Photon Detection Rate

9008-040

9008-040a

The photon detection rate in a quantum-noise limited heterodyne receiver is given by:

           eta.Pr
Nph = --------
              hf

where:

eta = quantum efficiency (0.5),
P_r = received optical power (1.60 x 10^-15 W),
h = Planck's constant (6.63 x 10^-34 J.s),
f = optical frequency (c/wl = 4.57 x 10¹⁴ Hz),
c = velocity of light (3 x 10⁸ m/s),
wl = wavelength (656 x 10^-9 m).

We have already stated that the 1 kW SETI transmitter at a distance of 10 light years produces a received signal P_r = 1.60 x 10^-15 W (-118 dBm). Using the values given above, we find that:

N_ph = 2640 photons/second

9008-040b

This relationship is plotted in the graphs 9008-023 & 9008-024 over 1000 A.U. and 1000 L.Y. ranges, respectively.

In digital systems we often measure the sensitivity of an optical receiver in terms of the number of photons required to be detected for each bit of error-free information. While clever digital encoding and modulation schemes can lower the number of photons required per second, present coherent fiber-optic systems under development can achieve values of about 10 photons/bit for Bit Error Rates (BER) 10^-9. Such systems have bandwidths of several hundred MHz to several GHz, so the optical power received is much greater than we are discussing here for this SETI application. The difference in received power is about ten orders of magnitude!

One could consider the "ideal" photonics detection system to be one in which only one or two photons are required to be detected for each bit of information.