rate The photon detection rate is given by:
eta.S N =  hf
where:
Substituting the values in parentheses for a center wavelength of 550 nm, we find that the "signal" photon detection rate N_{laser}: Signal 44,000 counts per pulse.
For a solartype star, we find that the stellar background "noise" photon detection rate N_{star}: Noise 6,000,000 counts per second.
9501001hConclusions The "signal" is buried in the noise and the ratio between the "signal" and "noise" photons is approximately 20 dB. However, during each one nanosecond laser pulse, the SNR is positive and nearly 70 dB! This is the very important benefit of searching for very short pulses in adjacent time slots corresponding to the expected pulse duration, even if the "signal" consists of only one or two detected photons per pulse. Another important benefit is that knowledge of the "magic frequency" is not required. Note that the National Ignition Facility upgrade to the NOVA laser at the Lawrence Livermore Laboratories will increase the peak power output from 10^{14} W to 10^{15} W, albeit at only one pulse per day. By the year 2002, we humans, over a period of 40 years, will have increased peak laser output powers on this planet from 3 kW to 10^{15} W. How long will it take to increase the peak output power from 10^{15} W at one pulse per day to 10^{18} W at one pulse per second? The answer, of course, is no time at all on the cosmic time scale.
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